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 "generator": {
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  "repository": "https://github.com/tdj28/neural-shrimp (release tag arxiv-v1)",
  "commit": "1314528118ac1300c2cffd34fb60cfbfc67d2c82",
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  "note": "Pinned to the final report, commit 13145281 (the supplementary report that accompanies the article of the same title). On 20 October 2026 the annotated release tag arxiv-v1 of the research repository points to this commit; the note links to the repository at that tag. Round 14 rebound every entry to this commit and recomputed its paper_line."
 },
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   "paper_text": "at 448 checked cells",
   "paper_line": 847,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "repro-chaotic",
   "section": "Summary surfaces and abstract",
   "claim": "chaotic float64 loops of Qwen2.5-0.5B that separate past 1e-2 under a batch-layout change",
   "appears_as": "190 of 192 chaotic float64 loops",
   "paper_text": "190 of 192 chaotic float64 loops of Qwen2.5-0.5B grow past",
   "paper_line": 218,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "repro-median",
   "section": "Summary surfaces and abstract",
   "claim": "median step at which those loops pass 1e-2",
   "appears_as": "median of 102 steps",
   "paper_text": "after a median of 102 steps",
   "paper_line": 219,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "repro-ratio",
   "section": "Summary surfaces and abstract",
   "claim": "median ratio of the divergence step to the exponent's prediction",
   "appears_as": "median ratio 0.91",
   "paper_text": "in line with the Lyapunov exponent (median ratio 0.91)",
   "paper_line": 219,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "repro-periodic",
   "section": "Summary surfaces and abstract",
   "claim": "periodic loops that pass 1e-2",
   "appears_as": "10 / 192",
   "paper_text": "& periodic & 10 / 192 &",
   "paper_line": 1253,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "repro-70b",
   "section": "Summary surfaces and abstract",
   "claim": "Llama-3.3-70B chaotic and periodic cells that diverge",
   "appears_as": "24 of 24 against none of 24",
   "paper_text": "Llama-3.3-70B with steering (24 of 24, none of 24)",
   "paper_line": 222,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "answers-05b",
   "section": "Summary surfaces and abstract",
   "claim": "answers changed by batching, Qwen2.5-0.5B, bfloat16",
   "appears_as": "56% and 55% of 96 additions",
   "paper_text": "56\\,\\% and 55\\,\\% of 96 arithmetic problems",
   "paper_line": 109,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "answers-greedy",
   "section": "Summary surfaces and abstract",
   "claim": "greedy baseline answers changed (paper 318f8980)",
   "appears_as": "against never and 10% for a forced greedy",
   "paper_text": "against never and 10\\,\\% for a forced greedy baseline",
   "paper_line": 224,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "gain-readout",
   "section": "Summary surfaces and abstract",
   "claim": "readout-factor increase of chaotic over nearly unsteered cells",
   "appears_as": "2.58 nats per step",
   "paper_text": "by $2.58$ nats per step (95\\,\\% interval $[1.78,3.59]$",
   "paper_line": 707,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "gain-network",
   "section": "Summary surfaces and abstract",
   "claim": "network-factor change of chaotic over nearly unsteered cells",
   "appears_as": "\\([-0.23, 0.12]\\)",
   "paper_text": "$-0.07$ $[-0.23,0.12]$",
   "paper_line": 708,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "logit-bias-share",
   "section": "Summary surfaces and abstract",
   "claim": "chaotic share under a logit bias alone",
   "appears_as": "makes 3.5%",
   "paper_text": "a logit bias alone, with the network unsteered, makes 3.5\\,\\% of its grid chaotic",
   "paper_line": 250,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "passages-42",
   "section": "Summary surfaces and abstract",
   "claim": "passages within one iterate of the forecast over both prospective tests",
   "appears_as": "42 of 48",
   "paper_text": "came within one iterate of 42 of 48 passages",
   "paper_line": 130,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "passages-misses",
   "section": "Summary surfaces and abstract",
   "claim": "shortfall of the six misses at the period-6 fold",
   "appears_as": "3.1 to 5.2% short",
   "paper_text": "short by 3.1 to 5.2\\,\\%",
   "paper_line": 1821,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "feigenbaum-last",
   "section": "Summary surfaces and abstract",
   "claim": "last finite-order doubling ratio against Feigenbaum's constant",
   "appears_as": "4.6688 against 4.6692",
   "paper_text": "the last, $4.6688$, against $4.6692$",
   "paper_line": 264,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "size-72b-prompts",
   "section": "Summary surfaces and abstract",
   "claim": "prompts on which Qwen2.5-72B is nearly free of unsteered chaos",
   "appears_as": "nearly free of unsteered chaos on five prompts",
   "paper_text": "five prompts on which the 72B model is nearly free of unsteered chaos",
   "paper_line": 3524,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "published-st-abs-21",
   "section": "Summary surfaces and abstract",
   "claim": "answers changed by the batch layout, Soft Thinking with published settings (abstract)",
   "appears_as": "changed the answers to 21% of 256 new GSM8K math problems in Qwen2.5-7B with the",
   "paper_text": "changed the answers to 21\\,\\% of 256 GSM8K problems not used before in this study in Qwen2.5-7B",
   "paper_line": 230,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "published-st-abs-6",
   "section": "Summary surfaces and abstract",
   "claim": "rate after replaying the fed-back tokens (abstract)",
   "appears_as": "fed-back tokens cut this to 6%",
   "paper_text": "replaying the fed-back tokens cut this to 6\\,\\%",
   "paper_line": 231,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "published-st-contrib-21",
   "section": "Summary surfaces and abstract",
   "claim": "answers changed by the batch layout (contribution list)",
   "appears_as": "changed the answers to 21% of 256 new GSM8K math problems with the batch layout",
   "paper_text": "changed the answers to 21\\,\\% of 256 GSM8K problems not used before in this study in Qwen2.5-7B",
   "paper_line": 230,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "published-st-contrib-6",
   "section": "Summary surfaces and abstract",
   "claim": "rate after replaying the fed-back tokens (contribution list)",
   "appears_as": "to 6%. Reasoning models that answer 86 to 90% of these problems correctly",
   "paper_text": "replaying the fed-back tokens cut this to 6\\,\\%",
   "paper_line": 231,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "damp-abstract-moe",
   "section": "Summary surfaces and abstract",
   "claim": "active and total parameters of the mixture of experts (abstract)",
   "appears_as": "3B of its 35B parameters active per token damps more",
   "paper_text": "a mixture of experts with 3B of its 35B parameters active per token damps more than a dense 9B model of its family",
   "paper_line": 281,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "damp-abstract-dense",
   "section": "Summary surfaces and abstract",
   "claim": "size of the dense comparison model (abstract)",
   "appears_as": "than a dense 9B model of its family",
   "paper_text": "a mixture of experts with 3B of its 35B parameters active per token damps more than a dense 9B model of its family",
   "paper_line": 281,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "damp-contrib-moe",
   "section": "Summary surfaces and abstract",
   "claim": "active and total parameters of the mixture of experts (contribution list)",
   "appears_as": "the mixture of experts, with 3B of its 35B",
   "paper_text": "a mixture of experts with 3B of its 35B parameters active per token",
   "paper_line": 281,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "damp-contrib-dense",
   "section": "Summary surfaces and abstract",
   "claim": "size of the dense comparison model (contribution list)",
   "appears_as": "damps more than a dense 9B model of its family",
   "paper_text": "damps more than a dense 9B model of its family",
   "paper_line": 282,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-abstract-offset",
   "section": "Summary surfaces and abstract",
   "claim": "starting distance of the copy and steps of identical text (abstract)",
   "appears_as": "second copy of that same loop, started a relative distance of \\(10^{-10}\\) away",
   "paper_text": "a copy started $10^{-10}$ away writes the same text for 9 to 150 steps",
   "paper_line": 232,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-contrib-steps",
   "section": "Summary surfaces and abstract",
   "claim": "steps of identical text in the contribution list",
   "appears_as": "writes the same tokens for 9 to 150 steps and then a different sequence",
   "paper_text": "writes the same text for 9 to 150 steps",
   "paper_line": 232,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "vocab",
   "section": "The soft-token map",
   "claim": "vocabulary size of Qwen2.5-0.5B",
   "appears_as": "151{,}936",
   "paper_text": "V=151{,}936",
   "paper_line": 314,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "dim",
   "section": "The soft-token map",
   "claim": "embedding dimension of Qwen2.5-0.5B",
   "appears_as": "d = 896",
   "paper_text": "d=896",
   "paper_line": 314,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "steer-max",
   "section": "The soft-token map",
   "claim": "largest steering push per vector",
   "appears_as": "at most 12% of the mean residual norm",
   "paper_text": "at most 12\\,\\% of the mean residual norm per vector",
   "paper_line": 384,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "steer-fig1",
   "section": "The soft-token map",
   "claim": "steering range of Figure 1",
   "appears_as": "7.75% in Figure 1",
   "paper_text": "6.25 to 7.75\\,\\% in Figure",
   "paper_line": 385,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "steer-curves",
   "section": "The soft-token map",
   "claim": "largest steering push on continued curves",
   "appears_as": "reach 13.1%",
   "paper_text": "the continued curves reach 13.1\\,\\%",
   "paper_line": 385,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "push-1pct",
   "section": "The soft-token map",
   "claim": "largest push keeping greedy accuracy within 5 points (Qwen2.5-7B)",
   "appears_as": "1% of the residual norm is the largest push",
   "paper_text": "1\\,\\% of the residual norm is the largest push that kept greedy accuracy on a multiplication task within 5 points",
   "paper_line": 386,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "random-dirs",
   "section": "The soft-token map",
   "claim": "chaotic share for three norm-matched Gaussian directions (0.5B)",
   "appears_as": "7.6, 8.3 and 12.5%",
   "paper_text": "7.6, 8.3 and 12.5\\,\\% of cells are chaotic for three Gaussian directions",
   "paper_line": 5616,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "philosophy-share",
   "section": "The soft-token map",
   "claim": "chaotic share along philosophy on the same grid",
   "appears_as": "against 6.8%",
   "paper_text": "against 6.8\\,\\% for philosophy",
   "paper_line": 5616,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "neuron-share",
   "section": "The soft-token map",
   "claim": "chaotic share along the most philosophy-specific neuron",
   "appears_as": "gives 9.9%",
   "paper_text": "gives 9.9\\,\\% chaotic cells for the neuron most specific to philosophy",
   "paper_line": 5624,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "llama-dirs",
   "section": "The soft-token map",
   "claim": "chaotic share across SAE, contrastive and random directions in Llama-3.1-8B",
   "appears_as": "(27 to 39% of cells)",
   "paper_text": "(27 to 39\\,\\% of cells)",
   "paper_line": 3987,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "70b-dirs",
   "section": "The soft-token map",
   "claim": "chaotic share, hostility-related versus random directions at 70B",
   "appears_as": "(4.3 and 3.5% against 1.1 and 0.2%",
   "paper_text": "(4.3 and 3.5\\,\\% against 1.1 and 0.2\\,\\%",
   "paper_line": 3988,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "f32-accuracy",
   "section": "The soft-token map",
   "claim": "float32 map accuracy per step",
   "appears_as": "\\(3\\times10^{-6}\\) to \\(2\\times10^{-5}\\)",
   "paper_text": "A float32 map is accurate to $3\\times10^{-6}$--$2\\times10^{-5}$ per step",
   "paper_line": 398,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "phase-agree",
   "section": "The soft-token map",
   "claim": "test cells whose float32 label agrees with float64",
   "appears_as": "245 of 256 test cells",
   "paper_text": "245 of 256 test cells agree with float64",
   "paper_line": 399,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "jvp-accuracy",
   "section": "The soft-token map",
   "claim": "one-step float32 Jacobian-vector product accuracy",
   "appears_as": "\\(5\\times10^{-5}\\)",
   "paper_text": "one-step float32 Jacobian-vector products are accurate to $5\\times10^{-5}$",
   "paper_line": 400,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "monodromy-error",
   "section": "The soft-token map",
   "claim": "error of the float32 8-step monodromy",
   "appears_as": "off by 3%",
   "paper_text": "is off by 3\\%",
   "paper_line": 401,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "horizon-check",
   "section": "The soft-token map",
   "claim": "chaotic labels that held under a longer horizon",
   "appears_as": "86 and 92 of 96",
   "paper_text": "kept 86 and 92 of 96 chaotic labels in two maps",
   "paper_line": 3945,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "transient-labels",
   "section": "The soft-token map",
   "claim": "chaotic labels that held near a cascade's accumulation point",
   "appears_as": "135 of 235",
   "paper_text": "only 135 of 235 chaotic labels held",
   "paper_line": 3946,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "map256",
   "section": "Chaos with periodic windows",
   "claim": "chaotic cells of the 256 x 256 scan",
   "appears_as": "35,650 of 65,536",
   "paper_text": "(35{,}650 of 65{,}536)",
   "paper_line": 868,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "map512",
   "section": "Chaos with periodic windows",
   "claim": "chaotic cells of Figure 1",
   "appears_as": "78,868 (30%) are labeled chaotic",
   "paper_text": "of which 78{,}868 (30\\,\\%) meet the criterion",
   "paper_line": 883,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "threshold",
   "section": "Chaos with periodic windows",
   "claim": "chaotic cells of Figure 1 at threshold 0.05",
   "appears_as": "leaves 73,437",
   "paper_text": "77{,}646, 76{,}761 or 73{,}437 of the 78{,}868",
   "paper_line": 5761,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "unresolved-fig1",
   "section": "Chaos with periodic windows",
   "claim": "cells of Figure 1 with neither a detected period nor an exponent above 1e-3 (paper 602c70ac)",
   "appears_as": "4.4% of the cells",
   "paper_text": "4.4\\,\\% of the cells, also gray",
   "paper_line": 96,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p3-probs",
   "section": "Chaos with periodic windows",
   "claim": "probabilities of the period-3 loop's leading tokens",
   "appears_as": "probabilities 0.74, 0.36 and 0.21",
   "paper_text": "$0.74$, $0.36$ and $0.21$ at $\\alpha=0.0642$",
   "paper_line": 895,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "coexist-2cycle",
   "section": "Chaos with periodic windows",
   "claim": "300-step exponent of the coexisting 2-cycle",
   "appears_as": "exponent \\(-1.19\\)",
   "paper_text": "exponent $-1.19$)",
   "paper_line": 900,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "coexist-p3",
   "section": "Chaos with periodic windows",
   "claim": "exponent of the period-3 loop from the fixed start",
   "appears_as": "\\(-0.13\\)). That start",
   "paper_text": "(exponent $-0.13$)",
   "paper_line": 900,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "coexist-chaos",
   "section": "Chaos with periodic windows",
   "claim": "exponent of the crescent's chaotic attractor",
   "appears_as": "(exponent \\(+0.095\\))",
   "paper_text": "(exponent $+0.095$)",
   "paper_line": 902,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "coexist-2cycle-b",
   "section": "Chaos with periodic windows",
   "claim": "exponent of the 2-cycle start at alpha 0.0652",
   "appears_as": "(\\(-1.29\\))",
   "paper_text": "($-1.29$)",
   "paper_line": 902,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "transcript-lambda",
   "section": "Chaos with periodic windows",
   "claim": "exponent of the chaotic transcript cell",
   "appears_as": "chaotic (λ = 0.13)",
   "paper_text": "chaotic ($\\lambda=0.13$)",
   "paper_line": 1578,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "qwen2-loops",
   "section": "Chaos with periodic windows",
   "claim": "distinct loops per map and loops shared by Qwen2 and Qwen2.5",
   "appears_as": "of 416 to 900 distinct loops per map",
   "paper_text": "Of 416 to 900 distinct loops per map, only 10 occur in both models",
   "paper_line": 5392,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "70b-chaotic",
   "section": "Chaos with periodic windows",
   "claim": "chaotic cells of the 70B scan (Figure 4)",
   "appears_as": "3410 of the 16,384 cells (20.8%)",
   "paper_text": "3410 of the 16{,}384 cells (20.8\\,\\%) are chaotic (largest exponent 0.64)",
   "paper_line": 3549,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "70b-unresolved",
   "section": "Chaos with periodic windows",
   "claim": "unresolved cells of the 70B scan",
   "appears_as": "1.7% have neither",
   "paper_text": "neither a detected period up to 32 nor a positive exponent, 1.7\\,\\% of the cells",
   "paper_line": 3551,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "70b-plateau",
   "section": "Chaos with periodic windows",
   "claim": "70B labels confirmed by the plateau test (chaotic, periodic)",
   "appears_as": "confirms 11 of the 12 chaotic and 5 of the 6 periodic labels",
   "paper_text": "confirms 11 of the 12 chaotic and 5 of the 6 periodic labels",
   "paper_line": 3542,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "70b-band",
   "section": "Chaos with periodic windows",
   "claim": "center of the 70B chaotic band",
   "appears_as": "\\(\\log_{10}T \\approx 0.23\\)",
   "paper_text": "$\\log_{10}T\\approx0.23$ at $\\alpha=0.06$ to $\\approx0.19$ at $\\alpha=0.12$",
   "paper_line": 3553,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-reuse-window",
   "section": "What a chaotic loop writes",
   "claim": "steps shown in the reuse example",
   "appears_as": "most probable token for 40 steps in a row, after",
   "paper_text": "the leading token at 40 consecutive steps after 600 transient steps",
   "paper_line": 1585,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-reuse-T",
   "section": "What a chaotic loop writes",
   "claim": "temperature of the reuse example",
   "appears_as": "at the same temperature, \\(\\log_{10}T = -0.115\\), and at four nearby steering",
   "paper_text": "$\\log_{10}T=-0.115$: the leading token at 40 consecutive steps",
   "paper_line": 1585,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-reuse-p8",
   "section": "What a chaotic loop writes",
   "claim": "steering strength of the period-8 reuse-example cell",
   "appears_as": "alpha = 0.071674, period 8",
   "paper_text": "$0.071674$ & period 8",
   "paper_line": 1577,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-reuse-chaos",
   "section": "What a chaotic loop writes",
   "claim": "steering strength of the chaotic reuse-example cell",
   "appears_as": "alpha = 0.072940, chaotic",
   "paper_text": "$0.072940$ & chaotic",
   "paper_line": 1578,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-transient",
   "section": "What a chaotic loop writes",
   "claim": "steps run before the recording",
   "appears_as": "The reference is iterated for 1000 steps in float64",
   "paper_text": "cells labeled chaotic for 1000 steps in float64",
   "paper_line": 938,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-offset",
   "section": "What a chaotic loop writes",
   "claim": "starting relative distance of the copy",
   "appears_as": "a copy started at a relative distance of \\(10^{-10}\\)",
   "paper_text": "a copy started at a relative distance of $10^{-10}$",
   "paper_line": 939,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-600",
   "section": "What a chaotic loop writes",
   "claim": "ratio of float32's relative rounding error to the copy's offset",
   "appears_as": "about 600 times smaller than the relative rounding error of float32",
   "paper_text": "about 600 times smaller than the relative rounding error of float32",
   "paper_line": 939,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-05b-splits",
   "section": "What a chaotic loop writes",
   "claim": "exponents and split steps of the two Qwen2.5-0.5B philosophy cells",
   "appears_as": "with exponents 0.44 and 0.36, split at steps 44 and 51",
   "paper_text": "with exponents 0.44 and 0.36, split at steps 44 and 51",
   "paper_line": 943,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-hostility-split",
   "section": "What a chaotic loop writes",
   "claim": "exponent and split step of the hostility cell",
   "appears_as": "with exponent 0.35, at step 45",
   "paper_text": "with exponent 0.35, at step 45",
   "paper_line": 943,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-decades",
   "section": "What a chaotic loop writes",
   "claim": "growth of the distance by the split, in decades, for those three cells",
   "appears_as": "8.5 to 10.2 decades",
   "paper_text": "grown by 8.5 to 10.2 decades",
   "paper_line": 944,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-norm-share",
   "section": "What a chaotic loop writes",
   "claim": "distance at the split as a share of the soft token's norm, over the seven recorded cells",
   "appears_as": "1.27% and 176% of the soft token's norm",
   "paper_text": "has grown to between 1.27\\,\\% and 176\\,\\% of the soft token's norm",
   "paper_line": 942,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-tie-44",
   "section": "What a chaotic loop writes",
   "claim": "probabilities of a blank line and ' is' at step 44",
   "appears_as": "probabilities 0.139 and 0.135",
   "paper_text": "have probabilities 0.139 and 0.135",
   "paper_line": 948,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-tie-45",
   "section": "What a chaotic loop writes",
   "claim": "probabilities of 'Yes' and 'No' at step 45 of the hostility cell",
   "appears_as": "have 0.303 and 0.298",
   "paper_text": "have 0.303 and 0.298",
   "paper_line": 948,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-split-seven",
   "section": "What a chaotic loop writes",
   "claim": "number of recorded splits",
   "appears_as": "At each of the seven splits we",
   "paper_text": "At each of the seven splits we recorded",
   "paper_line": 944,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-split-stats",
   "section": "What a chaotic loop writes",
   "claim": "largest top-token probability and lead at the splits, and splits where the copy writes the loop's second choice",
   "appears_as": "has a probability of at most 0.31 and leads the next by at most 0.08, and at five",
   "paper_text": "has a probability of at most 0.31 and leads the next by at most 0.08, and at five of them the copy writes the loop's second choice",
   "paper_line": 945,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-seventh",
   "section": "What a chaotic loop writes",
   "claim": "the seventh cell of Figure 3",
   "appears_as": "a seventh (Qwen2.5-1.5B, philosophy, \\(\\alpha = 0.07376\\), \\(\\log_{10}T = 0.0165\\)",
   "paper_text": "a seventh (Qwen2.5-1.5B, philosophy, $\\alpha=0.07376$, $\\log_{10}T=0.0165$)",
   "paper_line": 1135,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-seventh-split",
   "section": "What a chaotic loop writes",
   "claim": "split step of the seventh cell",
   "appears_as": "texts split at step 22)",
   "paper_text": "Their copies split at steps 22 and 10",
   "paper_line": 958,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-figalt-share",
   "section": "What a chaotic loop writes",
   "claim": "distance at the splits (Figure 3 alt text)",
   "appears_as": "at distances between 1.27% and 176%",
   "paper_text": "has grown to between 1.27\\,\\% and 176\\,\\% of the soft token's norm",
   "paper_line": 942,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-row1",
   "section": "What a chaotic loop writes",
   "claim": "Table 1, row 1: parameters, exponent and split step",
   "appears_as": "α = 0.0652, log10 T = -0.156: λ = 0.10, texts split at step 151",
   "paper_text": "$\\alpha=0.0652$, $\\log_{10}T=-0.156$: $\\lambda=0.10$, texts split at step 151",
   "paper_line": 976,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-row2",
   "section": "What a chaotic loop writes",
   "claim": "Table 1, row 2: parameters, exponent and split step",
   "appears_as": "α = 0.07484, log10 T = -0.1226: λ = 0.44, texts split at step 44",
   "paper_text": "$\\alpha=0.07484$, $\\log_{10}T=-0.1226$: $\\lambda=0.44$, texts split at step 44",
   "paper_line": 980,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-row3",
   "section": "What a chaotic loop writes",
   "claim": "Table 1, row 3: parameters, exponent and split step",
   "appears_as": "α = 0.07277, log10 T = -0.041: λ = 0.36, texts split at step 51",
   "paper_text": "$\\alpha=0.07277$, $\\log_{10}T=-0.041$: $\\lambda=0.36$, texts split at step 51",
   "paper_line": 984,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-row4",
   "section": "What a chaotic loop writes",
   "claim": "Table 1, row 4: parameters, exponent and split step",
   "appears_as": "α = 0.08946, log10 T = -0.05566: λ = 0.35, texts split at step 45",
   "paper_text": "$\\alpha=0.08946$, $\\log_{10}T=-0.05566$: $\\lambda=0.35$, texts split at step 45",
   "paper_line": 988,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-row5",
   "section": "What a chaotic loop writes",
   "claim": "Table 1, row 5: parameters, exponent and split step",
   "appears_as": "α = 0.10553, log10 T = 0.0322: λ = 0.80, texts split at step 10",
   "paper_text": "$\\alpha=0.10553$, $\\log_{10}T=0.0322$: $\\lambda=0.80$, texts split at step 10",
   "paper_line": 992,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-row6",
   "section": "What a chaotic loop writes",
   "claim": "Table 1, row 6: temperature, exponent and split step",
   "appears_as": "unsteered, log10 T = 0.657: λ = 0.59, texts split at step 43",
   "paper_text": "unsteered, $\\log_{10}T=0.657$: $\\lambda=0.59$, texts split at step 43",
   "paper_line": 996,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-window",
   "section": "What a chaotic loop writes",
   "claim": "steps shown around each split in Table 1",
   "appears_as": "from 14 steps before the first step at which they differ to 9 steps after it",
   "paper_text": "from 14 steps before the first step at which they differ to 9 steps after it",
   "paper_line": 1002,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-lyap-offsets",
   "section": "What a chaotic loop writes",
   "claim": "twin offsets and horizon of the exponents in Table 1",
   "appears_as": "twins at relative offsets \\(10^{-6}\\) and \\(10^{-8}\\) over 1000 steps after 1000 transient steps",
   "paper_text": "from twins at relative offsets $10^{-6}$ and $10^{-8}$ over 1000 steps after 1000 transient steps",
   "paper_line": 1004,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-crescent-lambda",
   "section": "What a chaotic loop writes",
   "claim": "exponent next to the period-3 crescent",
   "appears_as": "exponent is only 0.10",
   "paper_text": "where the exponent is only 0.10",
   "paper_line": 951,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-crescent-gap",
   "section": "What a chaotic loop writes",
   "claim": "closest approach of the probabilities of ' existence' and ' question'",
   "appears_as": "come within 0.0025 of each other",
   "paper_text": "whose probabilities come within 0.0025 of each other",
   "paper_line": 953,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-crescent-split",
   "section": "What a chaotic loop writes",
   "claim": "split step next to the crescent",
   "appears_as": "texts split at step 151. On the map",
   "paper_text": "there the texts split at step 151",
   "paper_line": 953,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-15b-lambdas",
   "section": "What a chaotic loop writes",
   "claim": "exponents of the two steered Qwen2.5-1.5B cells",
   "appears_as": "(exponents 0.83 and 0.80)",
   "paper_text": "(exponents 0.83 and 0.80)",
   "paper_line": 957,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-15b-splits",
   "section": "What a chaotic loop writes",
   "claim": "split steps of the two steered Qwen2.5-1.5B cells",
   "appears_as": "Their copies split at steps 22 and 10",
   "paper_text": "Their copies split at steps 22 and 10",
   "paper_line": 958,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-15b-tie",
   "section": "What a chaotic loop writes",
   "claim": "probabilities of 'What' and 'In' at step 10",
   "appears_as": "probabilities 0.091 and 0.090",
   "paper_text": "have probabilities 0.091 and 0.090",
   "paper_line": 959,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-hundredfold",
   "section": "What a chaotic loop writes",
   "claim": "first-step growth of the alpha = 0.10553 copy's distance",
   "appears_as": "copy's distance grew a hundredfold",
   "paper_text": "copy's distance grew a hundredfold in its first step",
   "paper_line": 960,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-unsteered-T",
   "section": "What a chaotic loop writes",
   "claim": "temperature of the unsteered Qwen2.5-1.5B cell",
   "appears_as": "at \\(\\log_{10}T = 0.657\\), the next-token distribution",
   "paper_text": "at $\\log_{10}T=0.657$, the next-token distribution",
   "paper_line": 960,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-unsteered-p",
   "section": "What a chaotic loop writes",
   "claim": "largest probability of the most probable token in the recorded steps",
   "appears_as": "exceeds a probability of 0.001",
   "paper_text": "never exceeds a probability of 0.001",
   "paper_line": 961,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-unsteered-lambda",
   "section": "What a chaotic loop writes",
   "claim": "exponent of the unsteered chaotic loop",
   "appears_as": "(exponent 0.59)",
   "paper_text": "(exponent 0.59)",
   "paper_line": 962,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-unsteered-split",
   "section": "What a chaotic loop writes",
   "claim": "split step of the unsteered cell",
   "appears_as": "its copy splits at step 43",
   "paper_text": "its copy splits at step 43",
   "paper_line": 963,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-fig-faster",
   "section": "What a chaotic loop writes",
   "claim": "growth of five steered copies up to 1e-2, relative to the exponent (Figure 3)",
   "appears_as": "grew 15 to 47% faster than",
   "paper_text": "grew 15 to 47\\,\\% faster than",
   "paper_line": 1141,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-fig-sixth",
   "section": "What a chaotic loop writes",
   "claim": "growth of the sixth steered copy (Figure 3)",
   "appears_as": "2.4 times as fast after a hundredfold expansion in its first step",
   "paper_text": "2.4 times as fast after a hundredfold expansion in its first step",
   "paper_line": 1141,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-fig-alpha",
   "section": "What a chaotic loop writes",
   "claim": "steering strength of the sixth copy (Figure 3)",
   "appears_as": "(\\(\\alpha = 0.10553\\))",
   "paper_text": "($\\alpha=0.10553$)",
   "paper_line": 1141,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-fig-unsteered",
   "section": "What a chaotic loop writes",
   "claim": "growth of the unsteered copy (Figure 3)",
   "appears_as": "the unsteered copy 11% more slowly",
   "paper_text": "the unsteered copy 11\\,\\% more slowly",
   "paper_line": 1142,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-fig-horizon",
   "section": "What a chaotic loop writes",
   "claim": "horizon of the exponents (Figure 3)",
   "appears_as": "deviate from the 1000-step exponents",
   "paper_text": "Finite stretches deviate from the 1000-step exponents",
   "paper_line": 1140,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-threads",
   "section": "What a chaotic loop writes",
   "claim": "thread counts of the two recordings of the crescent cell",
   "appears_as": "once with six threads and once",
   "paper_text": "once with six threads and once with four",
   "paper_line": 966,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-thread-transient",
   "section": "What a chaotic loop writes",
   "claim": "transient before those recordings",
   "appears_as": "During the 1000-step",
   "paper_text": "During the 1000-step transient",
   "paper_line": 966,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-thread-27",
   "section": "What a chaotic loop writes",
   "claim": "steps of identical text in the two recordings",
   "appears_as": "the same text for 27 steps and",
   "paper_text": "they wrote the same text for 27 steps and different texts from step 28 on",
   "paper_line": 968,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-thread-28",
   "section": "What a chaotic loop writes",
   "claim": "first differing step of the two recordings",
   "appears_as": "different texts from step 28 on",
   "paper_text": "different texts from step 28 on",
   "paper_line": 968,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-70b-fifteen",
   "section": "What a chaotic loop writes",
   "claim": "length of the unsteered Llama-3.3-70B loop",
   "appears_as": "unsteered model's fifteen-token loop",
   "paper_text": "the unsteered model's fifteen-token loop",
   "paper_line": 969,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-70b-eight",
   "section": "What a chaotic loop writes",
   "claim": "leading tokens listed for the 70B chaotic cell",
   "appears_as": "the first eight distinct leading tokens of",
   "paper_text": "the first eight distinct leading tokens of one chaotic cell confirmed at three twin offsets",
   "paper_line": 970,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-70b-17",
   "section": "What a chaotic loop writes",
   "claim": "distinct leading tokens of the 70B chaotic cell in 300 steps",
   "appears_as": "(17 distinct tokens in 300 steps)",
   "paper_text": "(17 distinct tokens in 300 steps)",
   "paper_line": 971,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "deriv-check",
   "section": "Why the loop can be chaotic",
   "claim": "relative error of the factorization against forward-mode derivatives",
   "appears_as": "\\(1.35\\times10^{-13}\\)",
   "paper_text": "at most $1.35\\times10^{-13}$ over eight random directions",
   "paper_line": 444,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sweep-band",
   "section": "Why the loop can be chaotic",
   "claim": "range of the chaotic bands in the four long unsteered sweeps",
   "appears_as": "\\(\\log_{10}T = -0.20\\) and 0.28",
   "paper_text": "every band lies between $\\log_{10}T=-0.20$ and $0.28$",
   "paper_line": 566,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "step-sv",
   "section": "Why the loop can be chaotic",
   "claim": "range of the largest step singular value along the period-8 orbit",
   "appears_as": "between 1.2 and 21",
   "paper_text": "lies between 1.2 and 21 at every step",
   "paper_line": 578,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "cycle-norm",
   "section": "Why the loop can be chaotic",
   "claim": "norm range of the cycle Jacobian",
   "appears_as": "between 0.059 and 0.644",
   "paper_text": "has norm between 0.059 and 0.644",
   "paper_line": 581,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "step-norm-product",
   "section": "Why the loop can be chaotic",
   "claim": "product of the step norms",
   "appears_as": "\\(1.1\\times10^{7}\\)",
   "paper_text": "against $1.1\\times10^{7}$ for the product of the step norms",
   "paper_line": 582,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "gain-scan",
   "section": "Why the loop can be chaotic",
   "claim": "cells of the gain-split scan",
   "appears_as": "5353 cells, 331 chaotic",
   "paper_text": "(block 12; 5353 cells, 331 chaotic)",
   "paper_line": 706,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "readout-contraction",
   "section": "Why the loop can be chaotic",
   "claim": "readout contraction without steering",
   "appears_as": "0.87 to 5.49 nats per step",
   "paper_text": "by $0.87$ to $5.49$ nats per step",
   "paper_line": 709,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "perm-p",
   "section": "Why the loop can be chaotic",
   "claim": "permutation p-value of entropy, gap and readout contrasts",
   "appears_as": "\\(p \\le 10^{-4}\\)",
   "paper_text": "$p\\le10^{-4}$ in a permutation test within temperature rows",
   "paper_line": 714,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "residual-share",
   "section": "Why the loop can be chaotic",
   "claim": "chaotic share under residual steering (paper 1e8e82f4)",
   "appears_as": "6.2% on the residual-steering grid",
   "paper_text": "against 6.2\\,\\% on the residual-steering grid (331 of 5353; the two grids share their temperature rows",
   "paper_line": 720,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "xo-cells",
   "section": "Why the loop can be chaotic",
   "claim": "chaotic cells reserved for the crossover",
   "appears_as": "Over 14 chaotic cells reserved",
   "paper_text": "Over 14 held-out chaotic cells",
   "paper_line": 736,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "xo-readout",
   "section": "Why the loop can be chaotic",
   "claim": "growth change from steering only the readout",
   "appears_as": "+0.81 [0.29, 1.35]",
   "paper_text": "$0.81$ nats per step ($[0.29,1.35]$)",
   "paper_line": 737,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "xo-network",
   "section": "Why the loop can be chaotic",
   "claim": "growth change from steering only the network",
   "appears_as": "−0.49 [−0.63, −0.35]",
   "paper_text": "$0.49$ ($[-0.63,-0.35]$)",
   "paper_line": 738,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "xo-interaction",
   "section": "Why the loop can be chaotic",
   "claim": "interaction term of the crossover",
   "appears_as": "+0.26 [0.09, 0.45]",
   "paper_text": "$+0.26$ ($[0.09,0.45]$)",
   "paper_line": 739,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "xo-gratitude",
   "section": "Why the loop can be chaotic",
   "claim": "crossover readout effect, gratitude",
   "appears_as": "+0.33 [0.07, 0.59]",
   "paper_text": "$+0.33$ ($[0.07,0.59]$)",
   "paper_line": 746,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "xo-gratitude-net",
   "section": "Why the loop can be chaotic",
   "claim": "crossover network effect, gratitude",
   "appears_as": "−0.14 [−0.29, 0.01]",
   "paper_text": "$-0.14$ ($[-0.29,0.01]$)",
   "paper_line": 746,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "xo-random",
   "section": "Why the loop can be chaotic",
   "claim": "crossover readout effect, random direction",
   "appears_as": "+0.77 [0.47, 1.12]",
   "paper_text": "$+0.77$ ($[0.47,1.12]$)",
   "paper_line": 747,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "xo-random-net",
   "section": "Why the loop can be chaotic",
   "claim": "crossover network effect, random direction",
   "appears_as": "−0.09 [−0.22, 0.06]",
   "paper_text": "$-0.09$ ($[-0.22,0.06]$)",
   "paper_line": 747,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "xo-7b-readout",
   "section": "Why the loop can be chaotic",
   "claim": "crossover readout effect, Qwen2.5-7B (paper 1e8e82f4)",
   "appears_as": "+0.23 [−0.11, 0.63]",
   "paper_text": "$+0.23$ ($[-0.11,0.63]$, an interval that includes zero)",
   "paper_line": 744,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "xo-7b-network",
   "section": "Why the loop can be chaotic",
   "claim": "crossover network effect, Qwen2.5-7B",
   "appears_as": "−1.14 [−1.61, −0.64]",
   "paper_text": "$1.14$ nats per step ($[-1.61,-0.64]$)",
   "paper_line": 744,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "xo-7b-cells",
   "section": "Why the loop can be chaotic",
   "claim": "chaotic cells of the 7B crossover",
   "appears_as": "Crossover, 7B, philosophy, 10 cells",
   "paper_text": "Over its 10 held-out chaotic cells",
   "paper_line": 743,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "entropy-gap",
   "section": "Why the loop can be chaotic",
   "claim": "next-token entropy, chaotic minus periodic",
   "appears_as": "+1.62 [1.26, 1.91]",
   "paper_text": "($+1.62$ nats, $[1.26,1.91]$)",
   "paper_line": 712,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "logit-gap",
   "section": "Why the loop can be chaotic",
   "claim": "top-two logit gap in units of T, chaotic minus periodic",
   "appears_as": "−1.37 [−1.98, −0.87]",
   "paper_text": "($-1.37$ in units of $T$, $[-1.98,-0.87]$)",
   "paper_line": 713,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "depth-shares",
   "section": "Why the loop can be chaotic",
   "claim": "chaotic share by steering layer",
   "appears_as": "5.9, 8.1, 6.8, 5.0 and 2.3%",
   "paper_text": "5.9, 8.1, 6.8, 5.0 and 2.3\\,\\%",
   "paper_line": 1475,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "depth-lowT",
   "section": "Why the loop can be chaotic",
   "claim": "lowest chaotic temperature for early steering",
   "appears_as": "\\(\\log_{10}T = -0.95\\) (layer 8)",
   "paper_text": "$\\log_{10}T=-0.95$ (block 8) and $-0.91$",
   "paper_line": 1476,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "twoblock-share",
   "section": "Why the loop can be chaotic",
   "claim": "chaotic share of the two-layer plane",
   "appears_as": "makes 21.7%",
   "paper_text": "makes 21.7\\,\\% of a $96\\times96$ plane chaotic",
   "paper_line": 1500,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "twoblock-single",
   "section": "Why the loop can be chaotic",
   "claim": "chaotic shares of the single pushes",
   "appears_as": "makes 12.5% and 5.2%",
   "paper_text": "make 12.5\\,\\% (gratitude at block 4 alone) and 5.2\\,\\%",
   "paper_line": 1502,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "twoblock-cells",
   "section": "Why the loop can be chaotic",
   "claim": "cells chaotic only in combination",
   "appears_as": "In 1561 cells, 16.9% of the plane and 78% of its chaotic cells",
   "paper_text": "1561 cells, 16.9\\,\\% of the plane and 78\\,\\% of its chaotic cells",
   "paper_line": 1503,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "rounding-levels",
   "section": "Reproducibility",
   "claim": "rounding-level relative differences in float64 and bfloat16",
   "appears_as": "about \\(10^{-16}\\) relative in float64 and about \\(10^{-3}\\) in bfloat16",
   "paper_text": "about $10^{-16}$ relative in float64 and about $10^{-3}$ in bfloat16",
   "paper_line": 1160,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "t-star-example",
   "section": "Reproducibility",
   "claim": "divergence step for d1 = 1e-15 and lambda = 0.3",
   "appears_as": "(about 100 steps for \\(d_1 \\approx 10^{-15}\\) and \\(\\lambda \\approx 0.3\\))",
   "paper_text": "(about 100 steps for $d_1\\approx 10^{-15}$ and $\\lambda\\approx0.3$)",
   "paper_line": 1166,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "published-st-top15",
   "section": "Reproducibility",
   "claim": "published settings: concept tokens of the 15 most probable tokens at T = 0.6",
   "appears_as": "restricted to the 15 most probable tokens, \\(T = 0.6\\) and",
   "paper_text": "restricted to the 15 most probable, $T=0.6$ and 64 soft steps",
   "paper_line": 1347,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "published-st-steps-problems",
   "section": "Reproducibility",
   "claim": "soft steps and problems of the published-settings test",
   "appears_as": "64 soft steps. The test used 256 GSM8K training problems",
   "paper_text": "$T=0.6$ and 64 soft steps. The test used 256 GSM8K training problems",
   "paper_line": 1347,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "published-st-layouts",
   "section": "Reproducibility",
   "claim": "batch sizes compared",
   "appears_as": "between batches of 8 and of 16 prompts of equal length",
   "paper_text": "between batches of 8 and of 16 prompts of equal length",
   "paper_line": 1348,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "published-st-primary",
   "section": "Reproducibility",
   "claim": "answers changed by the batch layout (primary)",
   "appears_as": "the answer changed for 21.1% of the problems (54 of 256;",
   "paper_text": "the answer changed for 21.1\\,\\% of the problems (54 of 256;",
   "paper_line": 1349,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "published-st-ci",
   "section": "Reproducibility",
   "claim": "interval of the primary rate, clustered by batch",
   "appears_as": "95% interval [16.3, 26.1]",
   "paper_text": "batch $[16.3,26.1]$)",
   "paper_line": 1350,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "published-st-pred",
   "section": "Reproducibility",
   "claim": "primary prediction",
   "appears_as": "the prediction of more than 10%",
   "paper_text": "This confirms the prediction of more than 10\\,\\%",
   "paper_line": 1350,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "published-st-full",
   "section": "Reproducibility",
   "claim": "rate with the full vocabulary",
   "appears_as": "The full vocabulary gave 22.3% (no prediction)",
   "paper_text": "The full vocabulary gave 22.3\\,\\% (no prediction)",
   "paper_line": 1369,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "published-st-acc",
   "section": "Reproducibility",
   "claim": "accuracy through the soft pipeline",
   "appears_as": "answers only 22 to 30% of the",
   "paper_text": "this model answers only 22 to 30\\,\\% of the problems correctly",
   "paper_line": 1370,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "published-st-correct",
   "section": "Reproducibility",
   "claim": "problems whose correctness changes with the layout",
   "appears_as": "6.2% of the problems. In float64",
   "paper_text": "for 6.2\\,\\% of the problems",
   "paper_line": 1371,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "published-st-f64",
   "section": "Reproducibility",
   "claim": "float64 contraction counts on the GSM8K test problems",
   "appears_as": "1312 and 1314 of the 1319 GSM8K test problems",
   "paper_text": "On 1312 and 1314 of the 1319 GSM8K test problems",
   "paper_line": 1371,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "published-st-f64-eps",
   "section": "Reproducibility",
   "claim": "size of the float64 perturbation",
   "appears_as": "a perturbation of \\(10^{-10}\\) ended below its initial size",
   "paper_text": "a perturbation of $10^{-10}$ ended below its initial size",
   "paper_line": 1372,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-batch-share",
   "section": "Reproducibility",
   "claim": "distance at which the texts split, in the examples of Table 1 (batch section)",
   "appears_as": "later, at 1.27 to 176%",
   "paper_text": "at 1.27 to 176\\,\\% of the state's norm in the examples of",
   "paper_line": 1167,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-batch-steps",
   "section": "Reproducibility",
   "claim": "steps between passing 1e-2 and the text split (batch section)",
   "appears_as": "(0 to 16 steps after the distance passes \\(10^{-2}\\))",
   "paper_text": "(0 to 16 steps after the distance passes $10^{-2}$)",
   "paper_line": 1168,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "perturb-steps",
   "section": "Reproducibility",
   "claim": "soft steps and precision of the perturbation test",
   "appears_as": "in float32, with 16 soft steps, at",
   "paper_text": "in float32, with 16 soft steps, at temperatures 0.3 and 1.0",
   "paper_line": 4598,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "perturb-temps",
   "section": "Reproducibility",
   "claim": "temperatures of the perturbation test",
   "appears_as": "temperatures 0.3 and 1.0. The settings",
   "paper_text": "temperatures 0.3 and 1.0, on 16 development and 64 held-out problems",
   "paper_line": 4599,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "perturb-dev",
   "section": "Reproducibility",
   "claim": "development problems of the perturbation test",
   "appears_as": "chosen on 16 development problems",
   "paper_text": "on 16 development and 64 held-out problems",
   "paper_line": 4599,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "perturb-test",
   "section": "Reproducibility",
   "claim": "test problems of the perturbation test",
   "appears_as": "64 other problems",
   "paper_text": "on 16 development and 64 held-out problems",
   "paper_line": 4599,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "perturb-target",
   "section": "Reproducibility",
   "claim": "target answer of the perturbation test",
   "appears_as": "the correct sum plus or minus 10",
   "paper_text": "The target was the correct sum plus or minus 10",
   "paper_line": 4599,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "perturb-radius",
   "section": "Reproducibility",
   "claim": "size of the optimized perturbation",
   "appears_as": "was confined to one token norm",
   "paper_text": "perturbed the first soft token by one token norm",
   "paper_line": 4600,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "perturb-gradient-steps",
   "section": "Reproducibility",
   "claim": "gradient steps of the optimizer",
   "appears_as": "It came from 20 steps of gradient ascent",
   "paper_text": "A 20-step projected gradient ascent on the target's log-probability",
   "paper_line": 4600,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "perturb-random",
   "section": "Reproducibility",
   "claim": "directions tried by random search",
   "appears_as": "tried 45 random directions of that length",
   "paper_text": "random search over 45 directions with at least as much computation",
   "paper_line": 4601,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "perturb-test-n",
   "section": "Reproducibility",
   "claim": "problems in the test",
   "appears_as": "On the 64 test problems",
   "paper_text": "on 16 development and 64 held-out problems",
   "paper_line": 4599,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "perturb-hits",
   "section": "Reproducibility",
   "claim": "baseline-correct problem-temperature pairs where the early perturbation reached the target",
   "appears_as": "5 of 101 problem-temperature pairs",
   "paper_text": "reached the target in 5 of 101 problem-temperature pairs",
   "paper_line": 4602,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "perturb-diff",
   "section": "Reproducibility",
   "claim": "difference between the optimizer and random search",
   "appears_as": "a difference of 4.2 points with each",
   "paper_text": "a difference of 4.2 points (95\\,\\% interval $[0.8,8.3]$)",
   "paper_line": 4603,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "perturb-ci",
   "section": "Reproducibility",
   "claim": "interval of that difference",
   "appears_as": "(95% interval [0.8, 8.3])",
   "paper_text": "interval $[0.8,8.3]$)",
   "paper_line": 4604,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "perturb-required",
   "section": "Reproducibility",
   "claim": "advantage the design required",
   "appears_as": "below the advantage of 10",
   "paper_text": "below the advantage of 10 points that the design required",
   "paper_line": 4604,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "perturb-late",
   "section": "Reproducibility",
   "claim": "pairs where the late perturbation reached the target",
   "appears_as": "in 14 of the 101",
   "paper_text": "reached the target in 14 of the 101",
   "paper_line": 4605,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "perturb-random-changed",
   "section": "Reproducibility",
   "claim": "answers changed by random early perturbations, one random direction",
   "appears_as": "random direction: 34 of the 101 eligible pairs",
   "paper_text": "about a third of the answers (one random direction: 34 of the 101 eligible pairs)",
   "paper_line": 4606,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "perturb-twins",
   "section": "Reproducibility",
   "claim": "shares of twins that expanded on the development problems at the two temperatures",
   "appears_as": "10% and 38% of twins expanded",
   "paper_text": "10 and 38\\,\\% of twins expanded",
   "paper_line": 4609,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "perturb-rates",
   "section": "Reproducibility",
   "claim": "median twin growth rates at the two temperatures",
   "appears_as": "growth rates of -0.131 and -0.058 per step",
   "paper_text": "$-0.131$ and $-0.058$ per step",
   "paper_line": 4610,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "quant-bits8",
   "section": "Reproducibility",
   "claim": "bits of the 8-bit quantization",
   "appears_as": "either in 8-bit blocks",
   "paper_text": "either in 8-bit blocks",
   "paper_line": 4631,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "quant-bits4",
   "section": "Reproducibility",
   "claim": "bits of the 4-bit quantization",
   "appears_as": "or in symmetric 4-bit blocks",
   "paper_text": "or in symmetric 4-bit blocks",
   "paper_line": 4631,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "quant-prompts",
   "section": "Reproducibility",
   "claim": "prompts of the quantization test",
   "appears_as": "48 prompts not used",
   "paper_text": "on 48 held-out prompts",
   "paper_line": 4632,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "quant-temps",
   "section": "Reproducibility",
   "claim": "temperatures of the quantization test",
   "appears_as": "at 8 temperatures over \\(\\log_{10}T \\in [-0.5, 0.5]\\)",
   "paper_text": "at 8 temperatures over $\\log_{10}T\\in[-0.5,0.5]$",
   "paper_line": 4632,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "quant-starts",
   "section": "Reproducibility",
   "claim": "starts per prompt and temperature",
   "appears_as": "from 2 starts each",
   "paper_text": "from 2 starts each",
   "paper_line": 4633,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "quant-kl8",
   "section": "Reproducibility",
   "claim": "mean one-step KL divergence of the 8-bit model on the original's attractor states",
   "appears_as": "is 0.0028 nats",
   "paper_text": "Kullback--Leibler divergence is 0.0028 nats",
   "paper_line": 4637,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "quant-top8",
   "section": "Reproducibility",
   "claim": "top-token agreement of the 8-bit model",
   "appears_as": "agrees in 94.5% of states",
   "paper_text": "agrees in 94.5\\,\\% of states",
   "paper_line": 4637,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "quant-period",
   "section": "Reproducibility",
   "claim": "period bound of the occupancy share",
   "appears_as": "period at most 8 shows no detectable change",
   "paper_text": "of period at most 8 shows no detectable change",
   "paper_line": 4638,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "quant-share8",
   "section": "Reproducibility",
   "claim": "change of the share under 8-bit quantization",
   "appears_as": "(+1.2 points, 95% interval [-1.9, 4.2])",
   "paper_text": "($+1.2$ points, 95\\,\\% interval $[-1.9,4.2]$)",
   "paper_line": 4638,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "quant-moved8",
   "section": "Reproducibility",
   "claim": "starts ending in a different class or period, 8-bit",
   "appears_as": "Yet 14.1% of the starts",
   "paper_text": "Yet 14.1\\,\\% of the starts end in a different class or period",
   "paper_line": 4639,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "quant-moved-noise",
   "section": "Reproducibility",
   "claim": "starts ending in a different class or period, random bias",
   "appears_as": "do 15.0% under the random bias",
   "paper_text": "as do 15.0\\,\\% under the random",
   "paper_line": 4639,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "quant-share4",
   "section": "Reproducibility",
   "claim": "change of the share under 4-bit quantization",
   "appears_as": "The share rises by 6.8 points ([2.6, 11.0])",
   "paper_text": "The share rises by 6.8 points ($[2.6,11.0]$)",
   "paper_line": 4641,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "quant-kl4",
   "section": "Reproducibility",
   "claim": "mean one-step KL divergence of the 4-bit model",
   "appears_as": "the mean divergence is 0.83 nats",
   "paper_text": "the mean divergence is 0.83 nats",
   "paper_line": 4642,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "quant-top4",
   "section": "Reproducibility",
   "claim": "top-token agreement of the 4-bit model",
   "appears_as": "agrees in only 52% of states",
   "paper_text": "agrees in only 52\\,\\% of states",
   "paper_line": 4643,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-schematic-share",
   "section": "Reproducibility",
   "claim": "distance at the text split and steps after passing 1e-2, in the examples of Table 1 (schematic note)",
   "appears_as": "at 1.27 to 176% of the state's norm, 0 to 16 steps after the difference passes",
   "paper_text": "at 1.27 to 176\\,\\% of the state's norm in the examples of",
   "paper_line": 1167,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "f32-f64-medians",
   "section": "Reproducibility",
   "claim": "median divergence step of chaotic cells, float32 and float64 batch layouts",
   "appears_as": "median of 20.5 steps in float32 and of 102 steps in float64",
   "paper_text": "batch layout, float32 & chaotic & 192 / 192 & 20.5",
   "paper_line": 1254,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "f32-vs-f64",
   "section": "Reproducibility",
   "claim": "chaotic cells separating between float32 and float64 runs",
   "appears_as": "all 192 pass \\(10^{-2}\\), after a median of 20",
   "paper_text": "float32 against float64 & chaotic & 192 / 192 & 20 & 92.7\\,\\%",
   "paper_line": 1256,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bf16-start",
   "section": "Reproducibility",
   "claim": "starting difference in bfloat16",
   "appears_as": "already about \\(10^{-3}\\)",
   "paper_text": "In bfloat16 the starting difference is already about $10^{-3}$",
   "paper_line": 1176,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "first-diff",
   "section": "Reproducibility",
   "claim": "first difference between the two float64 runs",
   "appears_as": "\\(6\\times10^{-15}\\), the rounding",
   "paper_text": "differ by about $6\\times10^{-15}$, the rounding level",
   "paper_line": 1187,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "token-diff",
   "section": "Reproducibility",
   "claim": "chaotic cells whose most probable token comes to differ",
   "appears_as": "at 173 of",
   "paper_text": "at 173 of the 192 chaotic cells",
   "paper_line": 1189,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "periodic-stay",
   "section": "Reproducibility",
   "claim": "periodic cells staying within 1e-2",
   "appears_as": "At 182 of the 192 periodic cells",
   "paper_text": "182 of the 192 periodic cells the two runs stay within $10^{-2}$ for all 1500 steps",
   "paper_line": 1191,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "periodic-median",
   "section": "Reproducibility",
   "claim": "median largest distance of periodic cells",
   "appears_as": "\\(2.3\\times10^{-12}\\)",
   "paper_text": "median largest distance of $2.3\\times10^{-12}$",
   "paper_line": 1191,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ratio-loglog",
   "section": "Reproducibility",
   "claim": "log-log correlation of divergence step and prediction",
   "appears_as": "log-log correlation of 0.73 over 190 cells",
   "paper_text": "log-log correlation of $0.73$ over 190 cells",
   "paper_line": 1197,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "nondiverge",
   "section": "Reproducibility",
   "claim": "exponents of the two chaotic cells that never diverge",
   "appears_as": "exponents of 0.013 and 0.0013",
   "paper_text": "exponents of $0.013$ and $0.0013$",
   "paper_line": 1199,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bf16-llama",
   "section": "Reproducibility",
   "claim": "Llama cells separating within one or two steps in bfloat16",
   "appears_as": "38 of the 40 Llama cells",
   "paper_text": "38 of the 40 Llama cells",
   "paper_line": 1244,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "t2-05b-f32",
   "section": "Reproducibility",
   "claim": "float32 chaotic median step and token share",
   "appears_as": "| 192 / 192 | 20.5 | 92.2% |",
   "paper_text": "chaotic & 192 / 192 & 20.5 & 92.2\\,\\%",
   "paper_line": 1254,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "t2-05b-f32-per",
   "section": "Reproducibility",
   "claim": "float32 periodic cells reaching 1e-2",
   "appears_as": "| 72 / 192 | | 22.9% |",
   "paper_text": "periodic & 72 / 192 & & 22.9\\,\\%",
   "paper_line": 1255,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "t2-05b-bf16",
   "section": "Reproducibility",
   "claim": "bfloat16 chaotic cells",
   "appears_as": "| 192 / 192 | 2 | 99.5% |",
   "paper_text": "chaotic & 192 / 192 & 2 & 99.5\\,\\%",
   "paper_line": 1258,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "t2-05b-bf16-per",
   "section": "Reproducibility",
   "claim": "bfloat16 periodic cells",
   "appears_as": "| 192 / 192 | 2 | 95.3% |",
   "paper_text": "periodic & 192 / 192 & 2 & 95.3\\,\\%",
   "paper_line": 1259,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "t2-05b-f64",
   "section": "Reproducibility",
   "claim": "float64 chaotic token share",
   "appears_as": "| 190 / 192 | 102 | 90.1% |",
   "paper_text": "chaotic & 190 / 192 & 102 & 90.1\\,\\%",
   "paper_line": 1252,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "t2-05b-f64-per",
   "section": "Reproducibility",
   "claim": "float64 periodic token share",
   "appears_as": "| 10 / 192 | | 3.6% |",
   "paper_text": "periodic & 10 / 192 & & 3.6\\,\\%",
   "paper_line": 1253,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "t2-7b",
   "section": "Reproducibility",
   "claim": "Qwen2.5-7B unsteered float64 chaotic cells",
   "appears_as": "| 24 / 24 | 56 | 95.8% |",
   "paper_text": "chaotic & 24 / 24 & 56 & 95.8\\,\\%",
   "paper_line": 1261,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "t2-8b",
   "section": "Reproducibility",
   "claim": "Llama-3.1-8B unsteered float64 chaotic cells",
   "appears_as": "| 20 / 20 | 68 | 100% |",
   "paper_text": "chaotic & 20 / 20 & 68 & 100\\,\\%",
   "paper_line": 1268,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "t2-8b-per",
   "section": "Reproducibility",
   "claim": "Llama-3.1-8B periodic cells reaching 1e-2",
   "appears_as": "| 1 / 20 | | 5% |",
   "paper_text": "periodic & 1 / 20 & & 5\\,\\%",
   "paper_line": 1269,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "t2-70b",
   "section": "Reproducibility",
   "claim": "Llama-3.3-70B steered float64 chaotic cells",
   "appears_as": "| 24 / 24 | 114.5 | 87.5% |",
   "paper_text": "chaotic & 24 / 24 & 114.5 & 87.5\\,\\%",
   "paper_line": 1275,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "answers-T1",
   "section": "Reproducibility",
   "claim": "answers changed by batching at T = 1 (0.5B, bfloat16)",
   "appears_as": "in 56% of the",
   "paper_text": "in 56\\,\\% of the problems at $T=1$",
   "paper_line": 1293,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "answers-T02",
   "section": "Reproducibility",
   "claim": "answers changed by batching at T = 10^0.2 (0.5B)",
   "appears_as": "in 8% at",
   "paper_text": "in 8\\,\\% at $T=10^{0.2}$",
   "paper_line": 1293,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "answers-excess",
   "section": "Reproducibility",
   "claim": "excess disagreement of soft over greedy decoding",
   "appears_as": "32.3",
   "paper_text": "is 32.3 percentage points (95\\,\\% interval $[26.5,38.1]$",
   "paper_line": 1298,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "answers-7b",
   "section": "Reproducibility",
   "claim": "7B soft-thinking answers changed by batching",
   "appears_as": "53 of the 96 problems (55%)",
   "paper_text": "53 of the 96 problems (55\\,\\%)",
   "paper_line": 1306,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "answers-7b-greedy",
   "section": "Reproducibility",
   "claim": "7B greedy answers changed by batching",
   "appears_as": "changed in 10 of the 96",
   "paper_text": "changed in 10 of the 96",
   "paper_line": 1311,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "answers-7b-excess",
   "section": "Reproducibility",
   "claim": "7B excess over greedy decoding",
   "appears_as": "17.7 points ([9.3, 25.6])",
   "paper_text": "17.7 points ($[9.3,25.6]$",
   "paper_line": 1312,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "answers-7b-kick",
   "section": "Reproducibility",
   "claim": "7B float64 growth of an injected perturbation",
   "appears_as": "median \\(+0.034\\) nats per step",
   "paper_text": "median $+0.034$ nats per step",
   "paper_line": 1316,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "answers-7b-f64",
   "section": "Reproducibility",
   "claim": "7B answers changed by float64 layouts",
   "appears_as": "changed 5% of the answers",
   "paper_text": "changed 5\\,\\% of the answers",
   "paper_line": 1317,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "reset-05b",
   "section": "Reproducibility",
   "claim": "answers changed without the reset (free condition), Qwen2.5-0.5B, bfloat16 on an H100, 128 newly drawn additions: 60 of 128 (47%) (paper 318f8980)",
   "appears_as": "answer changed in 60 of the 128 problems (47%) without the reset and in 1 (0.8%)",
   "paper_text": "the answer changed in 60 of the 128 problems (47\\,\\%) in the free arm and in 1 (0.8\\,\\%) with reset in the 0.5B model",
   "paper_line": 1334,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "reset-7b",
   "section": "Reproducibility",
   "claim": "answers changed without and with the reset, Qwen2.5-7B, bfloat16 on an H100: 52 of 128 (41%) against none (paper 318f8980)",
   "appears_as": "and in 52 (41%) against none in",
   "paper_text": "and in 52 (41\\,\\%) against none in Qwen2.5-7B at $T=10^{0.2}$",
   "paper_line": 1335,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "reset-acc",
   "section": "Reproducibility",
   "claim": "largest accuracy difference from the reference",
   "appears_as": "by more than 5 points",
   "paper_text": "by more than 5 points",
   "paper_line": 1338,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "reset-n",
   "section": "Reproducibility",
   "claim": "problems per condition",
   "appears_as": "problems per condition do not show",
   "paper_text": "128 problems per arm",
   "paper_line": 1340,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "behavior-n",
   "section": "Reproducibility",
   "claim": "fresh products in the behavior test",
   "appears_as": "4000 newly drawn products",
   "paper_text": "A frozen test then labeled 4000 newly drawn products",
   "paper_line": 1522,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "behavior-gap",
   "section": "Reproducibility",
   "claim": "accuracy gap of chaotic-loop prompts",
   "appears_as": "by\n7.1 points",
   "paper_text": "by 7.1 points (95\\,\\% interval $[4.8,9.3]$)",
   "paper_line": 1524,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "behavior-coef",
   "section": "Reproducibility",
   "claim": "label coefficient after covariates",
   "appears_as": "+0.15 points ([−1.4, 1.7], permutation \\(p = 0.84\\))",
   "paper_text": "$+0.15$ points, $[-1.4,1.7]$, permutation $p=0.84$",
   "paper_line": 1525,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "behavior-edge",
   "section": "Reproducibility",
   "claim": "range of the three adjusted edge contrasts",
   "appears_as": "within [−3.1, 3.0] points",
   "paper_text": "within $[-3.1,3.0]$ points",
   "paper_line": 1529,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "stripe-p6",
   "section": "Saddle-node bottleneck",
   "claim": "period-6 stripe orbit multipliers",
   "appears_as": "| +0.0052 | \\(3\\times10^{-6}\\) |",
   "paper_text": "$+0.0052$ & $3\\times10^{-6}$",
   "paper_line": 1549,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "stripe-p8",
   "section": "Saddle-node bottleneck",
   "claim": "period-8 stripe orbit multipliers",
   "appears_as": "| +0.0110 | \\(3\\times10^{-7}\\) |",
   "paper_text": "$+0.0110$ & $3\\times10^{-7}$",
   "paper_line": 1550,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "stripe-p10",
   "section": "Saddle-node bottleneck",
   "claim": "period-10 stripe orbit multipliers",
   "appears_as": "| +0.0025 | \\(2\\times10^{-7}\\) |",
   "paper_text": "$+0.0025$ & $2\\times10^{-7}$",
   "paper_line": 1551,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "stripe-p12",
   "section": "Saddle-node bottleneck",
   "claim": "period-12 stripe orbit multipliers",
   "appears_as": "| +0.0163 | \\(4\\times10^{-8}\\) |",
   "paper_text": "$+0.0163$ & $4\\times10^{-8}$",
   "paper_line": 1552,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "stripe-p14",
   "section": "Saddle-node bottleneck",
   "claim": "period-14 stripe orbit multipliers",
   "appears_as": "| +0.0369 | \\(2\\times10^{-9}\\) |",
   "paper_text": "$+0.0369$ & $2\\times10^{-9}$",
   "paper_line": 1553,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "stripe-p16",
   "section": "Saddle-node bottleneck",
   "claim": "period-16 stripe orbit multipliers",
   "appears_as": "| +0.0716 | \\(8\\times10^{-11}\\) |",
   "paper_text": "$+0.0716$ & $8\\times10^{-11}$",
   "paper_line": 1554,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "stripe-p18",
   "section": "Saddle-node bottleneck",
   "claim": "period-18 stripe orbit multipliers",
   "appears_as": "| +0.0792 | \\(1\\times10^{-12}\\) |",
   "paper_text": "$+0.0792$ & $1\\times10^{-12}$",
   "paper_line": 1555,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "stripe-p20",
   "section": "Saddle-node bottleneck",
   "claim": "period-20 stripe orbit multipliers",
   "appears_as": "| +0.0857 | \\(2\\times10^{-14}\\) |",
   "paper_text": "$+0.0857$ & $2\\times10^{-14}$",
   "paper_line": 1556,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "stripe-residuals",
   "section": "Saddle-node bottleneck",
   "claim": "Newton residuals of the stripe orbits",
   "appears_as": "Newton residuals \\(6\\times10^{-15}\\) to \\(8\\times10^{-13}\\)",
   "paper_text": "Newton residuals $6\\times10^{-15}$ to $8\\times10^{-13}$",
   "paper_line": 1561,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-alpha",
   "section": "Saddle-node bottleneck",
   "claim": "fold location of the 2-cycle",
   "appears_as": "\\(\\alpha_c = 0.06279827\\)",
   "paper_text": "$\\alpha_c=0.06279827$",
   "paper_line": 1612,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-mult",
   "section": "Saddle-node bottleneck",
   "claim": "fold multiplier error",
   "appears_as": "\\(3\\times10^{-13}\\), and the next",
   "paper_text": "multiplier $1$ to $3\\times10^{-13}$, next modulus $0.037$",
   "paper_line": 1613,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-a",
   "section": "Saddle-node bottleneck",
   "claim": "normal-form coefficient a",
   "appears_as": "\\(a = -4.834\\)",
   "paper_text": "$a=-4.834$",
   "paper_line": 1615,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-b",
   "section": "Saddle-node bottleneck",
   "claim": "normal-form coefficient b",
   "appears_as": "\\(b = -25.4285\\)",
   "paper_text": "$b=-25.4285$",
   "paper_line": 1615,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-ab",
   "section": "Saddle-node bottleneck",
   "claim": "product ab",
   "appears_as": "\\(ab = 122.93\\)",
   "paper_text": "$ab=122.93$",
   "paper_line": 1615,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "indep-b",
   "section": "Saddle-node bottleneck",
   "claim": "relative difference of b between implementations",
   "appears_as": "\\(2.2\\times10^{-6}\\) relatively",
   "paper_text": "$2.2\\times10^{-6}$ relatively",
   "paper_line": 1624,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "laminar",
   "section": "Saddle-node bottleneck",
   "claim": "laminar phase lengths of a free trajectory",
   "appears_as": "40 to 70 iterates each",
   "paper_text": "40 to 70 iterates each",
   "paper_line": 1607,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "passage-row1",
   "section": "Saddle-node bottleneck",
   "claim": "passages at eps 3e-6",
   "appears_as": "| 144 / 144 | 73 / 74 | 143 / 144 |",
   "paper_text": "144 / 144 & 73 / 74 & 143 / 144",
   "paper_line": 1652,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "passage-row2",
   "section": "Saddle-node bottleneck",
   "claim": "passages at eps 1e-5",
   "appears_as": "| 71 / 71 | 36 / 37 | 70 / 71 |",
   "paper_text": "71 / 71 & 36 / 37 & 70 / 71",
   "paper_line": 1653,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "passage-row3",
   "section": "Saddle-node bottleneck",
   "claim": "passages at eps 3e-5",
   "appears_as": "| 34 / 34 | 17 / 18 | 33 / 34 |",
   "paper_text": "34 / 34 & 17 / 18 & 33 / 34",
   "paper_line": 1654,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "passage-row4",
   "section": "Saddle-node bottleneck",
   "claim": "passages at eps 1e-4",
   "appears_as": "| 14 / 14 | 7 / 7 | 13 / 14 |",
   "paper_text": "14 / 14 & 7 / 7 & 13 / 14",
   "paper_line": 1655,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "passage-18",
   "section": "Saddle-node bottleneck",
   "claim": "fixed-start counts reproduced by the independent reimplementation",
   "appears_as": "all 18 fixed-start counts",
   "paper_text": "all 18 fixed-entrance counts",
   "paper_line": 5873,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "window-dN",
   "section": "Saddle-node bottleneck",
   "claim": "window-law product d_N N^2",
   "appears_as": "\\(d_N N^2 = 0.0263\\) to 0.0265",
   "paper_text": "$d_N N^2=0.0263$--$0.0265$ for $N=4$--$7$ (log-log slope $-2.00$)",
   "paper_line": 1693,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "window-natural",
   "section": "Saddle-node bottleneck",
   "claim": "natural passage on average 0.60 to 0.67 of the normal form's passage through the same channel (paper cda9ca04)",
   "appears_as": "lasts 0.60 to 0.67 of the normal form's passage through the same channel from end to",
   "paper_text": "on average a natural passage lasts 0.60 to 0.67 of the normal form's passage through the same channel from end to end",
   "paper_line": 1683,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "window-058",
   "section": "Saddle-node bottleneck",
   "claim": "passage fraction squared",
   "appears_as": "\\(0.58^2 \\approx 1/3\\)",
   "paper_text": "($0.58^2\\approx1/3$)",
   "paper_line": 1692,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "window-short",
   "section": "Saddle-node bottleneck",
   "claim": "length of a full passage at the window distances",
   "appears_as": "only 9 to 23 iterates",
   "paper_text": "a full passage lasts only 9 to 23 iterates",
   "paper_line": 1753,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "test1-short",
   "section": "Saddle-node bottleneck",
   "claim": "first test: forecasts of five iterates or fewer",
   "appears_as": "Seven of the 24 forecasts",
   "paper_text": "Seven of the 24 forecasts are five iterates or shorter",
   "paper_line": 1772,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "test2-design",
   "section": "Saddle-node bottleneck",
   "claim": "second test: minimum forecast lengths",
   "appears_as": "at least 16 iterates",
   "paper_text": "every full-channel forecast is at least 16 iterates and every midpoint forecast at least 8",
   "paper_line": 1810,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "test2-C",
   "section": "Saddle-node bottleneck",
   "claim": "second test: rows held at the 2-cycle fold",
   "appears_as": "held in all 12",
   "paper_text": "At the 2-cycle's fold the integral held in all 12 rows",
   "paper_line": 1814,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "t5-row1",
   "section": "Saddle-node bottleneck",
   "claim": "second test forecasts and measurements, q = 0.08",
   "appears_as": "| 22.40 / 11.20 | 23 / 12 | 23, 12, 23 | 22, 11, 22 |",
   "paper_text": "$22.40$ / $11.20$ & $23$ / $12$ & $23$,\\ $12$,\\ $23$ & $22$,\\ $11$,\\ $22$",
   "paper_line": 1830,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "t5-row2",
   "section": "Saddle-node bottleneck",
   "claim": "second test, q = 0.05",
   "appears_as": "| 44.29 / 22.14 | 45 / 23 | 45, 23, 45 | 42, 22, 42 |",
   "paper_text": "$44.29$ / $22.14$ & $45$ / $23$ & $45$,\\ $23$,\\ $45$ & $\\mathbf{42}$,\\ $22$,\\ $\\mathbf{42}$",
   "paper_line": 1831,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "t5-row3",
   "section": "Saddle-node bottleneck",
   "claim": "second test, q = 0.03",
   "appears_as": "| 85.29 / 42.64 | 86 / 44 | 86, 43, 86 | 81, 43, 82 |",
   "paper_text": "$85.29$ / $42.64$ & $86$ / $44$ & $86$,\\ $43$,\\ $86$ & $\\mathbf{81}$,\\ $43$,\\ $\\mathbf{82}$",
   "paper_line": 1832,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "t5-row4",
   "section": "Saddle-node bottleneck",
   "claim": "second test, q = 0.018",
   "appears_as": "| 154.74 / 77.37 | 155 / 80 | 155, 78, 155 | 149, 78, 150 |",
   "paper_text": "$154.74$ / $77.37$ & $155$ / $80$ & $155$,\\ $78$,\\ $155$ & $\\mathbf{149}$,\\ $78$,\\ $\\mathbf{150}$",
   "paper_line": 1833,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hostile-slope",
   "section": "Saddle-node bottleneck",
   "claim": "hostile window slope per repetition",
   "appears_as": "rise by 2.235",
   "paper_text": "rises by $2.235$ per lap",
   "paper_line": 2082,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hostile-pred",
   "section": "Saddle-node bottleneck",
   "claim": "normal-form prediction of the hostile slope",
   "appears_as": "2.296 predicted",
   "paper_text": "$\\sqrt{|ab|}/\\pi=2.296$ per lap",
   "paper_line": 2083,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "early-156",
   "section": "Cascade and proof",
   "claim": "first ratio along log10 T = -0.156",
   "appears_as": "14.93",
   "paper_text": "the first ratio is $14.93$",
   "paper_line": 1928,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "later-ratios",
   "section": "Cascade and proof",
   "claim": "later ratios along log10 T = -0.156",
   "appears_as": "3.124, 4.4988,",
   "paper_text": "$3.124$, $4.4988$, $4.6208$, $4.6618$, $4.6673$ and $4.6688$",
   "paper_line": 1933,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "aitken",
   "section": "Cascade and proof",
   "claim": "Aitken extrapolation of the last three ratios",
   "appears_as": "gives 4.6694",
   "paper_text": "the last three ratios gives $4.6694$",
   "paper_line": 1936,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "delta8-range",
   "section": "Cascade and proof",
   "claim": "range of the last ratio over the location uncertainty",
   "appears_as": "between 4.6685 and 4.6692",
   "paper_text": "between $4.6685$ and $4.6692$",
   "paper_line": 1947,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "logistic",
   "section": "Cascade and proof",
   "claim": "first ratios of the logistic map",
   "appears_as": "4.751, 4.656 and 4.668",
   "paper_text": "$4.751$, $4.656$, $4.668$",
   "paper_line": 1990,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "crit-mult",
   "section": "Cascade and proof",
   "claim": "critical multiplier error of the flips",
   "appears_as": "\\(5\\times10^{-8}\\), and for flip 9 by \\(4.1\\times10^{-7}\\)",
   "paper_text": "at most $5\\times10^{-8}$, and for flip 9 by $4.1\\times10^{-7}$",
   "paper_line": 2016,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "t6-1",
   "section": "Cascade and proof",
   "claim": "flip 1",
   "appears_as": "| 0.0644766567385 | 0.12 |",
   "paper_text": "$0.0644766567385$ & $0.12$",
   "paper_line": 2002,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "t6-2",
   "section": "Cascade and proof",
   "claim": "flip 2",
   "appears_as": "| 0.0650493555308 | 0.045 | 14.93 |",
   "paper_text": "$0.0650493555308$ & $0.045$ & $14.93$",
   "paper_line": 2003,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "t6-3",
   "section": "Cascade and proof",
   "claim": "flip 3",
   "appears_as": "| 0.0650877194158 | \\(7.0\\times10^{-5}\\) | 3.124 |",
   "paper_text": "$0.0650877194158$ & $7.0\\times10^{-5}$ & $3.124$",
   "paper_line": 2004,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "t6-4",
   "section": "Cascade and proof",
   "claim": "flip 4",
   "appears_as": "| 0.0650999993318 | \\(4.3\\times10^{-7}\\) | 4.4988 |",
   "paper_text": "$0.0650999993318$ & $4.3\\times10^{-7}$ & $4.4988$",
   "paper_line": 2005,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "t6-5",
   "section": "Cascade and proof",
   "claim": "flip 5",
   "appears_as": "| 0.0651027289524 | \\(1.8\\times10^{-13}\\) | 4.6208 |",
   "paper_text": "$0.0651027289524$ & $1.8\\times10^{-13}$ & $4.6208$",
   "paper_line": 2006,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "t6-6",
   "section": "Cascade and proof",
   "claim": "flip 6",
   "appears_as": "| 0.0651033196816 | \\(2.9\\times10^{-14}\\) | 4.6618 |",
   "paper_text": "$0.0651033196816$ & $2.9\\times10^{-14}$ & $4.6618$",
   "paper_line": 2007,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "t6-7",
   "section": "Cascade and proof",
   "claim": "flip 7",
   "appears_as": "| 0.0651034463988 | \\(1.5\\times10^{-14}\\) | 4.6673 |",
   "paper_text": "$0.0651034463988$ & $1.5\\times10^{-14}$ & $4.6673$",
   "paper_line": 2008,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "t6-8",
   "section": "Cascade and proof",
   "claim": "flip 8",
   "appears_as": "| 0.0651034735487 | \\(3.2\\times10^{-13}\\) | 4.6688 |",
   "paper_text": "$0.0651034735487$ & $3.2\\times10^{-13}$ & $4.6688$",
   "paper_line": 2009,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "t6-9",
   "section": "Cascade and proof",
   "claim": "flip 9",
   "appears_as": "| 0.0651034793638 | \\(2.9\\times10^{-14}\\) |",
   "paper_text": "$0.0651034793638$ & $2.9\\times10^{-14}$",
   "paper_line": 2010,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bubble-amplitude",
   "section": "Cascade and proof",
   "claim": "amplitude ratios at the smallest offset",
   "appears_as": "1.005 and 1.003",
   "paper_text": "the amplitude ratios are $1.005$ and $1.003$",
   "paper_line": 2054,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "proof-point",
   "section": "Cascade and proof",
   "claim": "parameter point of the proof",
   "appears_as": "At \\(\\alpha = 0.071674\\) and \\(\\log_{10}T = -0.115\\)",
   "paper_text": "At $\\alpha=0.071674$ and $\\log_{10}T=-0.115$",
   "paper_line": 5828,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "proof-radius",
   "section": "Cascade and proof",
   "claim": "box radius of the proof",
   "appears_as": "\\(2^{-640}\\)",
   "paper_text": "coordinate radius $2^{-640}$",
   "paper_line": 5832,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "proof-prefix",
   "section": "Cascade and proof",
   "claim": "prefix length in tokens",
   "appears_as": "37-token prefix",
   "paper_text": "the fixed 37-token prefix",
   "paper_line": 5831,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "proof-dirs",
   "section": "Cascade and proof",
   "claim": "directions enclosed per box",
   "appears_as": "\\(8\\times896\\) directions",
   "paper_text": "($8\\times896$ directions)",
   "paper_line": 5834,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "proof-2-80",
   "section": "Cascade and proof",
   "claim": "box radius at which RMS positivity is lost",
   "appears_as": "\\(2^{-80}\\)",
   "paper_text": "a box of radius $2^{-80}$ already gave enclosures too wide",
   "paper_line": 5751,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hb-offsets",
   "section": "Chaos behind a repeating text",
   "claim": "agreement of exponents at two twin offsets",
   "appears_as": "agree within 0.0031",
   "paper_text": "agree to within 0.0031 in every chaotic cell",
   "paper_line": 2228,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hb-65",
   "section": "Chaos behind a repeating text",
   "claim": "chaotic cells whose leading token repeats exactly",
   "appears_as": "In 65 of them",
   "paper_text": "In 65 of them the leading token repeats exactly for all 2000 steps",
   "paper_line": 2229,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hb-59",
   "section": "Chaos behind a repeating text",
   "claim": "of these, cells whose text period is a multiple of 7",
   "appears_as": "in 59 of these",
   "paper_text": "in 59 of these the period of the text is a multiple of 7",
   "paper_line": 2230,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hb-strong",
   "section": "Chaos behind a repeating text",
   "claim": "strongest case",
   "appears_as": "(\\(\\log_{10}T = 0.18995\\), largest exponent 0.091",
   "paper_text": "($\\log_{10}T=0.18995$, largest exponent 0.091 per step at both offsets)",
   "paper_line": 2232,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hb-sep",
   "section": "Chaos behind a repeating text",
   "claim": "minimum separation of the seven groups",
   "appears_as": "0.098 of the state norm",
   "paper_text": "at least 0.098 of the state norm apart",
   "paper_line": 2233,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hb-fit",
   "section": "Chaos behind a repeating text",
   "claim": "residual of the degree-8 fit",
   "appears_as": "\\(4\\times10^{-4}\\) of its",
   "paper_text": "fits it to $4\\times10^{-4}$ of its range",
   "paper_line": 2247,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hb-exp",
   "section": "Chaos behind a repeating text",
   "claim": "exponent of the fitted map against the full map",
   "appears_as": "0.647 per repetition",
   "paper_text": "0.647 per repetition, is within 2\\,\\% of the full map's 0.636 per repetition",
   "paper_line": 2247,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hb-62",
   "section": "Chaos behind a repeating text",
   "claim": "cells again chaotic behind a repeating text",
   "appears_as": "62 of the 65",
   "paper_text": "62 of the 65 cells are again chaotic",
   "paper_line": 2249,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hb-30",
   "section": "Chaos behind a repeating text",
   "claim": "cells where delay predictors improved the error",
   "appears_as": "30 of 61",
   "paper_text": "in 30 of 61 cells two- or three-delay predictors",
   "paper_line": 2262,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p5-mult",
   "section": "Shrimp-shaped windows",
   "claim": "largest multiplier beyond the leading pair",
   "appears_as": "the leading pair are below 0.0032",
   "paper_text": "the multipliers beyond the leading pair are below $0.0032$",
   "paper_line": 2418,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p5-nil",
   "section": "Shrimp-shaped windows",
   "claim": "location of the near-nilpotent point",
   "appears_as": "\\((\\alpha_1, \\alpha_2) = (-0.1184836, 0.1017217)\\)",
   "paper_text": "$(\\alpha_1,\\alpha_2)=(-0.1184836,0.1017217)$",
   "paper_line": 2425,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p5-nil-mod",
   "section": "Shrimp-shaped windows",
   "claim": "moduli of the three leading multipliers there",
   "appears_as": "\\(3.4\\) to \\(3.6\\times10^{-3}\\)",
   "paper_text": "$3.4$ to $3.6\\times10^{-3}$",
   "paper_line": 2426,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p5-280",
   "section": "Shrimp-shaped windows",
   "claim": "asymptotic linear contraction per period at the near-nilpotent point (1/3.578e-3 = 279.5, docs/review/p5-nilpotent.jsonl)",
   "appears_as": "a factor of about 280 per",
   "paper_text": "a factor of about 280 per period",
   "paper_line": 2428,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "growing-pert",
   "section": "Beyond the one-token loop and model size",
   "claim": "initial perturbation in the growing context",
   "appears_as": "perturbation of \\(10^{-10}\\)",
   "paper_text": "perturbation of $10^{-10}$",
   "paper_line": 3251,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "growing-rate",
   "section": "Beyond the one-token loop and model size",
   "claim": "growth rate inside the one-token chaotic band (7B)",
   "appears_as": "0.77 to 0.82 per step",
   "paper_text": "by 0.77 to 0.82 per step",
   "paper_line": 5252,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sampling",
   "section": "Beyond the one-token loop and model size",
   "claim": "mean laminar phase with means of 64 samples at the smallest offset (paper cda9ca04)",
   "appears_as": "\\(3\\times10^{-5}\\). With \\(m = 64\\) they last on average 10.5 steps at the smallest",
   "paper_text": "last on average 10.5 steps with $m=64$ and 7.8 with $m=8$",
   "paper_line": 3254,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "greedy-19",
   "section": "Beyond the one-token loop and model size",
   "claim": "greedy runs ending in a short loop",
   "appears_as": "19 runs end in a short loop within 256",
   "paper_text": "19 runs end in a short loop within 256 tokens",
   "paper_line": 5180,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "greedy-steered",
   "section": "Beyond the one-token loop and model size",
   "claim": "steered greedy runs that loop",
   "appears_as": "(218 of 220 runs at",
   "paper_text": "(218 of 220 runs at $\\alpha=0.1$)",
   "paper_line": 5181,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "size-qwen7b",
   "section": "Beyond the one-token loop and model size",
   "claim": "Qwen2.5-7B chaotic share in the fixed window",
   "appears_as": "chaotic at 12.7% of the",
   "paper_text": "Qwen2.5-7B is chaotic at 12.7\\,\\%",
   "paper_line": 3296,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "l33-temps",
   "section": "Beyond the one-token loop and model size",
   "claim": "unsteered Llama-3.3-70B: temperatures swept and horizon",
   "appears_as": "Over its 128 temperatures",
   "paper_text": "Over its 128 temperatures ($\\log_{10}T$ from $-1$ to $0.3$; 1000 transient and 2000 measured steps)",
   "paper_line": 3305,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "l33-15token",
   "section": "Beyond the one-token loop and model size",
   "claim": "low-temperature share of the fifteen-token loop",
   "appears_as": "At 46 of the 49 temperatures",
   "paper_text": "at 46 of the 49 temperatures from $\\log_{10}T=-1$ to $-0.5$, it writes a fifteen-token loop without end",
   "paper_line": 3307,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "l33-p16",
   "section": "Beyond the one-token loop and model size",
   "claim": "temperatures of the period-16 variants",
   "appears_as": "end in `established` (15 temperatures) or `acknowledged` (9)",
   "paper_text": "period-16 variants end in \\texttt{established} (15 temperatures) or \\texttt{acknowledged} (9)",
   "paper_line": 3309,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "l33-p21",
   "section": "Beyond the one-token loop and model size",
   "claim": "temperatures of the period-21 variant",
   "appears_as": "of a fellow AI to another artificial greetings` (8)",
   "paper_text": "a period-21 variant turns into \\texttt{\\ldots\\ of a fellow AI to another artificial greetings} (8)",
   "paper_line": 3310,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "l33-high",
   "section": "Beyond the one-token loop and model size",
   "claim": "cycle lengths and unresolved temperatures at higher temperature",
   "appears_as": "cycles of 24 to 63 steps, and 19 temperatures",
   "paper_text": "Higher temperatures give cycles of 24 to 63 steps, and 19 temperatures have neither a period up to 64 nor a positive exponent",
   "paper_line": 3311,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "l31-loops",
   "section": "Beyond the one-token loop and model size",
   "claim": "Llama-3.1-70B loop counts",
   "appears_as": "`\" to another AI\"` (31",
   "paper_text": "mostly writes the three-token loop \\texttt{\\ to another AI} (31 temperatures) or the four-token loop \\texttt{.\\ It'sup} (21), longer repetitions of \\texttt{\\ to another AI} with periods 6 to 18, and at four temperatures the fixed point \\texttt{It}",
   "paper_line": 3313,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "l31-longer",
   "section": "Beyond the one-token loop and model size",
   "claim": "periods of the longer Llama-3.1-70B repetitions",
   "appears_as": "with periods 6 to 18",
   "paper_text": "longer repetitions of \\texttt{\\ to another AI} with periods 6 to 18",
   "paper_line": 3314,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "z128-windows",
   "section": "Beyond the one-token loop and model size",
   "claim": "window periods below the 70B chaotic band",
   "appears_as": "windows of periods 3 to 13, most often 6",
   "paper_text": "windows of periods 3 to 13, most often 6, lie below it",
   "paper_line": 3316,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "prompt-test",
   "section": "Beyond the one-token loop and model size",
   "claim": "chaotic temperatures of 14B and 7B on eight test prompts",
   "appears_as": "(9 to 17, against 0 to 7 for the 7B)",
   "paper_text": "(9 to 17, against 0 to 7 for the 7B)",
   "paper_line": 3325,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "14b-range",
   "section": "Beyond the one-token loop and model size",
   "claim": "range of the 14B model's chaotic temperatures",
   "appears_as": "\\(\\log_{10}T = 0.36\\) and 0.90",
   "paper_text": "$\\log_{10}T=0.36$ and $0.90$",
   "paper_line": 3326,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "huginn-test",
   "section": "Beyond the one-token loop and model size",
   "claim": "Huginn test problems",
   "appears_as": "200 GSM8K test problems",
   "paper_text": "On 200 GSM8K test problems",
   "paper_line": 3638,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "damp-setup",
   "section": "Where the network damps",
   "claim": "models and temperatures of the stack resolution",
   "appears_as": "fourteen models at 24",
   "paper_text": "We measured this split along the unsteered loop of fourteen models at 24 temperatures each",
   "paper_line": 3439,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "damp-band",
   "section": "Where the network damps",
   "claim": "entropy band of the medians",
   "appears_as": "At 0.3 to 6 nats, the entropies where the loop's",
   "paper_text": "At 0.3 to 6 nats, the entropies where the loop's chaos occurs at low temperature",
   "paper_line": 3440,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "damp-qwen",
   "section": "Where the network damps",
   "claim": "Qwen2.5 median network factor by size",
   "appears_as": "In Qwen2.5 it falls from \\(-0.12\\) at 0.5B to \\(-1.99\\) at 72B, though not",
   "paper_text": "In Qwen2.5 it falls from $-0.12$ at 0.5B to $-1.99$ at 72B, though not monotonically ($-1.80$ at 3B, $-0.85$ at 7B)",
   "paper_line": 3443,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "damp-qwen-nonmono",
   "section": "Where the network damps",
   "claim": "Qwen2.5 non-monotone values",
   "appears_as": "monotonically (\\(-1.80\\) at 3B, \\(-0.85\\) at 7B)",
   "paper_text": "($-1.80$ at 3B, $-0.85$ at 7B)",
   "paper_line": 3443,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "damp-llama",
   "section": "Where the network damps",
   "claim": "Llama-3 median network factor by size",
   "appears_as": "In Llama-3 it falls from \\(-0.14\\) at 8B to \\(-1.50\\) and \\(-1.30\\) at 70B",
   "paper_text": "In Llama-3 it falls from $-0.14$ at 8B to $-1.50$ and $-1.30$ at 70B",
   "paper_line": 3445,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "damp-olmo",
   "section": "Where the network damps",
   "claim": "OLMo-2 median network factor by size",
   "appears_as": "In OLMo-2 it does not fall: \\(+0.11\\), \\(-0.52\\), \\(-0.79\\) and \\(-0.36\\) from 1B",
   "paper_text": "In OLMo-2 it does not fall: $+0.11$, $-0.52$, $-0.79$ and $-0.36$ from 1B to 32B",
   "paper_line": 3446,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "damp-72b-uniform",
   "section": "Where the network damps",
   "claim": "Qwen2.5-72B network factor at nearly uniform distributions",
   "appears_as": "uniform distributions: \\(-1.12\\) above 10 nats, against \\(+0.22\\) to \\(+2.97\\) for",
   "paper_text": "$-1.12$ above 10 nats, against $+0.22$ to $+2.97$ for the 1.5B to 32B models",
   "paper_line": 3449,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "damp-small",
   "section": "Where the network damps",
   "claim": "final relative change near 1 nat, small models",
   "appears_as": "\\(-0.32\\) (Qwen2.5-0.5B) and \\(-0.51\\) (Llama-3.1-8B)",
   "paper_text": "$-0.32$ (Qwen2.5-0.5B) and $-0.51$ (Llama-3.1-8B)",
   "paper_line": 3455,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "damp-large",
   "section": "Where the network damps",
   "claim": "final relative change near 1 nat, large models",
   "appears_as": "\\(-2.51\\) (Qwen2.5-72B) and \\(-2.08\\) (Llama-3.1-70B)",
   "paper_text": "$-2.51$ (Qwen2.5-72B) and $-2.08$ (Llama-3.1-70B)",
   "paper_line": 3456,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "damp-ko-max",
   "section": "Where the network damps",
   "claim": "largest rise from removing any single sublayer, at each model's knockout temperature nearest 1 nat",
   "appears_as": "0.44 nats in any of the fourteen models",
   "paper_text": "raises the network factor by at most 0.44 nats in any of the fourteen models",
   "paper_line": 3462,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "damp-ko-entropy",
   "section": "Where the network damps",
   "claim": "entropy range of the knockout temperatures nearest 1 nat",
   "appears_as": "knockout temperature nearest 1 nat (entropies 0.12",
   "paper_text": "at each model's knockout temperature nearest 1 nat (entropies 0.12 to 1.61 nats)",
   "paper_line": 3461,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "damp-ko-entropy-hi",
   "section": "Where the network damps",
   "claim": "entropy range of the knockout temperatures nearest 1 nat (upper end)",
   "appears_as": "to 1.61 nats), removing any single sublayer",
   "paper_text": "(entropies 0.12 to 1.61 nats), removing any",
   "paper_line": 3461,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "damp-ko-attn",
   "section": "Where the network damps",
   "claim": "first-attention amplification in Qwen2.5 1.5B to 32B",
   "appears_as": "lowers the factor by 1.67 to 3.74 nats near 1 nat",
   "paper_text": "removing it lowers the factor by 1.67 to 3.74 nats near 1 nat",
   "paper_line": 3465,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "damp-ko-mlp",
   "section": "Where the network damps",
   "claim": "first-MLP amplification in Qwen2.5-0.5B",
   "appears_as": "the first MLP does (2.40)",
   "paper_text": "In the 0.5B model, the first MLP does (2.40)",
   "paper_line": 3467,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "damp-ko-large",
   "section": "Where the network damps",
   "claim": "largest single-sublayer contribution at 70-72B",
   "appears_as": "  0.46.",
   "paper_text": "no sublayer contributes more than 0.46",
   "paper_line": 3468,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "damp-caption",
   "section": "Where the network damps",
   "claim": "twin offset and steps of the stack resolution",
   "appears_as": "relative offset \\(10^{-7}\\) along the evolving tangent; 500 transient and 500 measured steps",
   "paper_text": "a twin at relative offset $10^{-7}$ along the evolving tangent; 500 transient and 500 measured steps",
   "paper_line": 3478,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "moe-qwen",
   "section": "Mixtures of experts",
   "claim": "experts and active parameters of Qwen3.5-35B-A3B",
   "appears_as": "(8 of 256 experts per layer;",
   "paper_text": "(8 of 256 experts per layer; about 3B of its 35B parameters are active per token)",
   "paper_line": 3494,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "moe-olmoe",
   "section": "Mixtures of experts",
   "claim": "experts and active parameters of OLMoE-1B-7B",
   "appears_as": "OLMoE-1B-7B (8 of 64;",
   "paper_text": "(8 of 64; about 1B of 7B)",
   "paper_line": 3495,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "moe-twin",
   "section": "Mixtures of experts",
   "claim": "twin offset that never switched an expert",
   "appears_as": "about 1B of 7B). Along them, a twin at relative offset \\(10^{-7}\\) never chose",
   "paper_text": "a twin at relative offset $10^{-7}$ never chose different experts from the base orbit",
   "paper_line": 3495,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "moe-gaps",
   "section": "Mixtures of experts",
   "claim": "routing margins along the loops",
   "appears_as": "\\(1.1\\times10^{-4}\\) and \\(1.75\\times10^{-2}\\), and its minimum is about",
   "paper_text": "$1.1\\times10^{-4}$ and $1.75\\times10^{-2}$, and its minimum is about $3.38\\times10^{-7}$",
   "paper_line": 3499,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "moe-gap-min",
   "section": "Mixtures of experts",
   "claim": "smallest routing margin",
   "appears_as": "\\(3.38\\times10^{-7}\\). Rounding errors",
   "paper_text": "its minimum is about $3.38\\times10^{-7}$",
   "paper_line": 3499,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "moe-bf16",
   "section": "Mixtures of experts",
   "claim": "relative precision of bfloat16",
   "appears_as": "about \\(4\\times10^{-3}\\)) can cross gaps this small",
   "paper_text": "(relative precision about $4\\times10^{-3}$)",
   "paper_line": 3500,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "moe-irregular",
   "section": "Mixtures of experts",
   "claim": "irregular hostility cells of the mixture of experts",
   "appears_as": "irregular at 5% of the",
   "paper_text": "irregular at 5\\,\\% of the hostility cells",
   "paper_line": 3507,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "moe-damping",
   "section": "Mixtures of experts",
   "claim": "median network factors of the mixture of experts and comparison models",
   "appears_as": "Its median network factor between 0.3 and 6 nats is \\(-1.90\\),",
   "paper_text": "Its median network factor between 0.3 and 6 nats is $-1.90$, against $+0.05$ and $-1.41$ for the two dense models and $-1.73$ for the dense Qwen2.5-32B",
   "paper_line": 3507,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "moe-damping-b",
   "section": "Mixtures of experts",
   "claim": "dense comparison values",
   "appears_as": "against \\(+0.05\\) and \\(-1.41\\) for the two dense models and \\(-1.73\\) for the dense",
   "paper_text": "against $+0.05$ and $-1.41$ for the two dense models and $-1.73$ for the dense Qwen2.5-32B",
   "paper_line": 3507,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "moe-ko",
   "section": "Mixtures of experts",
   "claim": "first-attention knockouts in the three Qwen3.5 models",
   "appears_as": "1.33 (9B) and 0.76 nats (the mixture of experts)",
   "paper_text": "removing it lowers the network factor by 1.27 (4B), 1.33 (9B) and 0.76 nats (the mixture of experts)",
   "paper_line": 5451,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "moe-ko-temp",
   "section": "Mixtures of experts",
   "claim": "entropy at the knockout temperature",
   "appears_as": "the entropy is 2 to 4 nats, removing it lowers the network factor by 1.27 (4B),",
   "paper_text": "At the knockout temperature where the entropy is 2 to 4 nats",
   "paper_line": 5450,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "moe-olmoe-damping",
   "section": "Mixtures of experts",
   "claim": "OLMoE median network factor against dense OLMo-2",
   "appears_as": "mixture of experts, OLMoE-1B-7B, has a median network factor (\\(-0.36\\)) between",
   "paper_text": "Its median network factor between 0.3 and 6 nats ($-0.36$) lies between those of the dense OLMo-2-1B ($+0.11$) and OLMo-2-7B ($-0.52$)",
   "paper_line": 5459,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "moe-caption",
   "section": "Mixtures of experts",
   "claim": "sweep and map sizes of the mixture-of-experts comparison",
   "appears_as": "(128 temperatures, \\(\\log_{10}T \\in [-1, 0.3]\\)) and in 32 × 32 maps",
   "paper_text": "in the unsteered sweep (128 temperatures, $\\log_{10}T\\in[-1,0.3]$) and in $32\\times32$ maps steered along philosophy and hostility at the middle layer",
   "paper_line": 5468,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fc-formula",
   "section": "False chaos and real chaos",
   "claim": "noise model of the twin test",
   "appears_as": "\\lambda_{\\mathrm{meas}} \\approx \\max\\bigl\\{\\lambda,\\ \\log(\\sqrt{2}\\,\\sigma/\\varepsilon)\\bigr\\}",
   "paper_text": "\\lambda_{\\mathrm{meas}}\\approx\\max\\bigl\\{\\lambda,\\ \\log(\\sqrt2\\,\\sigma/\\varepsilon)\\bigr\\}",
   "paper_line": 4303,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fc-crossover",
   "section": "False chaos and real chaos",
   "claim": "offset above which the twin returns the true exponent",
   "appears_as": "\\(\\sqrt{2}\\,\\sigma e^{-\\lambda}\\)",
   "paper_text": "Above the offset $\\sqrt2\\,\\sigma e^{-\\lambda}$ the model gives the true exponent",
   "paper_line": 4306,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fc-steps",
   "section": "False chaos and real chaos",
   "claim": "transient and measured steps of the controlled test",
   "appears_as": "each with 400 transient and 800 measured steps",
   "paper_text": "each runs 400 transient and 800 measured steps",
   "paper_line": 4317,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fc-clean",
   "section": "False chaos and real chaos",
   "claim": "clean float64 exponents of the three cells over offsets 1e-12 to 1e-4",
   "appears_as": "\\(+0.092\\) to \\(+0.099\\), \\(-0.123\\) to \\(-0.128\\), and \\(-0.843\\) to",
   "paper_text": "$+0.092$ to $+0.099$, $-0.123$ to $-0.128$, and $-0.843$ to $-0.862$ for offsets from $10^{-12}$ to $10^{-4}$",
   "paper_line": 4318,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fc-noise-levels",
   "section": "False chaos and real chaos",
   "claim": "added noise levels",
   "appears_as": "\\(\\sigma = 10^{-10}\\), \\(10^{-8}\\) or \\(10^{-6}\\), added",
   "paper_text": "Gaussian noise with $\\sigma=10^{-10}$, $10^{-8}$ or $10^{-6}$",
   "paper_line": 4321,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fc-match-0006",
   "section": "False chaos and real chaos",
   "claim": "agreement of the formula where noise dominates",
   "appears_as": "which the formula matches within 0.006",
   "paper_text": "matches within 0.006: for example $4.951$ to $4.953$ against $\\log(100\\sqrt2)=4.952$ at $\\sigma=10^{-10}$ and $\\varepsilon=10^{-12}$",
   "paper_line": 4324,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fc-example",
   "section": "False chaos and real chaos",
   "claim": "example of a false exponent and its prediction",
   "appears_as": "4.951 to 4.953 against \\(\\log(100\\sqrt{2}) = 4.952\\)",
   "paper_text": "$4.951$ to $4.953$ against $\\log(100\\sqrt2)=4.952$",
   "paper_line": 4324,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fc-match-0047",
   "section": "False chaos and real chaos",
   "claim": "agreement well above the crossover",
   "appears_as": "0.047",
   "paper_text": "the prediction matches within 0.047",
   "paper_line": 4326,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fc-crossover-043",
   "section": "False chaos and real chaos",
   "claim": "excess over the prediction in the crossover",
   "appears_as": "to 0.43, because noise injected one step earlier",
   "paper_text": "by up to 0.43, because noise injected one step earlier has not yet contracted",
   "paper_line": 4328,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fc-chaotic-floor",
   "section": "False chaos and real chaos",
   "claim": "lowest chaotic estimate under noise",
   "appears_as": "Noise lowered no chaotic estimate below 0.087 (clean 0.092 to 0.099)",
   "paper_text": "Noise lowered no chaotic estimate below 0.087 (clean 0.092 to 0.099)",
   "paper_line": 4329,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fc-contract-0048",
   "section": "False chaos and real chaos",
   "claim": "largest lowering of the contracting estimates",
   "appears_as": "by at most 0.048",
   "paper_text": "It lowered the contracting estimates by at most 0.048",
   "paper_line": 4329,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fc-free-chaos",
   "section": "False chaos and real chaos",
   "claim": "free chaotic twin: saturation level and time",
   "appears_as": "near \\(10^{-1}\\) after about 240 steps",
   "paper_text": "saturates near $10^{-1}$ after about 240 steps",
   "paper_line": 4333,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fc-free-plateau",
   "section": "False chaos and real chaos",
   "claim": "free period-3 twin under noise: plateau and prediction",
   "appears_as": "\\(2\\times10^{-8}\\) (the model predicts",
   "paper_text": "jumps to a plateau at about $2\\times10^{-8}$ (the model predicts $3\\times10^{-8}$)",
   "paper_line": 4334,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fc-free-floor",
   "section": "False chaos and real chaos",
   "claim": "free period-3 twin in clean float64",
   "appears_as": "\\(10^{-14}\\), the rounding floor of the map",
   "paper_text": "in clean float64 it stays near $10^{-14}$, the rounding floor of the map",
   "paper_line": 4379,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fc-f32-positive",
   "section": "False chaos and real chaos",
   "claim": "false positive exponents under the float32 final normalization",
   "appears_as": "positive exponents, up to 2.03 for the period-3 loop",
   "paper_text": "both contracting orbits show positive exponents, up to 2.03 for the period-3 loop",
   "paper_line": 4339,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fc-f32-offsets",
   "section": "False chaos and real chaos",
   "claim": "offsets of the false positive exponents",
   "appears_as": "at offsets from \\(10^{-10}\\) to \\(10^{-8}\\), both",
   "paper_text": "At offsets from $10^{-10}$ to $10^{-8}$, both contracting orbits show positive exponents",
   "paper_line": 4339,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fc-f32-merged",
   "section": "False chaos and real chaos",
   "claim": "steps in which twin and base became identical",
   "appears_as": "identical in 454 to 771 of the 800 steps",
   "paper_text": "identical in 454 to 771 of the 800 steps",
   "paper_line": 4341,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fc-f32-large",
   "section": "False chaos and real chaos",
   "claim": "exponents from 1e-6 up under the float32 final normalization",
   "appears_as": "\\(-0.853\\) to \\(-0.783\\) (clean \\(-0.124\\) and \\(-0.848\\)), and the chaotic one",
   "paper_text": "From $10^{-6}$ up, the contracting orbits read $-0.177$ to $-0.123$ and $-0.853$ to $-0.783$ (clean $-0.124$ and $-0.848$)",
   "paper_line": 4343,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fc-f32-chaotic",
   "section": "False chaos and real chaos",
   "claim": "chaotic exponent of the changed map",
   "appears_as": "0.059 to 0.078 (clean 0.094)",
   "paper_text": "the chaotic one $0.059$ to $0.078$ (clean $0.094$)",
   "paper_line": 4344,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fc-map-change",
   "section": "False chaos and real chaos",
   "claim": "size of the map change from the float32 normalization",
   "appears_as": "\\(10^{-8}\\) at every step",
   "paper_text": "by about $10^{-8}$ at every step",
   "paper_line": 4346,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fc-72b",
   "section": "False chaos and real chaos",
   "claim": "offset dependence of the spurious 72B window",
   "appears_as": "near zero at \\(10^{-6}\\) and positive at",
   "paper_text": "Its exponent was negative at $10^{-5}$, near zero at $10^{-6}$ and positive at $10^{-7}$",
   "paper_line": 4348,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fc-cell-chaos",
   "section": "False chaos and real chaos",
   "claim": "chaotic cell of the test",
   "appears_as": "(\\(\\alpha = 0.0652\\), \\(\\log_{10}T = -0.156\\))",
   "paper_text": "A chaotic cell ($\\alpha=0.0652$, $\\log_{10}T=-0.156$)",
   "paper_line": 4371,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fc-cell-p3",
   "section": "False chaos and real chaos",
   "claim": "period-3 cell of the test",
   "appears_as": "(\\(\\alpha = 0.0642\\), \\(\\log_{10}T = -0.156\\); circles)",
   "paper_text": "($\\alpha=0.0642$, $\\log_{10}T=-0.156$; circles)",
   "paper_line": 4373,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fc-cell-strong",
   "section": "False chaos and real chaos",
   "claim": "strongly contracting cell of the test",
   "appears_as": "(\\(\\alpha = 0\\), \\(\\log_{10}T = 0.18\\); squares)",
   "paper_text": "($\\alpha=0$, $\\log_{10}T=0.18$; squares)",
   "paper_line": 4374,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "frontier-quant",
   "section": "Discussion",
   "claim": "one-step divergence and attractor changes under 8-bit quantization (frontier paragraph)",
   "appears_as": "next-token distributions by only 0.003 nats changes the attractor class or period",
   "paper_text": "distributions by only 0.003 nats changes the attractor class or period of one start in seven",
   "paper_line": 4069,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "horizon",
   "section": "Discussion",
   "claim": "steps for a 1e-6 perturbation to grow to order one; corrected after arxiv-v1 at paper 1b718635",
   "appears_as": "within roughly 12 to 50 steps",
   "paper_text": "within roughly 12 to 50 steps",
   "paper_line": 4729,
   "paper_file": "paper/llm/main.tex",
   "paper_commit": "1b71863581386048c50d41b1f8137a6ba6adec25"
  },
  {
   "id": "exp-range",
   "section": "Discussion",
   "claim": "largest unsteered exponents of the chaotic 7B to 14B models; corrected after arxiv-v1 at paper 1b718635",
   "appears_as": "0.30 to 1.14 per step",
   "paper_text": "0.30 to 1.14 per step",
   "paper_line": 4730,
   "paper_file": "paper/llm/main.tex",
   "paper_commit": "1b71863581386048c50d41b1f8137a6ba6adec25"
  },
  {
   "id": "published-st-claims-21",
   "section": "Claims table",
   "claim": "primary rate (claims table)",
   "appears_as": "21.1% of 256 new GSM8K answers change with the batch layout alone",
   "paper_text": "the answer changed for 21.1\\,\\% of the problems (54 of 256;",
   "paper_line": 1349,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "published-st-claims-replay",
   "section": "Claims table",
   "claim": "replay rate (claims table)",
   "appears_as": "Replay 5.9%",
   "paper_text": "fed-back tokens in both layouts: 5.9\\,\\%",
   "paper_line": 1357,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "published-st-claims-s16",
   "section": "Claims table",
   "claim": "16-step rate (claims table)",
   "appears_as": "16 soft steps 6.6%",
   "paper_text": "16 soft steps instead of 64: 6.6\\,\\%",
   "paper_line": 1359,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "published-st-claims-greedy",
   "section": "Claims table",
   "claim": "greedy chain-of-thought rate (claims table)",
   "appears_as": "greedy chain of thought 2.3%",
   "paper_text": "ordinary greedy chain-of-thought decoding: 2.3\\,\\%",
   "paper_line": 1361,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "published-st-claims-top1",
   "section": "Claims table",
   "claim": "top-1 feedback rate (claims table)",
   "appears_as": "top-1 feedback 17.6%",
   "paper_text": "feeding back only the most probable token: 17.6\\,\\%",
   "paper_line": 1363,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-claims-steps",
   "section": "Claims table",
   "claim": "steps of identical text in the claims table",
   "appears_as": "write the same tokens for 9 to 150 steps, then a different sequence",
   "paper_text": "writes the same text for 9 to 150 steps",
   "paper_line": 232,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ct-claims-periodic",
   "section": "Claims table",
   "claim": "periodic loops that separate under a batch-layout change (claims table)",
   "appears_as": "only 10 of 192 periodic loops separate",
   "paper_text": "& periodic & 10 / 192 &",
   "paper_line": 1253,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "cpu-gpu",
   "section": "Appendix A",
   "claim": "agreement of the first four flip parameters across processors",
   "appears_as": "agree to \\(4\\times10^{-15}\\)",
   "paper_text": "(CPU and H100, agreement $4\\times10^{-15}$)",
   "paper_line": 5880,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "search-maps",
   "section": "Appendix A",
   "claim": "distinct maps, cells and float64 maps in the initial census",
   "appears_as": "34 distinct maps (987,308 cells, 27 of them",
   "paper_text": "34 distinct maps (987\\,308 cells, 27 maps in float64)",
   "paper_line": 5778,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "search-reported",
   "section": "Appendix A",
   "claim": "maps reported",
   "appears_as": "29 of these maps",
   "paper_text": "Of these, 29 maps and the partial one appear here",
   "paper_line": 5779,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "search-families",
   "section": "Appendix A",
   "claim": "periodic families of at least six cells",
   "appears_as": "about 2600 periodic families",
   "paper_text": "about 2600 periodic families of at least six cells",
   "paper_line": 5782,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "search-windows",
   "section": "Appendix A",
   "claim": "windows given float64 work and their outcome",
   "appears_as": "About 26 windows or",
   "paper_text": "about 26 windows or families for float64 work: 20 are reported in detail, 2 only as map features and 4 not at all",
   "paper_line": 5782,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "search-newton",
   "section": "Appendix A",
   "claim": "Newton orbit attempts and failures",
   "appears_as": "Of 54 Newton orbit attempts, 7",
   "paper_text": "Of 54 Newton orbit attempts, 7 failed",
   "paper_line": 5785,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0000",
   "section": "Summary reasoning",
   "claim": "number 86 in 'Summary reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "reasoning models that solve 86 to 90% of grade-school",
   "paper_text": "reasoning models that answer 86 to 90\\,\\% of them correctly",
   "paper_line": 60,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0001",
   "section": "Summary reasoning",
   "claim": "number 90 in 'Summary reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "models that solve 86 to 90% of grade-school math problems",
   "paper_text": "reasoning models that answer 86 to 90\\,\\% of them correctly (DeepSeek-R1-Distill-Qwen-7B,",
   "paper_line": 60,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0002",
   "section": "Summary reasoning",
   "claim": "number 14.5 in 'Summary reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "grade-school math problems changed 14.5 and 19.5% of their answers",
   "paper_text": "DeepSeek-R1-Distill-Qwen-7B for 14.5\\,\\% of the problems ($[10.9,18.0]$)",
   "paper_line": 1410,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0003",
   "section": "Summary reasoning",
   "claim": "number 19.5 in 'Summary reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "problems changed 14.5 and 19.5% of their answers when",
   "paper_text": "(DeepSeek-R1-Distill-Qwen-7B, QwQ-32B) changed 14.5 and 19.5\\,\\%, the two layouts disagreeing on correctness for",
   "paper_line": 61,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0004",
   "section": "Summary reasoning",
   "claim": "number 14 in 'Summary reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "rounding alone changes about 14 and 18% of their answers,",
   "paper_text": "alone changes about 14 and 18\\,\\% of their answers, respectively.",
   "paper_line": 68,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0005",
   "section": "Summary reasoning",
   "claim": "number 18 in 'Summary reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "alone changes about 14 and 18% of their answers, respectively.",
   "paper_text": "alone changes about 14 and 18\\,\\% of their answers, respectively.",
   "paper_line": 68,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0006",
   "section": "Lead reasoning",
   "claim": "number 86 in 'Lead reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "solve 86 to 90% of grade-school",
   "paper_text": "reasoning models that answer 86 to 90\\,\\% of them correctly",
   "paper_line": 60,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0007",
   "section": "Lead reasoning",
   "claim": "number 90 in 'Lead reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "solve 86 to 90% of grade-school math problems",
   "paper_text": "reasoning models that answer 86 to 90\\,\\% of them correctly (DeepSeek-R1-Distill-Qwen-7B,",
   "paper_line": 60,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0008",
   "section": "Lead reasoning",
   "claim": "number 14.5 in 'Lead reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "grade-school math problems changed 14.5 and 19.5% of their",
   "paper_text": "(DeepSeek-R1-Distill-Qwen-7B, QwQ-32B) changed 14.5 and 19.5\\,\\%, the two layouts disagreeing on correctness",
   "paper_line": 61,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0009",
   "section": "Lead reasoning",
   "claim": "number 19.5 in 'Lead reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "problems changed 14.5 and 19.5% of their",
   "paper_text": "(DeepSeek-R1-Distill-Qwen-7B, QwQ-32B) changed 14.5 and 19.5\\,\\%, the two layouts disagreeing on correctness for",
   "paper_line": 61,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0010",
   "section": "Abstract reasoning",
   "claim": "number 86 in 'Abstract reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Reasoning models that answer 86 to 90% of these",
   "paper_text": "reasoning models that answer 86 to 90\\,\\% of them correctly",
   "paper_line": 60,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0011",
   "section": "Abstract reasoning",
   "claim": "number 90 in 'Abstract reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "models that answer 86 to 90% of these",
   "paper_text": "reasoning models that answer 86 to 90\\,\\% of them correctly (DeepSeek-R1-Distill-Qwen-7B,",
   "paper_line": 60,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0012",
   "section": "Abstract reasoning",
   "claim": "number 14.5 in 'Abstract reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(DeepSeek-R1-Distill-Qwen-7B and QwQ-32B) changed 14.5 and 19.5% of",
   "paper_text": "(DeepSeek-R1-Distill-Qwen-7B, QwQ-32B) changed 14.5 and 19.5\\,\\%, the two layouts disagreeing on correctness",
   "paper_line": 61,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0013",
   "section": "Abstract reasoning",
   "claim": "number 19.5 in 'Abstract reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "QwQ-32B) changed 14.5 and 19.5% of",
   "paper_text": "(DeepSeek-R1-Distill-Qwen-7B, QwQ-32B) changed 14.5 and 19.5\\,\\%, the two layouts disagreeing on correctness for",
   "paper_line": 61,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0014",
   "section": "Abstract reasoning",
   "claim": "correctness disagreement of the two layouts, smaller value, in 'Abstract reasoning'; range ends at their extremes, 11.7 and 14.5, since report f0a09f7f (paper 4e6e2ec6)",
   "appears_as": "for 11.7 and 14.5% of the problems;",
   "paper_text": "19.5\\,\\%, the two layouts disagreeing on correctness for 11.7 and 14.5\\,\\% of the problems.",
   "paper_line": 61,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0015",
   "section": "Abstract reasoning",
   "claim": "correctness disagreement of the two layouts, larger value, in 'Abstract reasoning'; range ends at their extremes, 11.7 and 14.5, since report f0a09f7f (paper 4e6e2ec6)",
   "appears_as": "for 11.7 and 14.5% of the problems; ordinary",
   "paper_text": "disagreeing on correctness for 11.7 and 14.5\\,\\% of the problems. Ordinary",
   "paper_line": 61,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0016",
   "section": "Abstract reasoning",
   "claim": "number 10^{-10} in 'Abstract reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of \\(10^{-10}\\) alone changes about 14",
   "paper_text": "a relative displacement of $10^{-10}$ alone changes about 14 and",
   "paper_line": 67,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0017",
   "section": "Abstract reasoning",
   "claim": "number 14 in 'Abstract reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(10^{-10}\\) alone changes about 14 and 18%",
   "paper_text": "alone changes about 14 and 18\\,\\% of their answers, respectively.",
   "paper_line": 68,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0018",
   "section": "Abstract reasoning",
   "claim": "number 18 in 'Abstract reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "alone changes about 14 and 18%",
   "paper_text": "alone changes about 14 and 18\\,\\% of their answers, respectively.",
   "paper_line": 68,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0019",
   "section": "Contributions reasoning2",
   "claim": "number 86 in 'Contributions reasoning2' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Reasoning models that answer 86 to 90% of these problems",
   "paper_text": "reasoning models that answer 86 to 90\\,\\% of the problems correctly",
   "paper_line": 231,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0020",
   "section": "Contributions reasoning2",
   "claim": "number 90 in 'Contributions reasoning2' (generated: post phrase matched to the paper's source text)",
   "appears_as": "models that answer 86 to 90% of these problems correctly",
   "paper_text": "reasoning models that answer 86 to 90\\,\\% of the problems correctly",
   "paper_line": 231,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0021",
   "section": "Contributions reasoning2",
   "claim": "number 14.5 in 'Contributions reasoning2' (generated: post phrase matched to the paper's source text)",
   "appears_as": "through soft thinking changed 14.5 and 19.5% of their answers",
   "paper_text": "(DeepSeek-R1-Distill-Qwen-7B and QwQ-32B), 14.5 and 19.5\\,\\% of the soft-thinking",
   "paper_line": 231,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0022",
   "section": "Contributions reasoning2",
   "claim": "number 19.5 in 'Contributions reasoning2' (generated: post phrase matched to the paper's source text)",
   "appears_as": "thinking changed 14.5 and 19.5% of their answers with",
   "paper_text": "(DeepSeek-R1-Distill-Qwen-7B and QwQ-32B), 14.5 and 19.5\\,\\% of the soft-thinking answers",
   "paper_line": 231,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0023",
   "section": "Contributions reasoning2",
   "claim": "correctness disagreement of the two layouts, smaller value, in 'Contributions reasoning2'; range ends at their extremes, 11.7 and 14.5, since report f0a09f7f (paper 4e6e2ec6)",
   "appears_as": "the two layouts disagreeing on correctness for 11.7 and 14.5% of the problems,",
   "paper_text": "19.5\\,\\%, the two layouts disagreeing on correctness for 11.7 and 14.5\\,\\% of the problems.",
   "paper_line": 61,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0024",
   "section": "Contributions reasoning2",
   "claim": "correctness disagreement of the two layouts, larger value, in 'Contributions reasoning2'; range ends at their extremes, 11.7 and 14.5, since report f0a09f7f (paper 4e6e2ec6)",
   "appears_as": "the two layouts disagreeing on correctness for 11.7 and 14.5% of the problems, and ordinary",
   "paper_text": "disagreeing on correctness for 11.7 and 14.5\\,\\% of the problems. Ordinary",
   "paper_line": 61,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0025",
   "section": "Contributions reasoning2",
   "claim": "number 10^{-10} in 'Contributions reasoning2' (generated: post phrase matched to the paper's source text)",
   "appears_as": "relative displacement of \\(10^{-10}\\) alone changes about 14",
   "paper_text": "a relative displacement of $10^{-10}$ alone changes about 14 and",
   "paper_line": 67,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0026",
   "section": "Contributions reasoning2",
   "claim": "number 14 in 'Contributions reasoning2' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(10^{-10}\\) alone changes about 14 and 18% of their",
   "paper_text": "alone changes about 14 and 18\\,\\% of their answers, respectively.",
   "paper_line": 68,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0027",
   "section": "Contributions reasoning2",
   "claim": "number 18 in 'Contributions reasoning2' (generated: post phrase matched to the paper's source text)",
   "appears_as": "alone changes about 14 and 18% of their",
   "paper_text": "alone changes about 14 and 18\\,\\% of their answers, respectively.",
   "paper_line": 68,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0028",
   "section": "Evidence reasoning",
   "claim": "number 14.5 in 'Evidence reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "([details](#reasoning-models)) | 14.5% (DeepSeek-R1-Distill-Qwen-7B)",
   "paper_text": "DeepSeek-R1-Distill-Qwen-7B for 14.5\\,\\% of the problems ($[10.9,18.0]$)",
   "paper_line": 1410,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0029",
   "section": "Evidence reasoning",
   "claim": "number 19.5 in 'Evidence reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(DeepSeek-R1-Distill-Qwen-7B) and 19.5% (QwQ-32B) of new GSM8K",
   "paper_text": "(DeepSeek-R1-Distill-Qwen-7B and QwQ-32B), 14.5 and 19.5\\,\\% of the soft-thinking answers",
   "paper_line": 231,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0030",
   "section": "Evidence reasoning",
   "claim": "number 88 in 'Evidence reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "batch layout alone, at 88 to 90% and 86 to 87% accuracy;",
   "paper_text": "problems ($[10.9,18.0]$) at 88 to 90\\,\\% accuracy, and QwQ-32B",
   "paper_line": 1411,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0031",
   "section": "Evidence reasoning",
   "claim": "number 90 in 'Evidence reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "layout alone, at 88 to 90% and 86 to 87% accuracy;",
   "paper_text": "reasoning models that answer 86 to 90\\,\\% of them correctly (DeepSeek-R1-Distill-Qwen-7B,",
   "paper_line": 60,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0032",
   "section": "Evidence reasoning",
   "claim": "number 86 in 'Evidence reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "alone, at 88 to 90% and 86 to 87% accuracy; correctness",
   "paper_text": "reasoning models that answer 86 to 90\\,\\% of them correctly",
   "paper_line": 60,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0033",
   "section": "Evidence reasoning",
   "claim": "number 87 in 'Evidence reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at 88 to 90% and 86 to 87% accuracy; correctness",
   "paper_text": "19.5\\,\\% ($[16.4,22.3]$) at 86 to 87\\,\\%, and DeepSeek-R1-Distill-Llama-8B",
   "paper_line": 1411,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0034",
   "section": "Evidence reasoning",
   "claim": "number 11.7 in 'Evidence reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "correctness changes for 11.7 and 14.5%; DeepSeek-R1-Distill-Llama-8B,",
   "paper_text": "The two layouts disagreed on correctness for 11.7, 14.5 and 18.0\\,\\% of the problems.",
   "paper_line": 1412,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0035",
   "section": "Evidence reasoning",
   "claim": "number 14.5 in 'Evidence reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "correctness changes for 11.7 and 14.5%; DeepSeek-R1-Distill-Llama-8B,",
   "paper_text": "DeepSeek-R1-Distill-Qwen-7B for 14.5\\,\\% of the problems ($[10.9,18.0]$)",
   "paper_line": 1410,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0036",
   "section": "Evidence reasoning",
   "claim": "number 28.9 in 'Evidence reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "a corrected tokenizer, 28.9% at 74 to 77% | Discrete",
   "paper_text": "DeepSeek-R1-Distill-Llama-8B for 28.9\\,\\% ($[23.4,34.4]$) at 74 to",
   "paper_line": 1412,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0037",
   "section": "Evidence reasoning",
   "claim": "number 74 in 'Evidence reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "corrected tokenizer, 28.9% at 74 to 77% | Discrete sampled",
   "paper_text": "28.9\\,\\% ($[23.4,34.4]$) at 74 to 77\\,\\%. The two layouts disagreed",
   "paper_line": 1412,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0038",
   "section": "Evidence reasoning",
   "claim": "number 77 in 'Evidence reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "tokenizer, 28.9% at 74 to 77% | Discrete sampled thinking",
   "paper_text": "28.9\\,\\% ($[23.4,34.4]$) at 74 to 77\\,\\%. The two layouts disagreed on correctness",
   "paper_line": 1412,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0039",
   "section": "Evidence reasoning",
   "claim": "number 10.2 in 'Evidence reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Discrete sampled thinking 10.2, 19.9 and 21.5% for the",
   "paper_text": "answers. On GSM8K the rates were 10.2, 19.9 and 21.5\\,\\% for the",
   "paper_line": 1414,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0040",
   "section": "Evidence reasoning",
   "claim": "number 19.9 in 'Evidence reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "sampled thinking 10.2, 19.9 and 21.5% for the three",
   "paper_text": "GSM8K the rates were 10.2, 19.9 and 21.5\\,\\% for the same three",
   "paper_line": 1414,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0041",
   "section": "Evidence reasoning",
   "claim": "number 21.5 in 'Evidence reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "thinking 10.2, 19.9 and 21.5% for the three models;",
   "paper_text": "the rates were 10.2, 19.9 and 21.5\\,\\% for the same three models.",
   "paper_line": 1414,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0042",
   "section": "Evidence reasoning",
   "claim": "number 7.4 in 'Evidence reasoning' (generated: post phrase matched to the paper's source text) (paper 318f8980)",
   "appears_as": "DeepSeek-R1-Distill-Llama-8B (+7.4 points, not corrected for the five combinations)",
   "paper_text": "Only in DeepSeek-R1-Distill-Llama-8B did soft thinking change more, by 7.4 points",
   "paper_line": 1415,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0043",
   "section": "Evidence reasoning",
   "claim": "number 11.7 in 'Evidence reasoning' (generated: post phrase matched to the paper's source text) (paper 318f8980)",
   "appears_as": "the five combinations); 11.7% on an A100 | Fixed before",
   "paper_text": "first model's soft rate was 11.7\\,\\% (difference 2.7 points,",
   "paper_line": 1421,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0044",
   "section": "Evidence reasoning",
   "claim": "number 13.5 in 'Evidence reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "float64 copies of QwQ-32B (13.5% of answers changed by",
   "paper_text": "displacement alone changed 13.5 and 18.4\\,\\% of the answers,",
   "paper_line": 1451,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0045",
   "section": "Evidence reasoning",
   "claim": "number 10^{-10} in 'Evidence reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "relative displacement of \\(10^{-10}\\)); thinking cap of 1536",
   "paper_text": "a relative displacement of $10^{-10}$ alone changes about 14 and",
   "paper_line": 67,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0046",
   "section": "Evidence reasoning",
   "claim": "number 1536 in 'Evidence reasoning' (generated: post phrase matched to the paper's source text) (paper 318f8980)",
   "appears_as": "\\(10^{-10}\\)); thinking cap of 1536 steps; nearly all changes",
   "paper_text": "its own within the original 1536 steps was reproduced exactly",
   "paper_line": 1440,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0047",
   "section": "Evidence reasoning",
   "claim": "number 4096 in 'Evidence reasoning' (generated: post phrase matched to the paper's source text)",
   "appears_as": "rerun with Cold Stop and a 4096-step budget still changed",
   "paper_text": "it, with a thinking budget of 4096 steps",
   "paper_line": 1435,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0048",
   "section": "Evidence reasoning",
   "claim": "number 8.6 in 'Evidence reasoning' (generated: post phrase matched to the paper's source text) (paper 318f8980)",
   "appears_as": "4096-step budget still changed 8.6 to 54.7% of answers, but",
   "paper_text": "still changed the answers: 8.6\\,\\% (soft) and 17.2\\,\\% (sampled)",
   "paper_line": 1437,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "abs2-0049",
   "section": "Evidence reasoning",
   "claim": "number 54.7 in 'Evidence reasoning' (generated: post phrase matched to the paper's source text) (paper 318f8980)",
   "appears_as": "budget still changed 8.6 to 54.7% of answers, but it also",
   "paper_text": "128 GSM8K problems, 50.0 and 54.7\\,\\% for it on MATH-500, and",
   "paper_line": 1438,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0000",
   "section": "Bridge to sampled decoding",
   "claim": "number 120 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "2-cycle `\" is it\"` last 120 and 63 steps at \\(\\varepsilon",
   "paper_text": "the 2-cycle ``is it'' last 120 and 63 steps at $\\eps=10^{-5}$",
   "paper_line": 5166,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0001",
   "section": "Bridge to sampled decoding",
   "claim": "number 63 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "`\" is it\"` last 120 and 63 steps at \\(\\varepsilon",
   "paper_text": "2-cycle ``is it'' last 120 and 63 steps at $\\eps=10^{-5}$ and",
   "paper_line": 5166,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0002",
   "section": "Bridge to sampled decoding",
   "claim": "number 10^{-5} in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "steps at \\(\\varepsilon = 10^{-5}\\) and",
   "paper_text": "last 120 and 63 steps at $\\eps=10^{-5}$ and $3\\times10^{-5}$. With",
   "paper_line": 5166,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0003",
   "section": "Bridge to sampled decoding",
   "claim": "number 3\\times10^{-5} in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "\\(3\\times10^{-5}\\). With \\(m = 64\\) they",
   "paper_text": "and $3\\times10^{-5}$. With $m=64$ they last on average",
   "paper_line": 5167,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0004",
   "section": "Bridge to sampled decoding",
   "claim": "number 64 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(3\\times10^{-5}\\). With \\(m = 64\\) they last on average 10.5 steps at the smallest",
   "paper_text": "last on average 10.5 steps with $m=64$ and 7.8 with $m=8$",
   "paper_line": 3254,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0005",
   "section": "Bridge to sampled decoding",
   "claim": "number 10.6 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "offset (10.3 to 10.7 over the three offsets), nearly independently of \\(\\varepsilon\\)",
   "paper_text": "(10.3 to 10.7 and 7.6 to 7.8 over the three offsets)",
   "paper_line": 3254,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0006",
   "section": "Bridge to sampled decoding",
   "claim": "number 57 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(57% of steps in the channel), and with \\(m = 8\\) on average 7.8 steps (7.6 to 7.8;",
   "paper_text": "(57\\% of steps in the channel)",
   "paper_line": 5167,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0007",
   "section": "Bridge to sampled decoding",
   "claim": "number 7.7 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
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   "section": "Bridge to sampled decoding",
   "claim": "number 16 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(K = 16\\)). Qwen2.5-0.5B, chaotic",
   "paper_text": "0.96 for $K=1$, 0.43 for $K=16$). Qwen2.5-0.5B, chaotic at",
   "paper_line": 5228,
   "paper_file": "paper/llm/main.tex"
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   "id": "bridge-0064",
   "section": "Bridge to sampled decoding",
   "claim": "number 16 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(K\\) | 1 | 2 | 4 | 8 | 16 |",
   "paper_text": "window: with a memory of 8 or 16 soft tokens Qwen2.5-7B is chaotic",
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   "paper_file": "paper/llm/main.tex"
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   "id": "bridge-0065",
   "section": "Bridge to sampled decoding",
   "claim": "number 0.96 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| Qwen2.5-7B | 8 (0.96) | 10 (1.08) | 13 (0.70)",
   "paper_text": "smaller exponents (largest 0.96 for $K=1$, 0.43 for $K=16$).",
   "paper_line": 5228,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "bridge-0066",
   "section": "Bridge to sampled decoding",
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   "appears_as": "Qwen2.5-7B | 8 (0.96) | 10 (1.08) | 13 (0.70) | 21",
   "paper_text": "past a relative distance of $10^{-2}$ after a median of 102",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "bridge-0067",
   "section": "Bridge to sampled decoding",
   "claim": "number 1.08 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Qwen2.5-7B | 8 (0.96) | 10 (1.08) | 13 (0.70) | 21 (0.58)",
   "paper_text": "Qwen2.5-7B & 8 (0.96) & 10 (1.08) & 13 (0.70) & 21 (0.58) &",
   "paper_line": 5237,
   "paper_file": "paper/llm/main.tex"
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   "id": "bridge-0068",
   "section": "Bridge to sampled decoding",
   "claim": "number 13 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "8 (0.96) | 10 (1.08) | 13 (0.70) | 21 (0.58) | 20",
   "paper_text": "parameters, OLMo-2 at 1B, 7B, 13B and 32B, Llama-3.1 at 8B and",
   "paper_line": 3280,
   "paper_file": "paper/llm/main.tex"
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   "section": "Bridge to sampled decoding",
   "claim": "number 0.70 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(0.96) | 10 (1.08) | 13 (0.70) | 21 (0.58) | 20 (0.43)",
   "paper_text": "8 (0.96) & 10 (1.08) & 13 (0.70) & 21 (0.58) & 20 (0.43) \\\\",
   "paper_line": 5237,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "bridge-0070",
   "section": "Bridge to sampled decoding",
   "claim": "number 21 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "10 (1.08) | 13 (0.70) | 21 (0.58) | 20 (0.43) |",
   "paper_text": "10 (1.08) & 13 (0.70) & 21 (0.58) & 20 (0.43)",
   "paper_line": 5237,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "bridge-0071",
   "section": "Bridge to sampled decoding",
   "claim": "number 0.58 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(1.08) | 13 (0.70) | 21 (0.58) | 20 (0.43) |",
   "paper_text": "10 (1.08) & 13 (0.70) & 21 (0.58) & 20 (0.43) \\\\ Qwen2.5-0.5B",
   "paper_line": 5237,
   "paper_file": "paper/llm/main.tex"
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   "id": "bridge-0072",
   "section": "Bridge to sampled decoding",
   "claim": "number 20 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "13 (0.70) | 21 (0.58) | 20 (0.43) |",
   "paper_text": "without steering (24 of 24 and 20 of 20 chaotic loops diverge,",
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   "paper_file": "paper/llm/main.tex"
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   "id": "bridge-0073",
   "section": "Bridge to sampled decoding",
   "claim": "number 0.43 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(0.70) | 21 (0.58) | 20 (0.43) |",
   "paper_text": "exponents (largest 0.96 for $K=1$, 0.43 for $K=16$). Qwen2.5-0.5B,",
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   "paper_file": "paper/llm/main.tex"
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   "id": "bridge-0074",
   "section": "Bridge to sampled decoding",
   "claim": "number 0.20 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| Qwen2.5-0.5B | 1 (0.20) | 1 (0.24) | 0 | 10 (0.31)",
   "paper_text": "(0.43) \\\\ Qwen2.5-0.5B & 1 (0.20) & 1 (0.24) & 0 & 10 (0.31)",
   "paper_line": 5237,
   "paper_file": "paper/llm/main.tex"
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   "id": "bridge-0075",
   "section": "Bridge to sampled decoding",
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   "appears_as": "Qwen2.5-0.5B | 1 (0.20) | 1 (0.24) | 0 | 10 (0.31) | 3 (0.23)",
   "paper_text": "Qwen2.5-0.5B & 1 (0.20) & 1 (0.24) & 0 & 10 (0.31) & 3 (0.23)",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Bridge to sampled decoding",
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   "appears_as": "(0.20) | 1 (0.24) | 0 | 10 (0.31) | 3 (0.23) |",
   "paper_text": "past a relative distance of $10^{-2}$ after a median of 102",
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   "paper_file": "paper/llm/main.tex"
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   "id": "bridge-0077",
   "section": "Bridge to sampled decoding",
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   "appears_as": "(0.20) | 1 (0.24) | 0 | 10 (0.31) | 3 (0.23) |",
   "paper_text": "(0.20) & 1 (0.24) & 0 & 10 (0.31) & 3 (0.23) \\\\ \\bottomrule",
   "paper_line": 5238,
   "paper_file": "paper/llm/main.tex"
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   "section": "Bridge to sampled decoding",
   "claim": "number 0.23 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(0.24) | 0 | 10 (0.31) | 3 (0.23) |",
   "paper_text": "(0.24) & 0 & 10 (0.31) & 3 (0.23) \\\\ \\bottomrule \\end{tabular}",
   "paper_line": 5238,
   "paper_file": "paper/llm/main.tex"
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   "id": "bridge-0079",
   "section": "Bridge to sampled decoding",
   "claim": "number 24 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "chaotic temperatures, of 24 between \\(\\log_{10}T =",
   "paper_text": "\\caption{Chaotic temperatures, of 24 between $\\log_{10}T=-0.3$ and",
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  {
   "id": "bridge-0080",
   "section": "Bridge to sampled decoding",
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   "appears_as": "between \\(\\log_{10}T = -0.3\\) and 0.6, when the loop",
   "paper_text": "temperatures, of 24 between $\\log_{10}T=-0.3$ and $0.6$, when the loop feeds",
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   "section": "Bridge to sampled decoding",
   "claim": "number 0.6 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = -0.3\\) and 0.6, when the loop feeds back",
   "paper_text": "between $\\log_{10}T=-0.3$ and $0.6$, when the loop feeds back",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Bridge to sampled decoding",
   "claim": "number 500 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "prompt, unsteered, float64, 500 transient and 1000 measured",
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   "paper_file": "paper/llm/main.tex"
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   "id": "bridge-0083",
   "section": "Bridge to sampled decoding",
   "claim": "number 1000 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "bridge-0084",
   "section": "Bridge to sampled decoding",
   "claim": "number 10^{-5} in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "1000 measured steps, twins at $10^{-5}$ and $10^{-7}$ (chaotic: both",
   "paper_line": 5242,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "bridge-0085",
   "section": "Bridge to sampled decoding",
   "claim": "number 10^{-7} in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "twins at \\(10^{-5}\\) and \\(10^{-7}\\) (chaotic: both positive",
   "paper_text": "steps, twins at $10^{-5}$ and $10^{-7}$ (chaotic: both positive and",
   "paper_line": 5243,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "bridge-0086",
   "section": "Bridge to sampled decoding",
   "claim": "number 64 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "positive and no period up to 64). Source: the report's memory-window",
   "paper_text": "positive and no period up to 64).} \\label{tab:window} \\end{table}",
   "paper_line": 5243,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "bridge-0087",
   "section": "Bridge to sampled decoding",
   "claim": "number 10^{-10} in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "twin trajectories by \\(10^{-10}\\), without renormalization;",
   "paper_text": "token of twin trajectories by $10^{-10}$, without renormalization;",
   "paper_line": 5249,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "bridge-0088",
   "section": "Bridge to sampled decoding",
   "claim": "number 0.77 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "one-token map's chaotic range: by 0.77 to 0.82 per step at $\\log_{10}T=0.17$",
   "paper_line": 5252,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "bridge-0089",
   "section": "Bridge to sampled decoding",
   "claim": "number 0.82 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "chaotic range: by 0.77 to 0.82 per step at \\(\\log_{10}T",
   "paper_text": "map's chaotic range: by 0.77 to 0.82 per step at $\\log_{10}T=0.17$",
   "paper_line": 5252,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0090",
   "section": "Bridge to sampled decoding",
   "claim": "number 0.17 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "step at \\(\\log_{10}T = 0.17\\) and",
   "paper_text": "0.82 per step at $\\log_{10}T=0.17$ and $0.21$, reaching $10^{-3}$",
   "paper_line": 5253,
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   "section": "Bridge to sampled decoding",
   "claim": "number 0.21 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.21, reaching \\(10^{-3}\\) within",
   "paper_text": "step at $\\log_{10}T=0.17$ and $0.21$, reaching $10^{-3}$ within",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "bridge-0092",
   "section": "Bridge to sampled decoding",
   "claim": "number 10^{-3} in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.21, reaching \\(10^{-3}\\) within 49 to 58 steps,",
   "paper_text": "$\\log_{10}T=0.17$ and $0.21$, reaching $10^{-3}$ within 49 to 58 steps, and",
   "paper_line": 5253,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "bridge-0093",
   "section": "Bridge to sampled decoding",
   "claim": "number 49 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "$0.21$, reaching $10^{-3}$ within 49 to 58 steps, and it reaches",
   "paper_line": 5253,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "bridge-0094",
   "section": "Bridge to sampled decoding",
   "claim": "number 58 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(10^{-3}\\) within 49 to 58 steps, and it reaches \\(10^{-3}\\)",
   "paper_text": "reaching $10^{-3}$ within 49 to 58 steps, and it reaches $10^{-3}$",
   "paper_line": 5253,
   "paper_file": "paper/llm/main.tex"
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   "id": "bridge-0095",
   "section": "Bridge to sampled decoding",
   "claim": "number 10^{-3} in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "steps, and it reaches \\(10^{-3}\\) within",
   "paper_text": "$\\log_{10}T=0.17$ and $0.21$, reaching $10^{-3}$ within 49 to 58 steps, and",
   "paper_line": 5253,
   "paper_file": "paper/llm/main.tex"
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   "section": "Bridge to sampled decoding",
   "claim": "number 400 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "it reaches $10^{-3}$ within 400 steps at nine other temperatures",
   "paper_line": 5253,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "bridge-0097",
   "section": "Bridge to sampled decoding",
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   "paper_line": 5254,
   "paper_file": "paper/llm/main.tex"
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   "section": "Bridge to sampled decoding",
   "claim": "number 0.40 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "temperatures between $-0.10$ and $0.40$, at 0.02 to 0.18 per step",
   "paper_line": 5254,
   "paper_file": "paper/llm/main.tex"
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   "section": "Bridge to sampled decoding",
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   "id": "bridge-0100",
   "section": "Bridge to sampled decoding",
   "claim": "number 0.18 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-0.10\\) and 0.40, at 0.02 to 0.18 per",
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  {
   "id": "bridge-0101",
   "section": "Bridge to sampled decoding",
   "claim": "number 0.8 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "$0.40$, at 0.02 to 0.18 per step (0.8 at $0.33$ for two of three",
   "paper_line": 5254,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "bridge-0102",
   "section": "Bridge to sampled decoding",
   "claim": "number 0.33 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "0.02 to 0.18 per step (0.8 at $0.33$ for two of three twins). It",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Bridge to sampled decoding",
   "claim": "number -0.14 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
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  {
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   "section": "Bridge to sampled decoding",
   "claim": "number 0.44 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Bridge to sampled decoding",
   "claim": "number 10^{-13} in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "($\\log_{10}T\\ge0.44$), where it stays between $10^{-13}$ and $10^{-7}$ for 400 steps.",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Bridge to sampled decoding",
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   "appears_as": "between \\(10^{-13}\\) and \\(10^{-7}\\) for 400",
   "paper_text": "stays between $10^{-13}$ and $10^{-7}$ for 400 steps. In Qwen2.5-0.5B",
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   "section": "Bridge to sampled decoding",
   "claim": "number 400 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "$10^{-13}$ and $10^{-7}$ for 400 steps. In Qwen2.5-0.5B the",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Bridge to sampled decoding",
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   "section": "Bridge to sampled decoding",
   "claim": "number 0.09 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
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   "paper_line": 5258,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "bridge-0112",
   "section": "Bridge to sampled decoding",
   "claim": "number 0.05 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "a late transient burst at $0.05$, and is absent from $0.13$",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Bridge to sampled decoding",
   "claim": "number 0.13 in 'Bridge to sampled decoding' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.05, and is absent from 0.13 up,",
   "paper_text": "$0.05$, and is absent from $0.13$ up, which includes its narrow",
   "paper_line": 5258,
   "paper_file": "paper/llm/main.tex"
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  },
  {
   "id": "bridge-0169",
   "section": "Two more systems",
   "claim": "number 0.196 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lambda_1 = 0.098\\), 0.437 and 0.196 per step over 3000",
   "paper_text": "$\\lambda_1=0.098$, 0.437 and 0.196 per step over 3000 steps, so",
   "paper_line": 3745,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0170",
   "section": "Two more systems",
   "claim": "number 3000 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and 0.196 per step over 3000",
   "paper_text": "0.437 and 0.196 per step over 3000 steps, so that $c^*=0.046$,",
   "paper_line": 3745,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0171",
   "section": "Two more systems",
   "claim": "number 0.046 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "steps, so that \\(c^* = 0.046\\), 0.177 and 0.089 (Figure",
   "paper_text": "over 3000 steps, so that $c^*=0.046$, 0.177 and 0.089 (Figure~\\ref{fig:sync};",
   "paper_line": 3745,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0172",
   "section": "Two more systems",
   "claim": "number 0.177 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "so that \\(c^* = 0.046\\), 0.177 and 0.089 (Figure",
   "paper_text": "steps, so that $c^*=0.046$, 0.177 and 0.089 (Figure~\\ref{fig:sync};",
   "paper_line": 3745,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0173",
   "section": "Two more systems",
   "claim": "number 0.089 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(c^* = 0.046\\), 0.177 and 0.089 (Figure",
   "paper_text": "that $c^*=0.046$, 0.177 and 0.089 (Figure~\\ref{fig:sync}",
   "paper_line": 3745,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0174",
   "section": "Two more systems",
   "claim": "number 0.30 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "rate, measured directly on the coupled map at seven couplings from 0 to 0.30 in",
   "paper_text": "measured directly on the coupled map at seven couplings from 0 to 0.30 in each cell, approximately follows",
   "paper_line": 3754,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0175",
   "section": "Two more systems",
   "claim": "number 0.44 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "each cell, approximately follows \\(\\lambda_1 + \\ln|1 - 2c|\\) from \\(+0.44\\) to",
   "paper_text": "approximately follows $\\lambda_1+\\ln|1-2c|$ from $+0.44$ to $-0.82$",
   "paper_line": 3755,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0176",
   "section": "Two more systems",
   "claim": "largest discrepancy of the measured transverse exponent from the prediction, 0.051 per step (paper fcf2d462)",
   "appears_as": "\\(-0.82\\): the largest discrepancy is 0.051 per step, up to four times the twins'",
   "paper_text": "the largest discrepancy is 0.051 per step, up to four times the twins' own standard errors",
   "paper_line": 3755,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0177",
   "section": "Two more systems",
   "claim": "number 0.051 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-0.82\\): the largest discrepancy is 0.051 per step, up to four times the twins'",
   "paper_text": "from $+0.44$ to $-0.82$: the largest discrepancy is 0.051 per step",
   "paper_line": 3755,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0178",
   "section": "Two more systems",
   "claim": "number 0.045 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "synchronized between \\(c = 0.045\\)",
   "paper_text": "synchronized between $c=0.045$ and 0.05 in 10,000-step runs, consistent with $c^*$",
   "paper_line": 3758,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0179",
   "section": "Two more systems",
   "claim": "number 0.05 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and 0.05, consistent with the predicted",
   "paper_text": "and 0.05 in 10,000-step runs, consistent with $c^*$",
   "paper_line": 3758,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0180",
   "section": "Two more systems",
   "claim": "number 0.18 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "copies synchronized between 0.18 and 0.19, when",
   "paper_text": "second they synchronized between 0.18 and 0.19 when ``synchronized''",
   "paper_line": 3758,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0181",
   "section": "Two more systems",
   "claim": "number 0.19 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "synchronized between 0.18 and 0.19, when",
   "paper_text": "synchronized between 0.18 and 0.19 when ``synchronized'' means",
   "paper_line": 3759,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0182",
   "section": "Two more systems",
   "claim": "number 10^{-6} in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "means a difference below \\(10^{-6}\\), consistent with \\(c^*\\);",
   "paper_text": "``synchronized'' means a difference below $10^{-6}$, consistent with $c^*$; on",
   "paper_line": 3759,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0183",
   "section": "Two more systems",
   "claim": "number 10^{-8} in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "stricter criterion of \\(10^{-8}\\) they had not synchronized",
   "paper_text": "the stricter criterion of $10^{-8}$ they had not synchronized",
   "paper_line": 3760,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0184",
   "section": "Two more systems",
   "claim": "number 0.19 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the stricter criterion of \\(10^{-8}\\) they had not synchronized by 0.19. Just below",
   "paper_text": "they had not synchronized by 0.19. Just below its predicted threshold",
   "paper_line": 3760,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0185",
   "section": "Two more systems",
   "claim": "number 0.16 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(c = 0.16\\) to 0.17, the difference",
   "paper_text": "Just below its predicted threshold, at $c=0.16$ to 0.17, the difference rose from below",
   "paper_line": 3760,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0186",
   "section": "Two more systems",
   "claim": "number 0.17 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(10^{-8}\\) to above \\(10^{-3}\\) 12 to 14 times in 10,000 steps",
   "paper_text": "the difference rose from below $10^{-8}$ to above $10^{-3}$ 12 to 14 times in 10,000 steps",
   "paper_line": 3761,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0187",
   "section": "Two more systems",
   "claim": "number 12 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(10^{-8}\\) to above \\(10^{-3}\\) 12 to 14 times in 10,000 steps",
   "paper_text": "the difference rose from below $10^{-8}$ to above $10^{-3}$ 12 to 14 times in 10,000 steps",
   "paper_line": 3761,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0188",
   "section": "Two more systems",
   "claim": "number 14 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(10^{-8}\\) to above \\(10^{-3}\\) 12 to 14 times in 10,000 steps",
   "paper_text": "the difference rose from below $10^{-8}$ to above $10^{-3}$ 12 to 14 times in 10,000 steps",
   "paper_line": 3761,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0189",
   "section": "Two more systems",
   "claim": "number 10,000 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(10^{-8}\\) to above \\(10^{-3}\\) 12 to 14 times in 10,000 steps",
   "paper_text": "the difference rose from below $10^{-8}$ to above $10^{-3}$ 12 to 14 times in 10,000 steps",
   "paper_line": 3761,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0190",
   "section": "Two more systems",
   "claim": "number -1.8 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "slopes lay between about \\(-1.8\\) and \\(-1.5\\), close to",
   "paper_text": "log-binned slopes lay between about $-1.8$ and $-1.5$, close to $-3/2$;",
   "paper_line": 3762,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0191",
   "section": "Two more systems",
   "claim": "number -1.5 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "between about \\(-1.8\\) and \\(-1.5\\), close to \\(-3/2\\).",
   "paper_text": "lay between about $-1.8$ and $-1.5$, close to $-3/2$; these descriptive",
   "paper_line": 3762,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0192",
   "section": "Two more systems",
   "claim": "third cell: synchronized between 0.15 and 0.16 (3000 steps) and between 0.12 and 0.15 (10,000 steps) on the 1e-8 criterion (paper fcf2d462)",
   "appears_as": "predicted 0.089: between 0.15 and 0.16 in 3000-step runs, and between 0.12 and 0.15",
   "paper_text": "between 0.15 and 0.16 in 3000-step runs and between 0.12 and 0.15 in 10,000-step runs on the $10^{-8}$ criterion",
   "paper_line": 3764,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0193",
   "section": "Two more systems",
   "claim": "third cell: synchronized between 0.15 and 0.16 (3000 steps) and between 0.12 and 0.15 (10,000 steps) on the 1e-8 criterion (paper fcf2d462)",
   "appears_as": "predicted 0.089: between 0.15 and 0.16 in 3000-step runs, and between 0.12 and 0.15",
   "paper_text": "between 0.15 and 0.16 in 3000-step runs and between 0.12 and 0.15 in 10,000-step runs on the $10^{-8}$ criterion",
   "paper_line": 3764,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0194",
   "section": "Two more systems",
   "claim": "number 0.089 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "predicted 0.089: between 0.15 and 0.16 in 3000-step runs, and between 0.12 and 0.15",
   "paper_text": "that $c^*=0.046$, 0.177 and 0.089 (Figure~\\ref{fig:sync}",
   "paper_line": 3745,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0195",
   "section": "Two more systems",
   "claim": "number 0.105 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(c = 0.105\\) to 0.115, where the difference",
   "paper_text": "At $c=0.105$ to 0.115, where the difference should shrink on average",
   "paper_line": 3765,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0196",
   "section": "Two more systems",
   "claim": "number 0.115 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(c = 0.105\\) to 0.115, where the difference should",
   "paper_text": "At $c=0.105$ to 0.115, where the difference should shrink on average",
   "paper_line": 3765,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0197",
   "section": "Two more systems",
   "claim": "number 10^{-14} in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "still burst from the rounding level (\\(10^{-14}\\)) to above \\(10^{-3}\\), 5 to 10",
   "paper_text": "burst from the rounding level ($10^{-14}$) to above $10^{-3}$, 5 to 10 times in 10,000 steps, consistent with attractor bubbling",
   "paper_line": 3766,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0198",
   "section": "Two more systems",
   "claim": "number 10 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "still burst from the rounding level (\\(10^{-14}\\)) to above \\(10^{-3}\\), 5 to 10",
   "paper_text": "burst from the rounding level ($10^{-14}$) to above $10^{-3}$, 5 to 10 times in 10,000 steps, consistent with attractor bubbling",
   "paper_line": 3766,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0199",
   "section": "Two more systems",
   "claim": "number 10,000 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "times in 10,000 steps, consistent with attractor bubbling.",
   "paper_text": "burst from the rounding level ($10^{-14}$) to above $10^{-3}$, 5 to 10 times in 10,000 steps, consistent with attractor bubbling",
   "paper_line": 3766,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0200",
   "section": "Two more systems",
   "claim": "rounding difference between two identical inputs in one batch, up to 9e-16 relative (paper fcf2d462)",
   "appears_as": "inputs in one batch give outputs that differ by up to \\(9\\times10^{-16}\\) relative.",
   "paper_text": "Two identical inputs in one batch give outputs that differ by up to $9\\times10^{-16}$ relative",
   "paper_line": 3768,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0201",
   "section": "Two more systems",
   "claim": "number 12 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "joint state (periods 6 to 12,",
   "paper_text": "the joint state (periods 6 to 12, verified to close within $2.2\\times10^{-13}$),",
   "paper_line": 3772,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0202",
   "section": "Two more systems",
   "claim": "number 2.2\\times10^{-13} in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "verified to close within \\(2.2\\times10^{-13}\\)), on which the two copies",
   "paper_text": "12, verified to close within $2.2\\times10^{-13}$), on which the two copies",
   "paper_line": 3772,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0203",
   "section": "Two more systems",
   "claim": "number 0.25 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "fixed map, and at \\(c = 0.25\\) they barely synchronized",
   "paper_text": "copies of a fixed map, and at $c=0.25$ they barely synchronized although",
   "paper_line": 3813,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0204",
   "section": "Two more systems",
   "claim": "number 0.25 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(c = 0.25\\) exceeds \\(c^*\\) for all",
   "paper_text": "barely synchronized although $c=0.25$ exceeds $c^*$ for all three",
   "paper_line": 3813,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0205",
   "section": "Two more systems",
   "claim": "number 12 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "philosophy direction, layer 12, float64). (a) Mean relative",
   "paper_text": "philosophy direction, layer 12, float64). (a) Mean relative",
   "paper_line": 3818,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0206",
   "section": "Two more systems",
   "claim": "number 0.165 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the second cell (\\(c = 0.165\\)): long synchronized stretches",
   "paper_text": "threshold of the second cell ($c=0.165$). (d) Bursts above the predicted",
   "paper_line": 3822,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0207",
   "section": "Two more systems",
   "claim": "number 0.115 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "in the third cell (\\(c = 0.115\\)), consistent with attractor bubbling.",
   "paper_text": "threshold in the third cell ($c=0.115$), as in attractor bubbling.}",
   "paper_line": 3823,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0208",
   "section": "Two more systems",
   "claim": "number 0.588 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "leading Jacobian pair is \\(0.588 \\pm 0.771i\\) (modulus 0.970).",
   "paper_text": "whose leading Jacobian pair is $0.588\\pm0.771i$ (modulus $0.970$).",
   "paper_line": 3561,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0209",
   "section": "Two more systems",
   "claim": "number 0.970 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(0.588 \\pm 0.771i\\) (modulus 0.970). The formula",
   "paper_text": "$0.588\\pm0.771i$ (modulus $0.970$)",
   "paper_line": 3562,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0210",
   "section": "Two more systems",
   "claim": "number 1.0775 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "circle at \\(\\lambda_c = 1.0775\\),",
   "paper_text": "$\\lambda_c=2(1-\\operatorname{Re}\\mu)/|1-\\mu|^2=1.0775$, transversally and away from",
   "paper_line": 3566,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0211",
   "section": "Two more systems",
   "claim": "rotation per step of the critical pair at Huginn's predicted crossing, consistent with a Neimark-Sacker bifurcation (paper 17353aec)",
   "appears_as": "the strong resonances (at 0.156 of a revolution per",
   "paper_text": "from the strong resonances (at 0.156 of a revolution per step), consistent with a Neimark--Sacker bifurcation",
   "paper_line": 3566,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0212",
   "section": "Two more systems",
   "claim": "number 1.0778 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "gives \\(\\lambda_c = 1.0778\\), with \\(A/\\sqrt{\\lambda",
   "paper_text": "amplitude gives $\\lambda_c=1.0778$, with $A/\\sqrt{\\lambda-\\lambda_c}=0.52$--$0.54$.",
   "paper_line": 3568,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0213",
   "section": "Two more systems",
   "claim": "number 0.52 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(A/\\sqrt{\\lambda - \\lambda_c} = 0.52\\) to 0.54. A",
   "paper_text": "$A/\\sqrt{\\lambda-\\lambda_c}=0.52$--$0.54$. A stable circle that",
   "paper_line": 3569,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0214",
   "section": "Two more systems",
   "claim": "number 0.54 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\lambda_c} = 0.52\\) to 0.54. A",
   "paper_text": "$A/\\sqrt{\\lambda-\\lambda_c}=0.52$--$0.54$. A stable circle that grows",
   "paper_line": 3569,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0215",
   "section": "Two more systems",
   "claim": "number 0.156 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "motion turns by 0.156 of a revolution per step,",
   "paper_text": "circle the motion turns by $0.156$ of a revolution per step,",
   "paper_line": 3573,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0216",
   "section": "Two more systems",
   "claim": "number 10^{-4} in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "changes smoothly, by about \\(10^{-4}\\) over",
   "paper_text": "changes smoothly, by about $10^{-4}$ over $\\lambda\\in[1.079,1.092]$,",
   "paper_line": 3574,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0217",
   "section": "Two more systems",
   "claim": "number 1.079 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lambda \\in [1.079, 1.092]\\), and no return",
   "paper_text": "$10^{-4}$ over $\\lambda\\in[1.079,1.092]$, and no return within",
   "paper_line": 3574,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0218",
   "section": "Two more systems",
   "claim": "number 1.092 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lambda \\in [1.079, 1.092]\\), and no return within",
   "paper_text": "$10^{-4}$ over $\\lambda\\in[1.079,1.092]$, and no return within 60",
   "paper_line": 3574,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0219",
   "section": "Two more systems",
   "claim": "number 60 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "1.092]\\), and no return within 60 steps was found at",
   "paper_text": "$\\lambda\\in[1.079,1.092]$, and no return within 60 steps was found at $10^{-3}$",
   "paper_line": 3574,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0220",
   "section": "Two more systems",
   "claim": "number 10^{-3} in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(10^{-3}\\) of the radius. This is",
   "paper_text": "within 60 steps was found at $10^{-3}$ of the radius. This is consistent",
   "paper_line": 3574,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0221",
   "section": "Two more systems",
   "claim": "number 1.094 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lambda \\approx 1.094\\) the circle deforms or",
   "paper_text": "excluded. From $\\lambda\\approx1.094$ the circle deforms or a second",
   "paper_line": 3576,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0222",
   "section": "Two more systems",
   "claim": "number 1.0814 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "fixed point (\\(\\lambda = 1.0814\\)).",
   "paper_text": "destabilizes the fixed point ($\\lambda=1.0814$). Fixed-point and Jacobian",
   "paper_line": 3577,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0223",
   "section": "Two more systems",
   "claim": "number 0.914 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "surround the origin, a real 0.914, complex pairs of modulus",
   "paper_text": "surround the origin, a real $0.914$, complex pairs of modulus",
   "paper_line": 3582,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0224",
   "section": "Two more systems",
   "claim": "number 0.85 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "complex pairs of modulus 0.85 to 0.89 at many",
   "paper_text": "$0.914$, complex pairs of modulus $0.85$--$0.89$ at many angles and",
   "paper_line": 3582,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0225",
   "section": "Two more systems",
   "claim": "number 0.89 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "pairs of modulus 0.85 to 0.89 at many",
   "paper_text": "complex pairs of modulus $0.85$--$0.89$ at many angles and negative",
   "paper_line": 3582,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0226",
   "section": "Two more systems",
   "claim": "number -0.8 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "negative real values near \\(-0.8\\), with no near-critical",
   "paper_text": "negative real values near $-0.8$, with no near-critical pair.",
   "paper_line": 3583,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0227",
   "section": "Two more systems",
   "claim": "number 1.03 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the best \\(\\lambda^* = 1.03\\) to 1.06 lowers the rate",
   "paper_text": "another, and the best $\\lambda^*=1.03$--$1.06$ lowers the rate from",
   "paper_line": 3588,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0228",
   "section": "Two more systems",
   "claim": "number 1.06 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lambda^* = 1.03\\) to 1.06 lowers the rate from 0.914",
   "paper_text": "the best $\\lambda^*=1.03$--$1.06$ lowers the rate from $0.914$",
   "paper_line": 3588,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0229",
   "section": "Two more systems",
   "claim": "number 0.914 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "1.06 lowers the rate from 0.914 to only 0.908 to",
   "paper_text": "$\\lambda^*=1.03$--$1.06$ lowers the rate from $0.914$ to only $0.908$--$0.911$.",
   "paper_line": 3588,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0230",
   "section": "Two more systems",
   "claim": "number 0.908 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "rate from 0.914 to only 0.908 to",
   "paper_text": "rate from $0.914$ to only $0.908$--$0.911$. (A finite computed",
   "paper_line": 3588,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0231",
   "section": "Two more systems",
   "claim": "number 0.911 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.911. (A finite computed spectrum",
   "paper_text": "from $0.914$ to only $0.908$--$0.911$. (A finite computed spectrum",
   "paper_line": 3588,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0232",
   "section": "Two more systems",
   "claim": "number 0.55 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "convergence (\\(\\lambda = 0.55\\): predicted 0.953, measured",
   "paper_text": "slows convergence ($\\lambda=0.55$: predicted $0.953$, measured",
   "paper_line": 3590,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0233",
   "section": "Two more systems",
   "claim": "number 0.953 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(\\(\\lambda = 0.55\\): predicted 0.953, measured",
   "paper_text": "($\\lambda=0.55$: predicted $0.953$, measured $0.951$ on one prompt).",
   "paper_line": 3590,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0234",
   "section": "Two more systems",
   "claim": "number 0.951 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.951 on one prompt). Third,",
   "paper_text": "predicted $0.953$, measured $0.951$ on one prompt). Third, over-relaxation",
   "paper_line": 3590,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0235",
   "section": "Two more systems",
   "claim": "number 1.074 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at \\(\\lambda_c = 1.074\\) to 1.126 (five prompts),",
   "paper_text": "$\\lambda_c=2\\operatorname{Re}(1-\\mu)/|1-\\mu|^2=1.074$--$1.126$ (five prompts), in",
   "paper_line": 3592,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0236",
   "section": "Two more systems",
   "claim": "number 1.126 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lambda_c = 1.074\\) to 1.126 (five prompts), in a flip",
   "paper_text": "$\\lambda_c=2\\operatorname{Re}(1-\\mu)/|1-\\mu|^2=1.074$--$1.126$ (five prompts), in a flip",
   "paper_line": 3592,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0237",
   "section": "Two more systems",
   "claim": "number 1.074 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lambda_c = 1.074\\), the measured rate at",
   "paper_text": "the prompt with $\\lambda_c=1.074$, the measured rate at $\\lambda=1.05$",
   "paper_line": 3593,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0238",
   "section": "Two more systems",
   "claim": "number 1.05 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "measured rate at \\(\\lambda = 1.05\\) is 0.955 against a",
   "paper_text": "the measured rate at $\\lambda=1.05$ is $0.955$ against a predicted",
   "paper_line": 3593,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0239",
   "section": "Two more systems",
   "claim": "number 0.955 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at \\(\\lambda = 1.05\\) is 0.955 against a",
   "paper_text": "rate at $\\lambda=1.05$ is $0.955$ against a predicted $0.956$",
   "paper_line": 3593,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0240",
   "section": "Two more systems",
   "claim": "number 0.956 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "predicted 0.956 (native 0.864). Independently,",
   "paper_text": "$0.955$ against a predicted $0.956$ (native $0.864$). Elsewhere",
   "paper_line": 3594,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0241",
   "section": "Two more systems",
   "claim": "number 0.864 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "predicted 0.956 (native 0.864). Independently, Wang et",
   "paper_text": "predicted $0.956$ (native $0.864$). Elsewhere the spectral radius",
   "paper_line": 3594,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0242",
   "section": "Two more systems",
   "claim": "number 19.41 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "from 19.41% to 8.34% at a constant",
   "paper_text": "report a Huginn GSM8K drop from $19.41\\,\\%$ to $8.34\\,\\%$ at a constant",
   "paper_line": 3596,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0243",
   "section": "Two more systems",
   "claim": "number 8.34 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "from 19.41% to 8.34% at a constant step of",
   "paper_text": "GSM8K drop from $19.41\\,\\%$ to $8.34\\,\\%$ at a constant step of",
   "paper_line": 3596,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0244",
   "section": "Two more systems",
   "claim": "number 1.2 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "8.34% at a constant step of 1.2, and at 0.8 a GSM8K score",
   "paper_text": "$8.34\\,\\%$ at a constant step of $1.2$; at $0.8$ GSM8K is $19.79\\,\\%$,",
   "paper_line": 3597,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0245",
   "section": "Two more systems",
   "claim": "number 0.8 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "constant step of 1.2, and at 0.8 a GSM8K score of 19.79%",
   "paper_text": "constant step of $1.2$; at $0.8$ GSM8K is $19.79\\,\\%$, while",
   "paper_line": 3597,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0246",
   "section": "Two more systems",
   "claim": "number 19.79 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at 0.8 a GSM8K score of 19.79%",
   "paper_text": "of $1.2$; at $0.8$ GSM8K is $19.79\\,\\%$, while their four-task",
   "paper_line": 3597,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0247",
   "section": "Two more systems",
   "claim": "number 0.002 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "convergence: rates agree to 0.002 to 0.006 where the slowest",
   "paper_text": "convergence. Rates agree to $0.002$--$0.006$ where the slowest",
   "paper_line": 3602,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0248",
   "section": "Two more systems",
   "claim": "number 0.006 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "rates agree to 0.002 to 0.006 where the slowest mode",
   "paper_text": "convergence. Rates agree to $0.002$--$0.006$ where the slowest mode dominates,",
   "paper_line": 3602,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0249",
   "section": "Two more systems",
   "claim": "number 1.075 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "question's \\(\\lambda_c\\) (1.075 to 1.149 for four questions)",
   "paper_text": "each question's $\\lambda_c$ ($1.075$--$1.149$ for four questions)",
   "paper_line": 3602,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0250",
   "section": "Two more systems",
   "claim": "number 1.149 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lambda_c\\) (1.075 to 1.149 for four questions) the",
   "paper_text": "question's $\\lambda_c$ ($1.075$--$1.149$ for four questions) the residual",
   "paper_line": 3602,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0251",
   "section": "Two more systems",
   "claim": "number 30 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "stops decaying. For 6 of 30 development questions the",
   "paper_text": "residual stops decaying. For 6 of 30 development questions the native",
   "paper_line": 3603,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0252",
   "section": "Two more systems",
   "claim": "number 1.009 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "itself unstable (\\(\\rho(1) = 1.009\\) to 1.273); the native",
   "paper_text": "is itself unstable ($\\rho(1)=1.009$--$1.273$; the fixed point,",
   "paper_line": 3604,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0253",
   "section": "Two more systems",
   "claim": "number 1.273 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(\\(\\rho(1) = 1.009\\) to 1.273); the native loop then",
   "paper_text": "unstable ($\\rho(1)=1.009$--$1.273$; the fixed point, located",
   "paper_line": 3604,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0254",
   "section": "Two more systems",
   "claim": "number 0.55 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "relaxation to 0.55 or 0.75 restores convergence",
   "paper_text": "of them), and relaxation to $0.55$ or $0.75$ restores convergence",
   "paper_line": 3606,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0255",
   "section": "Two more systems",
   "claim": "number 0.75 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "relaxation to 0.55 or 0.75 restores convergence to",
   "paper_text": "and relaxation to $0.55$ or $0.75$ restores convergence to $10^{-6}$.",
   "paper_line": 3606,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0256",
   "section": "Two more systems",
   "claim": "number 10^{-6} in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "restores convergence to \\(10^{-6}\\). An estimated spectral",
   "paper_text": "$0.75$ restores convergence to $10^{-6}$. For the other 24, no unstable",
   "paper_line": 3606,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0257",
   "section": "Two more systems",
   "claim": "number 0.73 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "with Spearman correlation 0.73 at \\(\\lambda = 1\\) and",
   "paper_text": "correlation with the residual is $0.73$ at $\\lambda=1$ and $0.75$",
   "paper_line": 3611,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0258",
   "section": "Two more systems",
   "claim": "number 0.75 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at \\(\\lambda = 1\\) and 0.75 at",
   "paper_text": "$0.73$ at $\\lambda=1$ and $0.75$ at $1.10$ over the 30 questions",
   "paper_line": 3611,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0259",
   "section": "Two more systems",
   "claim": "number 1.10 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "1.10 over the 30 questions.",
   "paper_text": "$\\lambda=1$ and $0.75$ at $1.10$ over the 30 questions (development",
   "paper_line": 3611,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0260",
   "section": "Two more systems",
   "claim": "number 30 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "1.10 over the 30 questions. Accuracy, however,",
   "paper_text": "and $0.75$ at $1.10$ over the 30 questions (development data).",
   "paper_line": 3611,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0261",
   "section": "Two more systems",
   "claim": "number 300 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "tolerates the instability (300",
   "paper_text": "tolerates the instability (300 training questions, 32 steps):",
   "paper_line": 3618,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0262",
   "section": "Two more systems",
   "claim": "number 32 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "training questions, 32 steps): it is 0.367 native,",
   "paper_text": "instability (300 training questions, 32 steps): it is $0.367$ native,",
   "paper_line": 3618,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0263",
   "section": "Two more systems",
   "claim": "number 0.367 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "questions, 32 steps): it is 0.367 native, 0.387 at \\(\\lambda",
   "paper_text": "questions, 32 steps): it is $0.367$ native, $0.387$ at $\\lambda=1.10$",
   "paper_line": 3618,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0264",
   "section": "Two more systems",
   "claim": "number 0.387 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "steps): it is 0.367 native, 0.387 at \\(\\lambda = 1.10\\) and",
   "paper_text": "steps): it is $0.367$ native, $0.387$ at $\\lambda=1.10$ and $0.373$",
   "paper_line": 3618,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0265",
   "section": "Two more systems",
   "claim": "number 1.10 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "native, 0.387 at \\(\\lambda = 1.10\\) and",
   "paper_text": "native, $0.387$ at $\\lambda=1.10$ and $0.373$ at $1.15$, where",
   "paper_line": 3618,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0266",
   "section": "Two more systems",
   "claim": "number 0.373 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.373 at 1.15, where the latent",
   "paper_text": "$0.387$ at $\\lambda=1.10$ and $0.373$ at $1.15$, where the latent",
   "paper_line": 3618,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0267",
   "section": "Two more systems",
   "claim": "number 1.15 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.373 at 1.15, where the latent state",
   "paper_text": "$\\lambda=1.10$ and $0.373$ at $1.15$, where the latent state oscillates",
   "paper_line": 3619,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0268",
   "section": "Two more systems",
   "claim": "number 0.08 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "oscillates with relative size 0.08 and 0.23.",
   "paper_text": "oscillates with relative size $0.08$ and $0.23$. Only at $1.25$",
   "paper_line": 3619,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0269",
   "section": "Two more systems",
   "claim": "number 0.23 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "relative size 0.08 and 0.23.",
   "paper_text": "with relative size $0.08$ and $0.23$. Only at $1.25$ (size $0.68$)",
   "paper_line": 3619,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0270",
   "section": "Two more systems",
   "claim": "number 1.25 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Only at 1.25 (size 0.68) does it fall,",
   "paper_text": "$0.08$ and $0.23$. Only at $1.25$ (size $0.68$) does it fall,",
   "paper_line": 3619,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0271",
   "section": "Two more systems",
   "claim": "number 0.68 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Only at 1.25 (size 0.68) does it fall, to 0.300.",
   "paper_text": "$0.23$. Only at $1.25$ (size $0.68$) does it fall, to $0.300$.",
   "paper_line": 3619,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0272",
   "section": "Two more systems",
   "claim": "number 0.300 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.68) does it fall, to 0.300. Yet the oscillation does",
   "paper_text": "(size $0.68$) does it fall, to $0.300$. Yet the oscillation does",
   "paper_line": 3620,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0273",
   "section": "Two more systems",
   "claim": "number 24 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "reading every step from 24 to 32 on 100 questions,",
   "paper_text": "answers. Reading every step from 24 to 32 on 100 questions, the",
   "paper_line": 3620,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0274",
   "section": "Two more systems",
   "claim": "number 32 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "reading every step from 24 to 32 on 100 questions, the chosen",
   "paper_text": "Reading every step from 24 to 32 on 100 questions, the margin",
   "paper_line": 3620,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0275",
   "section": "Two more systems",
   "claim": "number 100 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "every step from 24 to 32 on 100 questions, the chosen answer",
   "paper_text": "every step from 24 to 32 on 100 questions, the margin between",
   "paper_line": 3620,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0276",
   "section": "Two more systems",
   "claim": "number 12 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "within these nine steps for 12%, 16% and 33% of the questions",
   "paper_text": "within these nine steps for 12\\,\\%, 16\\,\\% and 33\\,\\% of the",
   "paper_line": 3622,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0277",
   "section": "Two more systems",
   "claim": "number 16 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "these nine steps for 12%, 16% and 33% of the questions",
   "paper_text": "these nine steps for 12\\,\\%, 16\\,\\% and 33\\,\\% of the questions.",
   "paper_line": 3622,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0278",
   "section": "Two more systems",
   "claim": "number 33 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "steps for 12%, 16% and 33% of the questions natively,",
   "paper_text": "steps for 12\\,\\%, 16\\,\\% and 33\\,\\% of the questions. The changes",
   "paper_line": 3623,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0279",
   "section": "Two more systems",
   "claim": "number 1.10 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "questions natively, at 1.10 and at",
   "paper_text": "native, $0.387$ at $\\lambda=1.10$ and $0.373$ at $1.15$, where",
   "paper_line": 3618,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0280",
   "section": "Two more systems",
   "claim": "number 1.15 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "1.15, in both directions, so",
   "paper_text": "$0.37$ at $1.10$ and $0.95$ at $1.15$, in alternating directions,",
   "paper_line": 3622,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0281",
   "section": "Two more systems",
   "claim": "number 16 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "costs 4 to 5 points at 8 to 16 steps and catches up by",
   "paper_text": "instead costs 4--5 points at 8--16 steps and catches up by 32",
   "paper_line": 3624,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0282",
   "section": "Two more systems",
   "claim": "number 32 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "steps and catches up by 32,",
   "paper_text": "8--16 steps and catches up by 32 (a slower transient), and Anderson",
   "paper_line": 3624,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0283",
   "section": "Two more systems",
   "claim": "number 32 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "greedy decoding and 32 recurrence steps per token",
   "paper_text": "format, greedy decoding and 32 recurrence steps per token",
   "paper_line": 3628,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0284",
   "section": "Two more systems",
   "claim": "number 119 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(development problems 0 to 119),",
   "paper_text": "token (development problems 0--119, every arm on the same problems",
   "paper_line": 3629,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0285",
   "section": "Two more systems",
   "claim": "number 0.375 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "accuracy is 0.375 natively, 0.425 at \\(\\lambda",
   "paper_text": "initial states), accuracy is $0.375$ natively, $0.425$ at $\\lambda=1.05$",
   "paper_line": 3629,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0286",
   "section": "Two more systems",
   "claim": "number 0.425 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "accuracy is 0.375 natively, 0.425 at \\(\\lambda = 1.05\\) and",
   "paper_text": "accuracy is $0.375$ natively, $0.425$ at $\\lambda=1.05$ and at $1.10$,",
   "paper_line": 3630,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0287",
   "section": "Two more systems",
   "claim": "number 1.05 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "natively, 0.425 at \\(\\lambda = 1.05\\) and at 1.10, 0.29 at",
   "paper_text": "natively, $0.425$ at $\\lambda=1.05$ and at $1.10$, $0.29$ at $1.15$",
   "paper_line": 3630,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0288",
   "section": "Two more systems",
   "claim": "number 1.10 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lambda = 1.05\\) and at 1.10, 0.29 at 1.15 (17",
   "paper_text": "$0.425$ at $\\lambda=1.05$ and at $1.10$, $0.29$ at $1.15$ (17 problems",
   "paper_line": 3630,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0289",
   "section": "Two more systems",
   "claim": "number 0.29 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lambda = 1.05\\) and at 1.10, 0.29 at 1.15 (17",
   "paper_text": "$\\lambda=1.05$ and at $1.10$, $0.29$ at $1.15$ (17 problems lost",
   "paper_line": 3630,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0290",
   "section": "Two more systems",
   "claim": "number 1.15 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "1.05\\) and at 1.10, 0.29 at 1.15 (17",
   "paper_text": "$\\lambda=1.05$ and at $1.10$, $0.29$ at $1.15$ (17 problems lost and 7 gained,",
   "paper_line": 3630,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0291",
   "section": "Two more systems",
   "claim": "number 17 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at 1.10, 0.29 at 1.15 (17",
   "paper_text": "at $1.10$, $0.29$ at $1.15$ (17 problems lost and 7 gained,",
   "paper_line": 3630,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0292",
   "section": "Two more systems",
   "claim": "number 0.03 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "one-sided McNemar \\(p = 0.03\\)) and 0.16 at 1.20 (29",
   "paper_text": "gained, one-sided McNemar $p=0.03$) and $0.16$ at $1.20$ (29",
   "paper_line": 3631,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0293",
   "section": "Two more systems",
   "claim": "number 0.16 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "McNemar \\(p = 0.03\\)) and 0.16 at 1.20 (29 lost,",
   "paper_text": "one-sided McNemar $p=0.03$) and $0.16$ at $1.20$ (29 lost, 3 gained,",
   "paper_line": 3631,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0294",
   "section": "Two more systems",
   "claim": "number 1.20 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(p = 0.03\\)) and 0.16 at 1.20 (29 lost,",
   "paper_text": "McNemar $p=0.03$) and $0.16$ at $1.20$ (29 lost, 3 gained, $p=10^{-6}$).",
   "paper_line": 3631,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0295",
   "section": "Two more systems",
   "claim": "number 29 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.03\\)) and 0.16 at 1.20 (29 lost,",
   "paper_text": "$p=0.03$) and $0.16$ at $1.20$ (29 lost, 3 gained, $p=10^{-6}$).",
   "paper_line": 3631,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0296",
   "section": "Two more systems",
   "claim": "number 10^{-6} in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "3 gained, \\(p = 10^{-6}\\)). Under-relaxation to",
   "paper_text": "$1.20$ (29 lost, 3 gained, $p=10^{-6}$). Under-relaxation to $0.8$",
   "paper_line": 3631,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0297",
   "section": "Two more systems",
   "claim": "number 0.8 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "10^{-6}\\)). Under-relaxation to 0.8 costs nothing at 32 steps",
   "paper_text": "$p=10^{-6}$). Under-relaxation to $0.8$ costs nothing at 32 steps",
   "paper_line": 3631,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0298",
   "section": "Two more systems",
   "claim": "number 32 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "to 0.8 costs nothing at 32 steps (0.41).",
   "paper_text": "Under-relaxation to $0.8$ costs nothing at 32 steps ($0.41$). The break lies",
   "paper_line": 3631,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0299",
   "section": "Two more systems",
   "claim": "number 0.41 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "costs nothing at 32 steps (0.41).",
   "paper_text": "costs nothing at 32 steps ($0.41$). The break lies between $1.10$",
   "paper_line": 3632,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0300",
   "section": "Two more systems",
   "claim": "number 1.10 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "The break lies between 1.10 and 1.15, at or just above",
   "paper_text": "($0.41$). The break lies between $1.10$ and $1.15$, at or just above",
   "paper_line": 3632,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0301",
   "section": "Two more systems",
   "claim": "number 1.15 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "break lies between 1.10 and 1.15, at or just above the spectral",
   "paper_text": "break lies between $1.10$ and $1.15$, at or just above the spectral",
   "paper_line": 3632,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0302",
   "section": "Two more systems",
   "claim": "number 200 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "independent review. On 200 GSM8K test problems,",
   "paper_text": "rounds of independent review. On 200 GSM8K test problems, accuracy",
   "paper_line": 3638,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0303",
   "section": "Two more systems",
   "claim": "number 0.330 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "accuracy is 0.330 natively, 0.395 at \\(\\lambda",
   "paper_text": "test problems, accuracy is $0.330$ natively, $0.395$ at $\\lambda=1.05$,",
   "paper_line": 3638,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0304",
   "section": "Two more systems",
   "claim": "number 0.395 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "accuracy is 0.330 natively, 0.395 at \\(\\lambda = 1.05\\),",
   "paper_text": "accuracy is $0.330$ natively, $0.395$ at $\\lambda=1.05$, $0.255$",
   "paper_line": 3638,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0305",
   "section": "Two more systems",
   "claim": "number 1.05 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "natively, 0.395 at \\(\\lambda = 1.05\\), 0.255 at 1.15 and 0.095",
   "paper_text": "natively, $0.425$ at $\\lambda=1.05$ and at $1.10$, $0.29$ at $1.15$",
   "paper_line": 3630,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0306",
   "section": "Two more systems",
   "claim": "number 0.255 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at \\(\\lambda = 1.05\\), 0.255 at 1.15 and 0.095 at",
   "paper_text": "$0.395$ at $\\lambda=1.05$, $0.255$ at $1.15$ and $0.095$ at $1.20$.",
   "paper_line": 3638,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0307",
   "section": "Two more systems",
   "claim": "number 1.15 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lambda = 1.05\\), 0.255 at 1.15 and 0.095 at",
   "paper_text": "$\\lambda=1.05$, $0.255$ at $1.15$ and $0.095$ at $1.20$. The",
   "paper_line": 3639,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0308",
   "section": "Two more systems",
   "claim": "number 0.095 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "1.05\\), 0.255 at 1.15 and 0.095 at",
   "paper_text": "$\\lambda=1.05$, $0.255$ at $1.15$ and $0.095$ at $1.20$. The two pre-stated",
   "paper_line": 3639,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0309",
   "section": "Two more systems",
   "claim": "number 1.20 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "1.20. Both stated predictions",
   "paper_text": "$0.255$ at $1.15$ and $0.095$ at $1.20$. The two pre-stated predictions",
   "paper_line": 3639,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0310",
   "section": "Two more systems",
   "claim": "number 1.20 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "pass: accuracy declines at 1.20 (\\(-23.5\\) points; 50",
   "paper_text": "pass: accuracy declines at $1.20$ ($-23.5$ points; 50 problems",
   "paper_line": 3639,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0311",
   "section": "Two more systems",
   "claim": "number -23.5 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "accuracy declines at 1.20 (\\(-23.5\\) points; 50",
   "paper_text": "accuracy declines at $1.20$ ($-23.5$ points; 50 problems lost and",
   "paper_line": 3639,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0312",
   "section": "Two more systems",
   "claim": "number 50 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "1.20 (\\(-23.5\\) points; 50",
   "paper_text": "at $1.20$ ($-23.5$ points; 50 problems lost and 3 gained,",
   "paper_line": 3639,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0313",
   "section": "Two more systems",
   "claim": "number 3\\times10^{-12} in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "one-sided McNemar \\(p = 3\\times10^{-12}\\)), and 1.05",
   "paper_text": "exact one-sided McNemar $p=3\\times10^{-12}$), and $1.05$ loses no more",
   "paper_line": 3640,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0314",
   "section": "Two more systems",
   "claim": "number 1.05 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "3\\times10^{-12}\\)), and 1.05",
   "paper_text": "$p=3\\times10^{-12}$), and $1.05$ loses no more than four points",
   "paper_line": 3640,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0315",
   "section": "Two more systems",
   "claim": "number 6.5 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "four points (difference \\(+6.5\\), one-sided 95% lower",
   "paper_text": "than four points (difference $+6.5$, one-sided 95\\,\\% lower bound",
   "paper_line": 3640,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0316",
   "section": "Two more systems",
   "claim": "number 95 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(difference \\(+6.5\\), one-sided 95% lower bound",
   "paper_text": "(difference $+6.5$, one-sided 95\\,\\% lower bound $+2.5$). At",
   "paper_line": 3641,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0317",
   "section": "Two more systems",
   "claim": "number 2.5 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(+2.5\\)). At 1.15 accuracy falls",
   "paper_text": "one-sided 95\\,\\% lower bound $+2.5$). At $1.15$ accuracy falls",
   "paper_line": 3641,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0318",
   "section": "Two more systems",
   "claim": "number 1.15 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(+2.5\\)). At 1.15 accuracy falls by 7.5 points",
   "paper_text": "95\\,\\% lower bound $+2.5$). At $1.15$ accuracy falls by $7.5$ points",
   "paper_line": 3641,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0319",
   "section": "Two more systems",
   "claim": "number 7.5 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "1.15 accuracy falls by 7.5 points (\\(p = 0.01\\), reported",
   "paper_text": "At $1.15$ accuracy falls by $7.5$ points ($p=0.01$, reported",
   "paper_line": 3641,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0320",
   "section": "Two more systems",
   "claim": "number 0.01 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "falls by 7.5 points (\\(p = 0.01\\), reported",
   "paper_text": "accuracy falls by $7.5$ points ($p=0.01$, reported descriptively).",
   "paper_line": 3641,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0321",
   "section": "Two more systems",
   "claim": "number 64 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "item-level prediction on 64",
   "paper_text": "the item-level prediction on 64 held-out ARC-Challenge questions.",
   "paper_line": 3653,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0322",
   "section": "Two more systems",
   "claim": "number 0.701 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "entering the 32nd update, is 0.701 (95% bootstrap interval",
   "paper_text": "entering the 32nd update, is $0.701$ (95\\,\\% bootstrap interval",
   "paper_line": 3659,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0323",
   "section": "Two more systems",
   "claim": "number 95 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "32nd update, is 0.701 (95% bootstrap interval",
   "paper_text": "the 32nd update, is $0.701$ (95\\,\\% bootstrap interval $[0.575,0.780]$;",
   "paper_line": 3659,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0324",
   "section": "Two more systems",
   "claim": "number 0.575 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "[0.575, 0.780]; 0.68, 0.73, 0.73",
   "paper_text": "(95\\,\\% bootstrap interval $[0.575,0.780]$; $0.68$, $0.73$, $0.73$",
   "paper_line": 3660,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0325",
   "section": "Two more systems",
   "claim": "number 0.780 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "[0.575, 0.780]; 0.68, 0.73, 0.73 and",
   "paper_text": "bootstrap interval $[0.575,0.780]$; $0.68$, $0.73$, $0.73$ and",
   "paper_line": 3660,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0326",
   "section": "Two more systems",
   "claim": "number 0.68 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "[0.575, 0.780]; 0.68, 0.73, 0.73 and 0.67 at",
   "paper_text": "interval $[0.575,0.780]$; $0.68$, $0.73$, $0.73$ and $0.67$",
   "paper_line": 3660,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0327",
   "section": "Two more systems",
   "claim": "number 0.73 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "[0.575, 0.780]; 0.68, 0.73, 0.73 and 0.67 at \\(\\lambda",
   "paper_text": "correlation with the residual is $0.73$ at $\\lambda=1$ and $0.75$",
   "paper_line": 3611,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bridge-0328",
   "section": "Two more systems",
   "claim": "number 0.73 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
   "appears_as": "[0.575, 0.780]; 0.68, 0.73, 0.73 and 0.67 at \\(\\lambda =",
   "paper_text": "correlation with the residual is $0.73$ at $\\lambda=1$ and $0.75$",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Two more systems",
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   "section": "Two more systems",
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   "section": "Two more systems",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Two more systems",
   "claim": "number 0.3 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Two more systems",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Two more systems",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Two more systems",
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   "paper_line": 3664,
   "paper_file": "paper/llm/main.tex"
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   "section": "Two more systems",
   "claim": "number 1.05 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
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   "section": "Two more systems",
   "claim": "number 1.08 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Two more systems",
   "claim": "number 1.10 in 'Two more systems' (generated: post phrase matched to the paper's source text)",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Two more systems",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Two more systems",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Two more systems",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Two more systems",
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   "section": "Two more systems",
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   "paper_text": "loop with paired-bootstrap 95\\,\\% intervals.} \\label{fig:huginn-gsm8k}",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Coupled agents",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Coupled agents",
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   "paper_file": "paper/llm/main.tex"
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   "paper_file": "paper/llm/main.tex"
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   "paper_file": "paper/llm/main.tex"
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   "section": "Coupled agents",
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   "section": "Coupled agents",
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   "section": "Coupled agents",
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   "paper_line": 4665,
   "paper_file": "paper/llm/main.tex"
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   "paper_file": "paper/llm/main.tex"
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   "section": "Coupled agents",
   "claim": "number 41.0 in 'Coupled agents' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "96\\,\\% of answers, including 41.0\\,\\% of pairs that gave the",
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   "section": "Coupled agents",
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   "section": "Coupled agents",
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   "section": "Coupled agents",
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   "section": "Dependence builds up",
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   "section": "Dependence builds up",
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   "section": "Dependence builds up",
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   "section": "Dependence builds up",
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   "id": "dep-0004",
   "section": "Dependence builds up",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Dependence builds up",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Dependence builds up",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Dependence builds up",
   "claim": "number 90 in 'Dependence builds up' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "$0.05$). The two layouts agree on 90 to 96\\,\\% of the answers after",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Dependence builds up",
   "claim": "number 96 in 'Dependence builds up' (generated: post phrase matched to the paper's source text)",
   "appears_as": "layouts agree on 90 to 96% of the answers after 2",
   "paper_text": "two layouts agree on 90 to 96\\,\\% of the answers after 2",
   "paper_line": 1379,
   "paper_file": "paper/llm/main.tex"
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   "id": "dep-0009",
   "section": "Dependence builds up",
   "claim": "number 51 in 'Dependence builds up' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "answers after 2 steps and on 51 to 70\\,\\% after 128, in every",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "dep-0010",
   "section": "Dependence builds up",
   "claim": "number 70 in 'Dependence builds up' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "after 2 steps and on 51 to 70\\,\\% after 128, in every configuration.",
   "paper_line": 1380,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "dep-0011",
   "section": "Dependence builds up",
   "claim": "number 128 in 'Dependence builds up' (generated: post phrase matched to the paper's source text)",
   "appears_as": "to 70% after 128, in every configuration.",
   "paper_text": "steps and on 51 to 70\\,\\% after 128, in every configuration. Among",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "dep-0012",
   "section": "Dependence builds up",
   "claim": "number 10^{-10} in 'Dependence builds up' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(10^{-10}\\) apart, separate the two.",
   "paper_text": "same configurations, started $10^{-10}$ apart, separate the two sources",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "dep-0013",
   "section": "Dependence builds up",
   "claim": "number 0.02 in 'Dependence builds up' (generated: post phrase matched to the paper's source text)",
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   "paper_line": 1384,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "dep-0014",
   "section": "Dependence builds up",
   "claim": "number 1.5 in 'Dependence builds up' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "text of at most 1.5% of the problems. The answers are barely sensitive to these",
   "paper_text": "the answer text of at most 1.5\\,\\% of the problems. The loop shows little answer sensitivity",
   "paper_line": 1384,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "dep-0015",
   "section": "Dependence builds up",
   "claim": "number 0.05 in 'Dependence builds up' (generated: post phrase matched to the paper's source text)",
   "appears_as": "**Strongly steered** (\\(\\alpha = 0.05\\)). The copies change the",
   "paper_text": "feedback. \\item At $\\alpha=0.05$ they change the answer text",
   "paper_line": 1385,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "dep-0016",
   "section": "Dependence builds up",
   "claim": "number 13.5 in 'Dependence builds up' (generated: post phrase matched to the paper's source text)",
   "appears_as": "text of 13.5% of the problems at \\(T",
   "paper_text": "they change the answer text of 13.5\\,\\% of the problems at $T=0.6$",
   "paper_line": 1386,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "dep-0017",
   "section": "Dependence builds up",
   "claim": "number 0.6 in 'Dependence builds up' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of the problems at \\(T = 0.6\\) and 27.5% at \\(T = 1.2\\),",
   "paper_text": "13.5\\,\\% of the problems at $T=0.6$ and 27.5\\,\\% at $T=1.2$, and",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "dep-0018",
   "section": "Dependence builds up",
   "claim": "number 27.5 in 'Dependence builds up' (generated: post phrase matched to the paper's source text)",
   "appears_as": "problems at \\(T = 0.6\\) and 27.5% at \\(T = 1.2\\), and the",
   "paper_text": "the problems at $T=0.6$ and 27.5\\,\\% at $T=1.2$, and the extracted",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "dep-0019",
   "section": "Dependence builds up",
   "claim": "number 1.2 in 'Dependence builds up' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.6\\) and 27.5% at \\(T = 1.2\\), and the",
   "paper_text": "$T=0.6$ and 27.5\\,\\% at $T=1.2$, and the extracted number",
   "paper_line": 1386,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "dep-0020",
   "section": "Dependence builds up",
   "claim": "number 4.5 in 'Dependence builds up' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "and the extracted number of 4.5 and 9.0\\,\\%. The loop itself",
   "paper_line": 1386,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "dep-0021",
   "section": "Dependence builds up",
   "claim": "number 9.0 in 'Dependence builds up' (generated: post phrase matched to the paper's source text)",
   "appears_as": "answer itself, of 4.5 and 9.0%. The loop itself is",
   "paper_text": "extracted number of 4.5 and 9.0\\,\\%. The loop itself is then",
   "paper_line": 1387,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "dep-0022",
   "section": "Dependence builds up",
   "claim": "number 0.5 in 'Dependence builds up' (generated: post phrase matched to the paper's source text)",
   "appears_as": "accuracy has fallen to between 0.5 and 2.5% in either layout.",
   "paper_text": "accuracy has fallen to between 0.5 and 2.5\\,\\% in either layout.",
   "paper_line": 1388,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "dep-0023",
   "section": "Dependence builds up",
   "claim": "number 2.5 in 'Dependence builds up' (generated: post phrase matched to the paper's source text)",
   "appears_as": "fallen to between 0.5 and 2.5% in either layout.",
   "paper_text": "has fallen to between 0.5 and 2.5\\,\\% in either layout. \\end{itemize}",
   "paper_line": 1388,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "e23-0000",
   "section": "Taming sensitivity",
   "claim": "number 512 in 'Taming sensitivity' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Qwen2.5-7B-Instruct in bfloat16, on 512 unused GSM8K training problems,",
   "paper_text": "Qwen2.5-7B-Instruct in bfloat16 (512 unused GSM8K training problems,",
   "paper_line": 4613,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "e23-0001",
   "section": "Taming sensitivity",
   "claim": "number 16 in 'Taming sensitivity' (generated: post phrase matched to the paper's source text)",
   "appears_as": "GSM8K training problems, 16 at",
   "paper_text": "16 at each of 32 prompt lengths, fixed before any outcome",
   "paper_line": 4614,
   "paper_file": "paper/llm/main.tex"
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   "paper_line": 1561,
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   "paper_text": "it'' itself has multipliers $-0.2706$ and $-0.0585$ at $(\\log_{10}T,\\alpha)=(-0.17263,0.061579)$.",
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   "paper_line": 1563,
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   "appears_as": "\\((\\log_{10}T, \\alpha) = (-0.17263, 0.061579)\\). The period-2 and",
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   "claim": "number 0.088 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
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   "section": "Saddle-node bottleneck",
   "claim": "number -0.115 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "\\paragraph{The fold.} At $\\log_{10}T=-0.115$ the 2-cycle ``is it'' dies",
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   "section": "Saddle-node bottleneck",
   "claim": "number 0.06279827 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
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   "appears_as": "\\(3\\times10^{-13}\\), and the next has modulus",
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   "paper_line": 1612,
   "paper_file": "paper/llm/main.tex"
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   "section": "Saddle-node bottleneck",
   "claim": "number 0.037 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and the next has modulus 0.037. There it meets an unstable",
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   "paper_line": 1613,
   "paper_file": "paper/llm/main.tex"
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   "section": "Saddle-node bottleneck",
   "claim": "number -4.834 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "$\\eps=\\alpha-\\alpha_c$; here $a=-4.834$ per unit $\\alpha$ and $b=-25.4285$,",
   "paper_line": 1615,
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   "section": "Saddle-node bottleneck",
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   "appears_as": "\\(b = -25.4285\\), so \\(ab = 122.93\\).",
   "paper_text": "$a=-4.834$ per unit $\\alpha$ and $b=-25.4285$, so $ab=122.93$",
   "paper_line": 1615,
   "paper_file": "paper/llm/main.tex"
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   "appears_as": "\\(b = -25.4285\\), so \\(ab = 122.93\\).",
   "paper_text": "$b=-25.4285$, so $ab=122.93$",
   "paper_line": 1615,
   "paper_file": "paper/llm/main.tex"
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   "section": "Saddle-node bottleneck",
   "claim": "number 123.1 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
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   "section": "Saddle-node bottleneck",
   "claim": "number 120.6 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Saddle-node bottleneck",
   "claim": "number 3\\times10^{-12} in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(3\\times10^{-12}\\). Its \\(b\\), from nested",
   "paper_text": "$6\\times10^{-15}$ and $a$ to $3\\times10^{-12}$. Its $b$, from nested automatic",
   "paper_line": 1623,
   "paper_file": "paper/llm/main.tex"
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   "section": "Saddle-node bottleneck",
   "claim": "number -25.42846 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-25.42846\\); ours differs from it",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Saddle-node bottleneck",
   "claim": "number 2.2\\times10^{-6} in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-25.42846\\); ours differs from it by about \\(2.2\\times10^{-6}\\) relatively, the",
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   "section": "Saddle-node bottleneck",
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   "paper_text": "$v'=v+|a|\\eps+|b|v^2$ (lines), take 144, 71, 34 and 14 iterates, as predicted.",
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   "paper_text": "(lines), take 144, 71, 34 and 14 iterates, as predicted. (d)",
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   "section": "Saddle-node bottleneck",
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   "paper_text": "A free trajectory at $\\eps=10^{-5}$ alternates between laminar",
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   "paper_text": "\\midrule $3\\times10^{-6}$ & 144 / 144 & 73 / 74 & 143 / 144",
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   "section": "Saddle-node bottleneck",
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   "appears_as": "\\(3\\times10^{-6}\\) | 144 / 144 | 73 / 74 | 143 / 144 |",
   "paper_text": "\\midrule $3\\times10^{-6}$ & 144 / 144 & 73 / 74 & 143 / 144",
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   "section": "Saddle-node bottleneck",
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   "appears_as": "\\(3\\times10^{-6}\\) | 144 / 144 | 73 / 74 | 143 / 144 |",
   "paper_text": "$3\\times10^{-6}$ & 144 / 144 & 73 / 74 & 143 / 144 \\\\ $1\\times10^{-5}$",
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   "section": "Saddle-node bottleneck",
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   "appears_as": "\\(3\\times10^{-6}\\) | 144 / 144 | 73 / 74 | 143 / 144 |",
   "paper_text": "$3\\times10^{-6}$ & 144 / 144 & 73 / 74 & 143 / 144 \\\\ $1\\times10^{-5}$",
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   "paper_text": "$3\\times10^{-6}$ & 144 / 144 & 73 / 74 & 143 / 144 \\\\ $1\\times10^{-5}$ &",
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   "section": "Saddle-node bottleneck",
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   "paper_text": "144 & 73 / 74 & 143 / 144 \\\\ $1\\times10^{-5}$ & 71 / 71 & 36 / 37 & 70 /",
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   "paper_text": "/ 144 \\\\ $1\\times10^{-5}$ & 71 / 71 & 36 / 37 & 70 / 71 \\\\",
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   "section": "Saddle-node bottleneck",
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   "appears_as": "\\(1\\times10^{-5}\\) | 71 / 71 | 36 / 37 | 70 / 71 |",
   "paper_text": "/ 144 \\\\ $1\\times10^{-5}$ & 71 / 71 & 36 / 37 & 70 / 71 \\\\",
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   "section": "Saddle-node bottleneck",
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   "appears_as": "\\(1\\times10^{-5}\\) | 71 / 71 | 36 / 37 | 70 / 71 |",
   "paper_text": "$1\\times10^{-5}$ & 71 / 71 & 36 / 37 & 70 / 71 \\\\ $3\\times10^{-5}$",
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   "appears_as": "\\(1\\times10^{-5}\\) | 71 / 71 | 36 / 37 | 70 / 71 |",
   "paper_text": "$1\\times10^{-5}$ & 71 / 71 & 36 / 37 & 70 / 71 \\\\ $3\\times10^{-5}$",
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   "appears_as": "\\(1\\times10^{-5}\\) | 71 / 71 | 36 / 37 | 70 / 71 |",
   "paper_text": "$1\\times10^{-5}$ & 71 / 71 & 36 / 37 & 70 / 71 \\\\ $3\\times10^{-5}$ &",
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   "paper_text": "71 & 36 / 37 & 70 / 71 \\\\ $3\\times10^{-5}$ & 34 / 34 & 17 / 18 & 33 /",
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   "paper_text": "/ 71 \\\\ $3\\times10^{-5}$ & 34 / 34 & 17 / 18 & 33 / 34 \\\\",
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   "appears_as": "\\(3\\times10^{-5}\\) | 34 / 34 | 17 / 18 | 33 / 34 |",
   "paper_text": "/ 71 \\\\ $3\\times10^{-5}$ & 34 / 34 & 17 / 18 & 33 / 34 \\\\",
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   "section": "Saddle-node bottleneck",
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   "appears_as": "\\(3\\times10^{-5}\\) | 34 / 34 | 17 / 18 | 33 / 34 |",
   "paper_text": "$3\\times10^{-5}$ & 34 / 34 & 17 / 18 & 33 / 34 \\\\ $1\\times10^{-4}$",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Saddle-node bottleneck",
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   "appears_as": "\\(3\\times10^{-5}\\) | 34 / 34 | 17 / 18 | 33 / 34 |",
   "paper_text": "$+0.0716$ & $8\\times10^{-11}$ \\\\ 18 & . This (is it)$^6$ is a is",
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   "section": "Saddle-node bottleneck",
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   "appears_as": "\\(3\\times10^{-5}\\) | 34 / 34 | 17 / 18 | 33 / 34 |",
   "paper_text": "$3\\times10^{-5}$ & 34 / 34 & 17 / 18 & 33 / 34 \\\\ $1\\times10^{-4}$ &",
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   "section": "Saddle-node bottleneck",
   "claim": "number 34 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "34 / 34 | 17 / 18 | 33 / 34 |",
   "paper_text": "/ 71 \\\\ $3\\times10^{-5}$ & 34 / 34 & 17 / 18 & 33 / 34 \\\\",
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   "section": "Saddle-node bottleneck",
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   "appears_as": "| \\(1\\times10^{-4}\\) | 14 / 14 | 7 / 7 | 13",
   "paper_text": "34 & 17 / 18 & 33 / 34 \\\\ $1\\times10^{-4}$ & 14 / 14 & 7 / 7 & 13 / 14",
   "paper_line": 1654,
   "paper_file": "paper/llm/main.tex"
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   "id": "fold-0100",
   "section": "Saddle-node bottleneck",
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   "appears_as": "| \\(1\\times10^{-4}\\) | 14 / 14 | 7 / 7 | 13 / 14",
   "paper_text": "$1\\times10^{-4}$ & 14 / 14 & 7 / 7 & 13 / 14",
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   "id": "fold-0101",
   "section": "Saddle-node bottleneck",
   "claim": "number 14 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text) (paper 318f8980)",
   "appears_as": "\\(1\\times10^{-4}\\) | 14 / 14 | 7 / 7 | 13 / 14 |",
   "paper_text": "$1\\times10^{-4}$ & 14 / 14 & 7 / 7 & 13 / 14",
   "paper_line": 1655,
   "paper_file": "paper/llm/main.tex"
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   "id": "fold-0102",
   "section": "Saddle-node bottleneck",
   "claim": "number 13 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(1\\times10^{-4}\\) | 14 / 14 | 7 / 7 | 13 / 14 |",
   "paper_text": "$6\\times10^{-15}$ to $8\\times10^{-13}$, leading multiplier $\\mu_1$",
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   "paper_file": "paper/llm/main.tex"
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   "id": "fold-0103",
   "section": "Saddle-node bottleneck",
   "claim": "number 14 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text) (paper 318f8980)",
   "appears_as": "14 / 14 | 7 / 7 | 13 / 14 |",
   "paper_text": "$1\\times10^{-4}$ & 14 / 14 & 7 / 7 & 13 / 14",
   "paper_line": 1655,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "fold-0104",
   "section": "Saddle-node bottleneck",
   "claim": "number 18 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "reimplementation reproduces all 18 fixed-entrance counts of the",
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   "paper_file": "paper/llm/main.tex"
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   "id": "fold-0105",
   "section": "Saddle-node bottleneck",
   "claim": "number 12 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of these runs exactly (12 are listed here). Source:",
   "paper_text": "(Table~\\ref{tab:passages} lists 12 of them). \\item Prospectively",
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   "paper_file": "paper/llm/main.tex"
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   "id": "fold-0106",
   "section": "Saddle-node bottleneck",
   "claim": "number 12 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "philosophy direction at layer 12, $\\log_{10}T=-0.115$). Left:",
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   "paper_file": "paper/llm/main.tex"
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   "id": "fold-0107",
   "section": "Saddle-node bottleneck",
   "claim": "number -0.115 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "layer 12, \\(\\log_{10}T = -0.115\\)): measured passage times",
   "paper_text": "direction at layer 12, $\\log_{10}T=-0.115$). Left: measured passage times",
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   "paper_file": "paper/llm/main.tex"
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   "id": "fold-0108",
   "section": "Saddle-node bottleneck",
   "claim": "natural-phase forecasts at the four offsets up to 1e-4 (paper cda9ca04)",
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   "paper_text": "offsets up to $\\eps=10^{-4}$ lies between $-7.7\\%$ and $-4.1\\%$",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "fold-0109",
   "section": "Saddle-node bottleneck",
   "claim": "number 0.6 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text) (paper 318f8980)",
   "appears_as": "lasts 0.60 to 0.67 of the normal form's passage through the same channel from end to",
   "paper_text": "on average a natural passage lasts 0.60 to 0.67 of the normal form's passage through the same channel from end to end",
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   "paper_file": "paper/llm/main.tex"
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   "id": "fold-0110",
   "section": "Saddle-node bottleneck",
   "claim": "number 0.58 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the passage fraction (\\(0.58^2 \\approx 1/3\\)). The distances",
   "paper_text": "square of the passage fraction ($0.58^2\\approx1/3$). The distances",
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   "paper_file": "paper/llm/main.tex"
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   "id": "fold-0111",
   "section": "Saddle-node bottleneck",
   "claim": "number -0.115 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "cut along \\(\\log_{10}T = -0.115\\) give",
   "paper_text": "float32 cut along $\\log_{10}T=-0.115$ give $d_N N^2=0.0263$--$0.0265$",
   "paper_line": 1692,
   "paper_file": "paper/llm/main.tex"
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   "section": "Saddle-node bottleneck",
   "claim": "number 0.0263 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(d_N N^2 = 0.0263\\) to 0.0265 for \\(N = 4\\)",
   "paper_text": "$\\log_{10}T=-0.115$ give $d_N N^2=0.0263$--$0.0265$ for $N=4$--$7$ (log-log",
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   "paper_file": "paper/llm/main.tex"
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   "id": "fold-0113",
   "section": "Saddle-node bottleneck",
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   "appears_as": "\\(d_N N^2 = 0.0263\\) to 0.0265 for \\(N = 4\\) to 7 (log-log",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "fold-0164",
   "section": "Saddle-node bottleneck",
   "claim": "number 28 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "1% at periods 22, 24 and 28) and fall outside",
   "paper_text": "1\\,\\% at periods 22, 24 and 28) and fall outside the model's",
   "paper_line": 1744,
   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Saddle-node bottleneck",
   "claim": "number 30 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "range except at period 30. So the law extrapolates,",
   "paper_text": "model's range except at period 30. So the law extrapolates, but",
   "paper_line": 1744,
   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Saddle-node bottleneck",
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   "appears_as": "the fold edges of periods 16 to 32 (\\(N = 5\\) to 13),",
   "paper_text": "Over the fold edges of periods 16 to 32 ($N=5$ to 13), $\\ln(\\alpha_N-\\alpha_c)$",
   "paper_line": 1747,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "fold-0167",
   "section": "Saddle-node bottleneck",
   "claim": "number 32 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "edges of periods 16 to 32 (\\(N = 5\\) to 13),",
   "paper_text": "fold edges of periods 16 to 32 ($N=5$ to 13), $\\ln(\\alpha_N-\\alpha_c)$",
   "paper_line": 1747,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "fold-0168",
   "section": "Saddle-node bottleneck",
   "claim": "number 13 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "16 to 32 (\\(N = 5\\) to 13),",
   "paper_text": "periods 16 to 32 ($N=5$ to 13), $\\ln(\\alpha_N-\\alpha_c)$",
   "paper_line": 1747,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "fold-0169",
   "section": "Saddle-node bottleneck",
   "claim": "number -2.00 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "against \\(\\ln N\\) has slope \\(-2.00\\). The estimated",
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   "paper_line": 1748,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "fold-0170",
   "section": "Saddle-node bottleneck",
   "claim": "smallest free exponent over the fit ranges in 'Saddle-node bottleneck'",
   "appears_as": "\\(\\gamma\\) from 2.13 to 2.45",
   "paper_text": "$\\gamma$ runs from 2.13 to 2.45",
   "paper_line": 1752,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "fold-0171",
   "section": "Saddle-node bottleneck",
   "claim": "largest free exponent over the fit ranges in 'Saddle-node bottleneck'",
   "appears_as": "\\(\\gamma\\) from 2.13 to 2.45",
   "paper_text": "$\\gamma$ runs from 2.13 to 2.45",
   "paper_line": 1752,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "fold-0172",
   "section": "Saddle-node bottleneck",
   "claim": "number 1.35 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "is 1.35 to 3.51 times \\(U\\), and",
   "paper_text": "scale $\\sqrt{|a|\\eps/|b|}$ is 1.35 to 3.51 times $U$, and a full",
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   "paper_file": "paper/llm/main.tex"
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   "id": "fold-0173",
   "section": "Saddle-node bottleneck",
   "claim": "number 3.51 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "is 1.35 to 3.51 times \\(U\\), and a full",
   "paper_text": "$\\sqrt{|a|\\eps/|b|}$ is 1.35 to 3.51 times $U$, and a full passage",
   "paper_line": 1753,
   "paper_file": "paper/llm/main.tex"
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   "section": "Saddle-node bottleneck",
   "claim": "number 23 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "passage lasts only 9 to 23 iterates of",
   "paper_text": "full passage lasts only 9 to 23 iterates of $G$. The windows",
   "paper_line": 1753,
   "paper_file": "paper/llm/main.tex"
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   "id": "fold-0175",
   "section": "Saddle-node bottleneck",
   "claim": "number 12 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "philosophy direction at layer 12, \\(\\log_{10}T = -0.115\\)),",
   "paper_text": "philosophy direction at layer 12, $\\log_{10}T=-0.115$). Left:",
   "paper_line": 1667,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0176",
   "section": "Saddle-node bottleneck",
   "claim": "number -0.115 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "layer 12, \\(\\log_{10}T = -0.115\\)), with stripe centers",
   "paper_text": "2-cycle ``is it'' at $\\log_{10}T=-0.115$ (Qwen2.5-0.5B-Instruct, philosophy",
   "paper_line": 1597,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0177",
   "section": "Saddle-node bottleneck",
   "claim": "number 12 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "philosophy direction at layer 12), at increasing distance",
   "paper_text": "philosophy direction at layer 12), at increasing distance from",
   "paper_line": 1762,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0178",
   "section": "Saddle-node bottleneck",
   "claim": "number -0.140 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = -0.140\\), \\(\\alpha_c = 0.0670549\\),",
   "paper_text": "new temperature: $\\log_{10}T=-0.140$, $\\alpha_c=0.0670549$, $a=-7.055$,",
   "paper_line": 1769,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "fold-0179",
   "section": "Saddle-node bottleneck",
   "claim": "number 0.0670549 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "-0.140\\), \\(\\alpha_c = 0.0670549\\), \\(a = -7.055\\),",
   "paper_text": "$\\log_{10}T=-0.140$, $\\alpha_c=0.0670549$, $a=-7.055$, $b=-24.927$.",
   "paper_line": 1769,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0180",
   "section": "Saddle-node bottleneck",
   "claim": "number -7.055 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\alpha_c = 0.0670549\\), \\(a = -7.055\\),",
   "paper_text": "$\\log_{10}T=-0.140$, $\\alpha_c=0.0670549$, $a=-7.055$, $b=-24.927$. Target B is",
   "paper_line": 1769,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0181",
   "section": "Saddle-node bottleneck",
   "claim": "number -24.927 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(b = -24.927\\). Target B is the fold",
   "paper_text": "$\\alpha_c=0.0670549$, $a=-7.055$, $b=-24.927$. Target B is the fold of the",
   "paper_line": 1769,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0182",
   "section": "Saddle-node bottleneck",
   "claim": "number 0.0717 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "temperature at \\(\\alpha = 0.0717\\):",
   "paper_text": "continued in temperature at $\\alpha=0.0717$: $\\log_{10}T_c=-0.1033462$,",
   "paper_line": 1770,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0183",
   "section": "Saddle-node bottleneck",
   "claim": "number -0.1033462 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T_c = -0.1033462\\), \\(G = F^8\\), \\(a = -11.900\\) per unit",
   "paper_text": "$\\log_{10}T_c=-0.1033462$, $G=F^8$, $a=-11.900$ per unit $\\log_{10}T$ and $b=-152.05$",
   "paper_line": 1771,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0184",
   "section": "Saddle-node bottleneck",
   "claim": "number -11.900 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(G = F^8\\), \\(a = -11.900\\) per unit \\(\\log_{10}T\\)",
   "paper_text": "$G=F^8$, $a=-11.900$ per unit $\\log_{10}T$ and $b=-152.05$. Of the 24",
   "paper_line": 1771,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0185",
   "section": "Saddle-node bottleneck",
   "claim": "number -152.05 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and \\(b = -152.05\\).",
   "paper_text": "$a=-11.900$ per unit $\\log_{10}T$ and $b=-152.05$",
   "paper_line": 1771,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0186",
   "section": "Saddle-node bottleneck",
   "claim": "number 24 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "transverse kick. Of the 24 forecasts of the primary",
   "paper_text": "$b=-152.05$. Of the 24 forecasts (four distances and",
   "paper_line": 1771,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0187",
   "section": "Saddle-node bottleneck",
   "claim": "number 23 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "quadratic map, 23 fell within one iterate",
   "paper_text": "start after a transverse kick), 23 fell within one iterate of",
   "paper_line": 1771,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0188",
   "section": "Saddle-node bottleneck",
   "claim": "number 24 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "). Seven of the 24 forecasts are five iterates",
   "paper_text": "(Table~\\ref{tab:prospective}). Seven of the 24 forecasts are five iterates",
   "paper_line": 1772,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0189",
   "section": "Saddle-node bottleneck",
   "claim": "number 20 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "where a single iterate is 20% or more of the passage;",
   "paper_text": "shorter, where a single iterate is 20\\,\\% or more of the passage;",
   "paper_line": 1772,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0190",
   "section": "Saddle-node bottleneck",
   "claim": "number 17 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of the passage; of the 17 longer forecasts,",
   "paper_text": "more of the passage; of the 17 longer forecasts, 16 fell within",
   "paper_line": 1773,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0191",
   "section": "Saddle-node bottleneck",
   "claim": "number 16 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "16 fell within one iterate.",
   "paper_text": "of the 17 longer forecasts, 16 fell within one iterate. The",
   "paper_line": 1773,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0192",
   "section": "Saddle-node bottleneck",
   "claim": "number 3\\times10^{-6} in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "start, \\(\\varepsilon = 3\\times10^{-6}\\),",
   "paper_text": "A, midpoint entrance, $\\eps=3\\times10^{-6}$, the forecast was 61 and the",
   "paper_line": 1773,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0193",
   "section": "Saddle-node bottleneck",
   "claim": "number 61 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the forecast was 61 and the measurement 59.",
   "paper_text": "$\\eps=3\\times10^{-6}$, the forecast was 61 and the measurement 59. All",
   "paper_line": 1774,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0194",
   "section": "Saddle-node bottleneck",
   "claim": "number 59 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "61 and the measurement 59. All full-channel passages",
   "paper_text": "was 61 and the measurement 59. All full-channel passages",
   "paper_line": 1774,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0195",
   "section": "Saddle-node bottleneck",
   "claim": "number 17 in 'Saddle-node bottleneck' (nonzero midpoint or kicked-start residuals, all negative; no sign-test probability, Codex Task 36 R5)",
   "appears_as": "every one of the 17 nonzero residuals",
   "paper_text": "every one of the 17 nonzero residuals of a midpoint or kicked start",
   "paper_line": 1775,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "fold-0198",
   "section": "Saddle-node bottleneck",
   "claim": "number 24 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "one iterate of all 24 measurements (errors from",
   "paper_text": "came within one iterate of all 24 measurements (errors from $-0.41$",
   "paper_line": 1782,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "fold-0199",
   "section": "Saddle-node bottleneck",
   "claim": "number -0.41 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "measurements (errors from \\(-0.41\\) to \\(+0.92\\)) and gives",
   "paper_text": "measurements (errors from $-0.41$ to $+0.92$) and gives 58.56",
   "paper_line": 1782,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "fold-0200",
   "section": "Saddle-node bottleneck",
   "claim": "number 0.92 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(errors from \\(-0.41\\) to \\(+0.92\\)) and gives",
   "paper_text": "measurements (errors from $-0.41$ to $+0.92$) and gives 58.56 for the failing",
   "paper_line": 1782,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "fold-0201",
   "section": "Saddle-node bottleneck",
   "claim": "number 58.56 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "58.56 for the failing row. At",
   "paper_text": "$-0.41$ to $+0.92$) and gives 58.56 for the failing row. At that",
   "paper_line": 1782,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0202",
   "section": "Saddle-node bottleneck",
   "claim": "number 2.4 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "by 2.4 iterates before any measurement:",
   "paper_text": "two forms already differed by 2.4 iterates before any measurement:",
   "paper_line": 1783,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "fold-0203",
   "section": "Saddle-node bottleneck",
   "claim": "number 3\\times10^{-6} in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text) (paper 318f8980)",
   "appears_as": "| \\(3\\times10^{-6}\\) | 118/118, **59/61**,",
   "paper_text": "$3\\times10^{-6}$ & $118/118$,\\ $\\mathbf{59/61}$,\\ $117/118$",
   "paper_line": 1794,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0204",
   "section": "Saddle-node bottleneck",
   "claim": "number 118 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| \\(3\\times10^{-6}\\) | 118/118, **59/61**, 117/118",
   "paper_text": "\\midrule $3\\times10^{-6}$ & $118/118$,\\ $\\mathbf{59/61}$,\\ $117/118$",
   "paper_line": 1793,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0205",
   "section": "Saddle-node bottleneck",
   "claim": "number 59 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(3\\times10^{-6}\\) | 118/118, **59/61**, 117/118 | 26/26,",
   "paper_text": "was 61 and the measurement 59. All full-channel passages",
   "paper_line": 1774,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0206",
   "section": "Saddle-node bottleneck",
   "claim": "number 117 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(3\\times10^{-6}\\) | 118/118, **59/61**, 117/118 | 26/26, 13/14, 25/26",
   "paper_text": "$118/118$,\\ $\\mathbf{59/61}$,\\ $117/118$ & $26/26$,\\ $13/14$,\\",
   "paper_line": 1794,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0207",
   "section": "Saddle-node bottleneck",
   "claim": "number 26 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "118/118, **59/61**, 117/118 | 26/26, 13/14, 25/26 |",
   "paper_text": "$\\mathbf{59/61}$,\\ $117/118$ & $26/26$,\\ $13/14$,\\ $25/26$ \\\\",
   "paper_line": 1794,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0208",
   "section": "Saddle-node bottleneck",
   "claim": "number 13 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "**59/61**, 117/118 | 26/26, 13/14, 25/26 |",
   "paper_text": "$6\\times10^{-15}$ to $8\\times10^{-13}$, leading multiplier $\\mu_1$",
   "paper_line": 1561,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0209",
   "section": "Saddle-node bottleneck",
   "claim": "number 25 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "117/118 | 26/26, 13/14, 25/26 |",
   "paper_text": "accuracy stayed between 23 and 25\\,\\% in every arm. One batched",
   "paper_line": 1330,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0210",
   "section": "Saddle-node bottleneck",
   "claim": "number 1\\times10^{-5} in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| \\(1\\times10^{-5}\\) | 56/56, 28/29, 56/56",
   "paper_text": "144 & 73 / 74 & 143 / 144 \\\\ $1\\times10^{-5}$ & 71 / 71 & 36 / 37 & 70 /",
   "paper_line": 1652,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0211",
   "section": "Saddle-node bottleneck",
   "claim": "number 56 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| \\(1\\times10^{-5}\\) | 56/56, 28/29, 56/56 | 10/10,",
   "paper_text": "$25/26$ \\\\ $1\\times10^{-5}$ & $56/56$,\\ $28/29$,\\ $56/56$ & $10/10$,\\",
   "paper_line": 1794,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "fold-0212",
   "section": "Saddle-node bottleneck",
   "claim": "number 28 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(1\\times10^{-5}\\) | 56/56, 28/29, 56/56 | 10/10, 5/5,",
   "paper_text": "$1\\times10^{-5}$ & $56/56$,\\ $28/29$,\\ $56/56$ & $10/10$,\\ $5/5$,\\",
   "paper_line": 1795,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "fold-0213",
   "section": "Saddle-node bottleneck",
   "claim": "number 56 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(1\\times10^{-5}\\) | 56/56, 28/29, 56/56 | 10/10, 5/5, 10/10",
   "paper_text": "$25/26$ \\\\ $1\\times10^{-5}$ & $56/56$,\\ $28/29$,\\ $56/56$ & $10/10$,\\",
   "paper_line": 1794,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0214",
   "section": "Saddle-node bottleneck",
   "claim": "number 10 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 56/56, 28/29, 56/56 | 10/10, 5/5, 10/10 |",
   "paper_text": "times the displacement and $10^{-3}$, the median growth rates",
   "paper_line": 1450,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0215",
   "section": "Saddle-node bottleneck",
   "claim": "number 10 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "28/29, 56/56 | 10/10, 5/5, 10/10 |",
   "paper_text": "times the displacement and $10^{-3}$, the median growth rates",
   "paper_line": 1450,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "fold-0216",
   "section": "Saddle-node bottleneck",
   "claim": "number 3\\times10^{-5} in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| \\(3\\times10^{-5}\\) | 26/26, 13/14, 26/26",
   "paper_text": "71 & 36 / 37 & 70 / 71 \\\\ $3\\times10^{-5}$ & 34 / 34 & 17 / 18 & 33 /",
   "paper_line": 1653,
   "paper_file": "paper/llm/main.tex"
  },
  {
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   "paper_text": "$\\mathbf{59/61}$,\\ $117/118$ & $26/26$,\\ $13/14$,\\ $25/26$ \\\\",
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   "paper_text": "34 & 17 / 18 & 33 / 34 \\\\ $1\\times10^{-4}$ & 14 / 14 & 7 / 7 & 13 / 14",
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   "paper_text": "times the displacement and $10^{-3}$, the median growth rates",
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   "paper_text": "times the displacement and $10^{-3}$, the median growth rates",
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   "paper_text": "$\\alpha_c=0.0756329$, $G=F^6$, $a=-72.695$, $b=72.237$. Distances $\\eps=q^2/(ab)$",
   "paper_line": 1812,
   "paper_file": "paper/llm/main.tex"
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   "paper_line": 1813,
   "paper_file": "paper/llm/main.tex"
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   "paper_text": "$\\eps=q^2/(ab)$ with $q=0.08$, $0.05$, $0.03$ and $0.018$ give both",
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   "paper_text": "$\\eps=q^2/(ab)$ with $q=0.08$, $0.05$, $0.03$ and $0.018$ give both targets",
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   "paper_text": "(philosophy direction, layer 12) run twice from the same start,",
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   "appears_as": "22.40 / 11.20 | 23 / 12 | 23, 12, 23 | 22, 11, 22 |",
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   "paper_text": "(philosophy direction, layer 12) run twice from the same start,",
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   "paper_text": "their base row (14 in R1-Llama, 23 in QwQ), and the copies of",
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   "paper_text": "& $+0.0716$ & $8\\times10^{-11}$ \\\\ 18 & . This (is it)$^6$",
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   "appears_as": "0.05 | 44.29 / 22.14 | 45 / 23 | 45, 23, 45 | **42**,",
   "paper_text": "with exponent 0.35, at step 45. By then the distance had grown",
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   "paper_text": "with exponent 0.35, at step 45. By then the distance had grown",
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   "appears_as": "22.14 | 45 / 23 | 45, 23, 45 | **42**, 22, **42** |",
   "paper_text": "with exponent 0.35, at step 45. By then the distance had grown",
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   "appears_as": "23, 45 | **42**, 22, **42** |",
   "paper_text": "$\\log_{10}T=0.1$ both pairs give 33 and 42\\,\\%. Each plane keeps a periodic",
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   "paper_file": "paper/llm/main.tex"
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   "paper_text": "$\\eps=q^2/(ab)$ with $q=0.08$, $0.05$, $0.03$ and $0.018$ give both targets",
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   "paper_text": "$\\mathbf{42}$ \\\\ $0.03$ & $85.29$ / $42.64$ & $86$ / $44$ &",
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   "paper_text": "reasoning models that answer 86 to 90\\,\\% of them correctly",
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   "paper_text": "$24\\times24$ map at block 20 of 80, down to $\\log_{10}T=-0.14$,",
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   "claim": "number 115 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
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   "paper_line": 4712,
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   "claim": "number -0.402 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\log_{10}T) = (0.0776, -0.402)\\), with two reversals",
   "paper_text": "$(\\alpha,\\log_{10}T)=(0.0776,-0.402)$, with two reversals of its",
   "paper_line": 4713,
   "paper_file": "paper/llm/main.tex"
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   "claim": "number 0.0750 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "its parameter tangent near $(0.0750,-0.219)$ and $(0.0746,-0.206)$,",
   "paper_line": 4713,
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   "paper_text": "parameter tangent near $(0.0750,-0.219)$ and $(0.0746,-0.206)$, and",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Saddle-node bottleneck",
   "claim": "number -0.206 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "-0.219)\\) and \\((0.0746, -0.206)\\), and the fold curve",
   "paper_text": "$(0.0750,-0.219)$ and $(0.0746,-0.206)$, and the fold curve keeps",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Saddle-node bottleneck",
   "claim": "number 120 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "its multiplier at $+1$ for 120 points to $(0.0758,-0.200)$.",
   "paper_line": 4714,
   "paper_file": "paper/llm/main.tex"
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   "paper_line": 4714,
   "paper_file": "paper/llm/main.tex"
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   "section": "Saddle-node bottleneck",
   "claim": "number -0.200 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "120 points to \\((0.0758, -0.200)\\). Located by bisection",
   "paper_text": "for 120 points to $(0.0758,-0.200)$. Located by bisection along",
   "paper_line": 4714,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "fold-0308",
   "section": "Saddle-node bottleneck",
   "claim": "number 0.074955 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of the flip curve, at \\((0.074955, -0.219336)\\)",
   "paper_text": "reversals of the flip curve, at $(0.074955,-0.219336)$ and $(0.074608,-0.206007)$,",
   "paper_line": 4715,
   "paper_file": "paper/llm/main.tex"
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   "section": "Saddle-node bottleneck",
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   "appears_as": "curve, at \\((0.074955, -0.219336)\\)",
   "paper_text": "the flip curve, at $(0.074955,-0.219336)$ and $(0.074608,-0.206007)$,",
   "paper_line": 4715,
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   "section": "Saddle-node bottleneck",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Saddle-node bottleneck",
   "claim": "number -0.206007 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and \\((0.074608, -0.206007)\\), carry no second multiplier",
   "paper_text": "$(0.074955,-0.219336)$ and $(0.074608,-0.206007)$, carry no second multiplier",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Saddle-node bottleneck",
   "claim": "number 3\\times10^{-7} in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "next ones are \\(3\\times10^{-7}\\) and \\(1\\times10^{-5}\\)).",
   "paper_text": "circle (the next ones are $3\\times10^{-7}$ and $1\\times10^{-5}$). On",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Saddle-node bottleneck",
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   "paper_file": "paper/llm/main.tex"
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   "id": "fold-0314",
   "section": "Saddle-node bottleneck",
   "claim": "number 0.0628 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((\\alpha, \\log_{10}T) = (0.0628, -0.115)\\) in both directions",
   "paper_text": "from $(\\alpha,\\log_{10}T)=(0.0628,-0.115)$ in both directions",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Saddle-node bottleneck",
   "claim": "number -0.115 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\log_{10}T) = (0.0628, -0.115)\\) in both directions (38",
   "paper_text": "$(\\alpha,\\log_{10}T)=(0.0628,-0.115)$ in both directions (38 and",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Saddle-node bottleneck",
   "claim": "number 38 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "-0.115)\\) in both directions (38 and 126",
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   "paper_file": "paper/llm/main.tex"
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   "id": "fold-0317",
   "section": "Saddle-node bottleneck",
   "claim": "number 126 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "both directions (38 and 126",
   "paper_text": "in both directions (38 and 126 points, critical multiplier",
   "paper_line": 4722,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0318",
   "section": "Saddle-node bottleneck",
   "claim": "number 10^{-7} in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "critical multiplier 1 to \\(10^{-7}\\), no cusp), traces the",
   "paper_text": "critical multiplier $1$ to $10^{-7}$, no cusp), traces the boundary",
   "paper_line": 4722,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0319",
   "section": "Saddle-node bottleneck",
   "claim": "number 11 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "unit circle (moduli up to 11). Located along the",
   "paper_text": "the unit circle (moduli up to 11). Located along the curve,",
   "paper_line": 4725,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0320",
   "section": "Saddle-node bottleneck",
   "claim": "number 0.035628 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((\\alpha, \\log_{10}T) = (0.035628, -0.341724)\\), where the",
   "paper_text": "$+1$ at $(\\alpha,\\log_{10}T)=(0.035628,-0.341724)$, where the eigenvectors",
   "paper_line": 4726,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0321",
   "section": "Saddle-node bottleneck",
   "claim": "number -0.341724 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\log_{10}T) = (0.035628, -0.341724)\\), where the eigenvectors",
   "paper_text": "$(\\alpha,\\log_{10}T)=(0.035628,-0.341724)$, where the eigenvectors of",
   "paper_line": 4726,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0322",
   "section": "Saddle-node bottleneck",
   "claim": "number 3\\times10^{-4} in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at \\(+1\\) coincide to \\(3\\times10^{-4}\\) degrees: a double multiplier",
   "paper_text": "multipliers at $+1$ coincide to $3\\times10^{-4}$ degrees: a double multiplier",
   "paper_line": 4727,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0323",
   "section": "Saddle-node bottleneck",
   "claim": "number 2.235 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "their fold edges rise by 2.235",
   "paper_text": "$1/\\sqrt{\\log_{10}T_c-\\log_{10}T_{\\rm fold}}$ rises by $2.235$ per lap. The fold's normal",
   "paper_line": 2081,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0324",
   "section": "Saddle-node bottleneck",
   "claim": "number 2.296 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "against 2.296 predicted by the fold's",
   "paper_text": "$\\log_{10}T$) predicts $\\sqrt{|ab|}/\\pi=2.296$ per lap for full passages",
   "paper_line": 2082,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0325",
   "section": "Saddle-node bottleneck",
   "claim": "number 10 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(d_N(N + N_0)^2\\) within 10% over at least four windows",
   "paper_text": "constant $d_N(N+N_0)^2$ within 10\\,\\% over at least four windows",
   "paper_line": 5408,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0326",
   "section": "Saddle-node bottleneck",
   "claim": "number 14 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(philosophy direction, layer 14, \\(\\alpha = 0.058588\\)).",
   "paper_text": "(philosophy direction, layer 14, $\\alpha=0.058588$) the period-4",
   "paper_line": 5410,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0327",
   "section": "Saddle-node bottleneck",
   "claim": "number 0.058588 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "direction, layer 14, \\(\\alpha = 0.058588\\)). The",
   "paper_text": "direction, layer 14, $\\alpha=0.058588$) the period-4 orbit folds",
   "paper_line": 5410,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0328",
   "section": "Saddle-node bottleneck",
   "claim": "number -0.0912029 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "folds at \\(\\log_{10}T_c = -0.0912029\\) (multiplier 1 to",
   "paper_text": "orbit folds at $\\log_{10}T_c=-0.0912029$ (multiplier $1$ to $3\\times10^{-14}$,",
   "paper_line": 5411,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0329",
   "section": "Saddle-node bottleneck",
   "claim": "number 3\\times10^{-14} in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(3\\times10^{-14}\\), next modulus 0.008),",
   "paper_text": "$\\log_{10}T_c=-0.0912029$ (multiplier $1$ to $3\\times10^{-14}$, next modulus $0.008$), with",
   "paper_line": 5411,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0330",
   "section": "Saddle-node bottleneck",
   "claim": "number 0.008 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(3\\times10^{-14}\\), next modulus 0.008), with normal-form coefficients",
   "paper_text": "$3\\times10^{-14}$, next modulus $0.008$), with normal-form coefficients",
   "paper_line": 5412,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0331",
   "section": "Saddle-node bottleneck",
   "claim": "number -7.16 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(a = -7.16\\) per unit \\(\\log_{10}T\\)",
   "paper_text": "normal-form coefficients $a=-7.16$ per unit $\\log_{10}T$ and",
   "paper_line": 5412,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0332",
   "section": "Saddle-node bottleneck",
   "claim": "number -21.09 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T\\) and \\(b = -21.09\\), so \\(ab = 151.0\\). A",
   "paper_text": "per unit $\\log_{10}T$ and $b=-21.09$, so $ab=151.0$. A float64",
   "paper_line": 5412,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0333",
   "section": "Saddle-node bottleneck",
   "claim": "number 151.0 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(b = -21.09\\), so \\(ab = 151.0\\). A",
   "paper_text": "$\\log_{10}T$ and $b=-21.09$, so $ab=151.0$. A float64 line of 1700 cells,",
   "paper_line": 5412,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0334",
   "section": "Saddle-node bottleneck",
   "claim": "number 1700 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "float64 line of 1700 cells, 1570 of them above",
   "paper_text": "$ab=151.0$. A float64 line of 1700 cells, 1570 of them above the",
   "paper_line": 5413,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0335",
   "section": "Saddle-node bottleneck",
   "claim": "number 1570 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "float64 line of 1700 cells, 1570 of them above the fold,",
   "paper_text": "float64 line of 1700 cells, 1570 of them above the fold, shows",
   "paper_line": 5413,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0336",
   "section": "Saddle-node bottleneck",
   "claim": "number 44 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "single cells at periods 44 to 64 to a",
   "paper_text": "from single cells at periods 44--64 to a wide period-12 window.",
   "paper_line": 5414,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0337",
   "section": "Saddle-node bottleneck",
   "claim": "number 64 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "cells at periods 44 to 64 to a",
   "paper_text": "single cells at periods 44--64 to a wide period-12 window.",
   "paper_line": 5414,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0338",
   "section": "Saddle-node bottleneck",
   "claim": "number 28 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "resolved windows (periods 28 to 40) meet",
   "paper_text": "nearest resolved windows (periods 28--40) meet the criterion within",
   "paper_line": 5414,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0339",
   "section": "Saddle-node bottleneck",
   "claim": "number 40 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "windows (periods 28 to 40) meet",
   "paper_text": "resolved windows (periods 28--40) meet the criterion within",
   "paper_line": 5414,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0340",
   "section": "Saddle-node bottleneck",
   "claim": "number 0.12 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the criterion within 0.12% (\\(\\delta = -0.99\\), \\(C",
   "paper_text": "meet the criterion within $0.12\\,\\%$ ($\\delta=-0.99$, $C=0.0612$).",
   "paper_line": 5414,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0341",
   "section": "Saddle-node bottleneck",
   "claim": "number -0.99 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "within 0.12% (\\(\\delta = -0.99\\), \\(C = 0.0612\\)). With",
   "paper_text": "within $0.12\\,\\%$ ($\\delta=-0.99$, $C=0.0612$). With the windows",
   "paper_line": 5415,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0342",
   "section": "Saddle-node bottleneck",
   "claim": "number 0.0612 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(\\(\\delta = -0.99\\), \\(C = 0.0612\\)). With the windows",
   "paper_text": "$0.12\\,\\%$ ($\\delta=-0.99$, $C=0.0612$). With the windows farther",
   "paper_line": 5415,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0343",
   "section": "Saddle-node bottleneck",
   "claim": "number 10.3 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "out the spread rises to 10.3 to 14.0%; there several",
   "paper_text": "farther out the spread rises to $10.3$--$14.0\\,\\%$; there several",
   "paper_line": 5415,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0344",
   "section": "Saddle-node bottleneck",
   "claim": "number 14.0 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "spread rises to 10.3 to 14.0%; there several periods",
   "paper_text": "the spread rises to $10.3$--$14.0\\,\\%$; there several periods",
   "paper_line": 5415,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0345",
   "section": "Saddle-node bottleneck",
   "claim": "number 10^{-5} in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "disconnected runs on the line's \\(10^{-5}\\) grid, and grid-spaced",
   "paper_text": "disconnected runs on the line's $10^{-5}$ grid, and grid-spaced edges",
   "paper_line": 5416,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0346",
   "section": "Saddle-node bottleneck",
   "claim": "number 0.051429 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "**Qwen2.5-7B** (\\(\\alpha = 0.051429\\)). The period-2 orbit",
   "paper_text": "edges. In Qwen2.5-7B ($\\alpha=0.051429$) the period-2 orbit folds",
   "paper_line": 5417,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0347",
   "section": "Saddle-node bottleneck",
   "claim": "number -0.2040156 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T_c = -0.2040156\\) (next modulus 0.0092,",
   "paper_text": "orbit folds at $\\log_{10}T_c=-0.2040156$ (next modulus $0.0092$, $ab=55.7$),",
   "paper_line": 5417,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0348",
   "section": "Saddle-node bottleneck",
   "claim": "number 0.0092 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "-0.2040156\\) (next modulus 0.0092, \\(ab = 55.7\\)), and odd",
   "paper_text": "$\\log_{10}T_c=-0.2040156$ (next modulus $0.0092$, $ab=55.7$), and odd windows",
   "paper_line": 5417,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0349",
   "section": "Saddle-node bottleneck",
   "claim": "number 55.7 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "modulus 0.0092, \\(ab = 55.7\\)), and odd",
   "paper_text": "(next modulus $0.0092$, $ab=55.7$), and odd windows accumulate",
   "paper_line": 5417,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0350",
   "section": "Saddle-node bottleneck",
   "claim": "number 11 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "four and five (periods 11 to 17 and 9 to",
   "paper_text": "nearest four and five (periods 11--17 and 9--17) meet the criterion",
   "paper_line": 5418,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0351",
   "section": "Saddle-node bottleneck",
   "claim": "number 17 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and five (periods 11 to 17 and 9 to",
   "paper_text": "four and five (periods 11--17 and 9--17) meet the criterion",
   "paper_line": 5418,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0352",
   "section": "Saddle-node bottleneck",
   "claim": "number 17 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "17) meet the criterion within",
   "paper_text": "four and five (periods 11--17 and 9--17) meet the criterion",
   "paper_line": 5418,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0353",
   "section": "Saddle-node bottleneck",
   "claim": "number 4.5 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "meet the criterion within 4.5%, and six (to period 7)",
   "paper_text": "meet the criterion within $4.5\\,\\%$, and six (to period 7)",
   "paper_line": 5418,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0354",
   "section": "Saddle-node bottleneck",
   "claim": "number 6.1 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "six (to period 7) within 6.1%. Each",
   "paper_text": "and six (to period 7) within $6.1\\,\\%$. Each window's own doubling",
   "paper_line": 5419,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0355",
   "section": "Saddle-node bottleneck",
   "claim": "number 16 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of periods 16 to 20; this organization",
   "paper_text": "the 0.5B windows of periods 16--20; this organization is consistent",
   "paper_line": 5420,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0356",
   "section": "Saddle-node bottleneck",
   "claim": "number 20 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of periods 16 to 20; this organization is consistent",
   "paper_text": "0.5B windows of periods 16--20; this organization is consistent",
   "paper_line": 5420,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0357",
   "section": "Saddle-node bottleneck",
   "claim": "number 0.97 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\sqrt{Cab}/\\pi\\) is about 0.97 at 1.5B and",
   "paper_text": "$f=\\sqrt{Cab}/\\pi$ is about $0.97$ at 1.5B and $0.78$ to $0.81$",
   "paper_line": 5421,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0358",
   "section": "Saddle-node bottleneck",
   "claim": "number 0.78 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.78 to 0.81 at 7B, against",
   "paper_text": "is about $0.97$ at 1.5B and $0.78$ to $0.81$ at 7B, against $0.58$",
   "paper_line": 5421,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0359",
   "section": "Saddle-node bottleneck",
   "claim": "number 0.81 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.78 to 0.81 at 7B, against 0.58 at",
   "paper_text": "$0.97$ at 1.5B and $0.78$ to $0.81$ at 7B, against $0.58$ at 0.5B.",
   "paper_line": 5421,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0360",
   "section": "Saddle-node bottleneck",
   "claim": "number 0.58 in 'Saddle-node bottleneck' (generated: post phrase matched to the paper's source text)",
   "appears_as": "to 0.81 at 7B, against 0.58 at 0.5B. The fold and its",
   "paper_text": "$0.78$ to $0.81$ at 7B, against $0.58$ at 0.5B. The fold and its",
   "paper_line": 5422,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0361",
   "section": "Transcripts",
   "claim": "number 1.9 in 'Transcripts' (generated: post phrase matched to the paper's source text) (paper 318f8980)",
   "appears_as": "of how spread out it is: 1.9 and 2.4 for",
   "paper_text": "$0.071674$ & period 8 & 1.9 &",
   "paper_line": 1577,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0362",
   "section": "Transcripts",
   "claim": "number 2.4 in 'Transcripts' (generated: post phrase matched to the paper's source text)",
   "appears_as": "spread out it is: 1.9 and 2.4 for",
   "paper_text": "the sixth ($\\alpha=0.10553$) 2.4 times as fast after a hundredfold",
   "paper_line": 1141,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0363",
   "section": "Transcripts",
   "claim": "number 1.8 in 'Transcripts' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the first pair, 1.8 and 2.4 for the second.",
   "paper_text": "slopes lay between about $-1.8$ and $-1.5$, close to $-3/2$;",
   "paper_line": 3762,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0364",
   "section": "Transcripts",
   "claim": "number 2.4 in 'Transcripts' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the first pair, 1.8 and 2.4 for the second.",
   "paper_text": "the sixth ($\\alpha=0.10553$) 2.4 times as fast after a hundredfold",
   "paper_line": 1141,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0365",
   "section": "Transcripts",
   "claim": "number 2000 in 'Transcripts' (generated: post phrase matched to the paper's source text)",
   "appears_as": "over 2000 steps after 1000 transient",
   "paper_text": "$\\lambda$: largest exponent over 2000 steps after 1000 transient",
   "paper_line": 1587,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0366",
   "section": "Transcripts",
   "claim": "number 1000 in 'Transcripts' (generated: post phrase matched to the paper's source text)",
   "appears_as": "over 2000 steps after 1000 transient steps, the same",
   "paper_text": "exponent over 2000 steps after 1000 transient steps, the same to",
   "paper_line": 1587,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0367",
   "section": "Transcripts",
   "claim": "number 10^{-6} in 'Transcripts' (generated: post phrase matched to the paper's source text)",
   "appears_as": "offsets \\(10^{-6}\\) and \\(10^{-9}\\):",
   "paper_text": "twins at relative offsets $10^{-6}$ and $10^{-8}$ over 1000 steps",
   "paper_line": 1004,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0368",
   "section": "Transcripts",
   "claim": "number 10^{-9} in 'Transcripts' (generated: post phrase matched to the paper's source text)",
   "appears_as": "offsets \\(10^{-6}\\) and \\(10^{-9}\\):",
   "paper_text": "twin offsets $10^{-6}$ and $10^{-9}$. $H$: mean entropy of the",
   "paper_line": 1587,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fold-0369",
   "section": "Transcripts",
   "claim": "number 0.071674 in 'Transcripts' (generated: post phrase matched to the paper's source text)",
   "appears_as": "alpha = 0.071674, period 8:            is",
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   "paper_text": "effect: 13.0 points ($[7.2,18.8]$ over 24 prohibited instances)",
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   "paper_text": "prohibited instances) after the 32 steps at the final strength,",
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   "paper_file": "paper/llm/main.tex"
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   "paper_line": 5602,
   "paper_file": "paper/llm/main.tex"
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   "section": "Steering controls",
   "claim": "number 0.66 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
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   "paper_line": 5602,
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   "paper_line": 5602,
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   "paper_text": "to 52; within $\\log_{10}T\\in[-0.3,0.3]$ its chaotic share, 41\\,\\%,",
   "paper_line": 5603,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "last-0023",
   "section": "Steering controls",
   "claim": "number 0.3 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "52; within $\\log_{10}T\\in[-0.3,0.3]$ its chaotic share, 41\\,\\%,",
   "paper_line": 5603,
   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Steering controls",
   "claim": "number 41 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
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   "paper_line": 5603,
   "paper_file": "paper/llm/main.tex"
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   "paper_line": 5603,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "last-0026",
   "section": "Steering controls",
   "claim": "number -0.07 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
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   "paper_line": 5604,
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   "section": "Steering controls",
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   "paper_text": "between $\\log_{10}T=-0.07$ and $0.28$ (exponents up to $0.74$),",
   "paper_line": 5604,
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   "claim": "number 0.74 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
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   "paper_line": 5604,
   "paper_file": "paper/llm/main.tex"
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   "id": "last-0029",
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   "paper_text": "$0.74$), and OLMo-2 7B has 32 between $0.04$ and $0.14$ (up",
   "paper_line": 5604,
   "paper_file": "paper/llm/main.tex"
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  {
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   "paper_line": 5604,
   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Steering controls",
   "claim": "number 0.14 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Steering controls",
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   "paper_line": 5643,
   "paper_file": "paper/llm/main.tex"
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   "paper_line": 5643,
   "paper_file": "paper/llm/main.tex"
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   "paper_line": 5643,
   "paper_file": "paper/llm/main.tex"
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   "claim": "number 1000 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "mixture-of-experts models; 1000 transient and 2000 measured",
   "paper_line": 5644,
   "paper_file": "paper/llm/main.tex"
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   "claim": "number 2000 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
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   "paper_line": 5644,
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   "claim": "number 64 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
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   "paper_line": 5644,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "last-0039",
   "section": "Steering controls",
   "claim": "number 10^{-3} in 'Steering controls' (generated: post phrase matched to the paper's source text)",
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   "section": "Steering controls",
   "claim": "number 128 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "(Figure~\\ref{fig:controls}). On the same $128^2$ grid, 7.6, 8.3 and 12.5\\,\\%",
   "paper_line": 5615,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "last-0041",
   "section": "Steering controls",
   "claim": "number 7.6 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "(Figure~\\ref{fig:controls}). On the same $128^2$ grid, 7.6, 8.3 and 12.5\\,\\% of cells",
   "paper_line": 5615,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "last-0042",
   "section": "Steering controls",
   "claim": "number 8.3 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
   "appears_as": "same \\(128^2\\) grid, 7.6, 8.3",
   "paper_text": "the same $128^2$ grid, 7.6, 8.3 and 12.5\\,\\% of cells are chaotic",
   "paper_line": 5615,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "last-0043",
   "section": "Steering controls",
   "claim": "number 12.5 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "$128^2$ grid, 7.6, 8.3 and 12.5\\,\\% of cells are chaotic for",
   "paper_line": 5615,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "last-0044",
   "section": "Steering controls",
   "claim": "number 6.8 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
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   "paper_line": 5616,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "last-0045",
   "section": "Steering controls",
   "claim": "number 7.5 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "6.8\\,\\% for philosophy and 7.5\\,\\% for gratitude. In all five",
   "paper_line": 5617,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "last-0046",
   "section": "Steering controls",
   "claim": "number 0.01 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lvert\\alpha\\rvert < 0.01\\) to between 5",
   "paper_text": "from about 1\\,\\% at $|\\alpha|<0.01$ to between 5 and 22\\,\\% at",
   "paper_line": 5617,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "last-0047",
   "section": "Steering controls",
   "claim": "number 22 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and 22% at larger \\(\\lvert\\alpha\\rvert\\),",
   "paper_text": "$|\\alpha|<0.01$ to between 5 and 22\\,\\% at larger $|\\alpha|$, and",
   "paper_line": 5618,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "last-0048",
   "section": "Steering controls",
   "claim": "number 13 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
   "appears_as": "chaotic share stays between 13 and 24% at every one",
   "paper_text": "chaotic share stays between 13 and 24\\,\\% at every one of",
   "paper_line": 5622,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "last-0049",
   "section": "Steering controls",
   "claim": "number 24 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
   "appears_as": "share stays between 13 and 24% at every one",
   "paper_text": "share stays between 13 and 24\\,\\% at every one of 103 angles",
   "paper_line": 5622,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "last-0050",
   "section": "Steering controls",
   "claim": "number 103 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of 103 angles.",
   "paper_text": "and 24\\,\\% at every one of 103 angles (Figure~\\ref{fig:morph});",
   "paper_line": 766,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "last-0051",
   "section": "Steering controls",
   "claim": "number 9.9 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
   "appears_as": ") gives 9.9% chaotic cells for the",
   "paper_text": "philosophy texts is 0.27) gives 9.9\\,\\% chaotic cells for the neuron",
   "paper_line": 5624,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "last-0052",
   "section": "Steering controls",
   "claim": "number 5.1 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
   "appears_as": "fixed before any map, 5.1% for its index neighbor",
   "paper_text": "rule fixed before any map, 5.1\\,\\% for its index neighbor",
   "paper_line": 5626,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "last-0053",
   "section": "Steering controls",
   "claim": "number 12.9 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
   "appears_as": "its index neighbor and 12.9% for a random neuron",
   "paper_text": "for its index neighbor and 12.9\\,\\% for a random neuron (Figure~\\ref{fig:neurons});",
   "paper_line": 5626,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "last-0054",
   "section": "Steering controls",
   "claim": "number 0.4 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\alpha = 0\\) the share is 0.4 to",
   "paper_text": "near $\\alpha=0$ the share is 0.4 to 1.2\\,\\%. The direction does",
   "paper_line": 5627,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "last-0055",
   "section": "Steering controls",
   "claim": "number 1.2 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
   "appears_as": "1.2%. The direction does select",
   "paper_text": "$\\alpha=0$ the share is 0.4 to 1.2\\,\\%. The direction does select",
   "paper_line": 5627,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "last-0056",
   "section": "Steering controls",
   "claim": "number 26 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
   "appears_as": "loop, but beyond it only 26 to 56% of one map's cells",
   "paper_text": "period-5 loop, but beyond it only 26 to 56\\,\\% of one map's cells",
   "paper_line": 5628,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "last-0057",
   "section": "Steering controls",
   "claim": "number 56 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
   "appears_as": "but beyond it only 26 to 56% of one map's cells",
   "paper_text": "loop, but beyond it only 26 to 56\\,\\% of one map's cells carry",
   "paper_line": 5628,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "last-0058",
   "section": "Steering controls",
   "claim": "number 26 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the same layer give 26 and 17% chaotic cells against",
   "paper_text": "directions at the same layer give 26 and 17\\,\\% chaotic cells against",
   "paper_line": 5629,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "last-0059",
   "section": "Steering controls",
   "claim": "number 17 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
   "appears_as": "same layer give 26 and 17% chaotic cells against",
   "paper_text": "the same layer give 26 and 17\\,\\% chaotic cells against 28\\,\\%",
   "paper_line": 5629,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "last-0060",
   "section": "Steering controls",
   "claim": "number 28 in 'Steering controls' (generated: post phrase matched to the paper's source text)",
   "appears_as": "17% chaotic cells against 28% along the concept direction;",
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   "section": "Discussion",
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   "section": "Discussion",
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   "section": "Discussion",
   "claim": "number 448 in 'Discussion' (generated: post phrase matched to the paper's source text) (paper 318f8980)",
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   "paper_file": "paper/llm/main.tex"
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   "paper_text": "with bin means and bootstrap 95\\,\\% intervals.} \\label{fig:reservoir}",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Discussion",
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   "paper_file": "paper/llm/main.tex"
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   "paper_file": "paper/llm/main.tex"
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   "section": "Methods in detail",
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   "section": "Methods in detail",
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   "paper_text": "last state returns to within $10^{-8}\\max(1,\\lVert x\\rVert)$ of the",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Methods in detail",
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   "section": "Methods in detail",
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   "section": "Methods in detail",
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  {
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   "section": "Methods in detail",
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  {
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   "section": "Methods in detail",
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   "paper_text": "legend reads `Lyapunov $>$ 0.005' follow an older convention",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Methods in detail",
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   "section": "Methods in detail",
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   "paper_text": "the two differ in at most $0.56\\,\\%$ of a map's cells. A $256^2$",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Methods in detail",
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   "paper_text": "the tool recovers a cusp to $10^{-6}$ (with $c=-1$ and $\\det K=1$)",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Methods in detail",
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   "paper_text": "strict crossing $v>U$, with $U=0.1/|b|$. We compare passage counts",
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   "section": "Methods in detail",
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   "section": "Methods in detail",
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   "paper_file": "paper/llm/main.tex"
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   "paper_text": "the rotation video ran on RTX 4090 GPUs; the first reset test",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "methods-0032",
   "section": "Methods in detail",
   "claim": "number 4\\times10^{-15} in 'Methods in detail' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "computations on a CPU and an H100 to $4\\times10^{-15}$. Continuing a just-born doubled",
   "paper_line": 1853,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0033",
   "section": "Evidence grading",
   "claim": "number 18 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "which also reproduces all 18 fixed-start passage counts);",
   "paper_text": "reimplementation reproduces all 18 fixed-entrance counts of the",
   "paper_line": 5873,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0034",
   "section": "Evidence grading",
   "claim": "number 4\\times10^{-15} in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "computations agree to \\(4\\times10^{-15}\\)); the hostile 2-cycle",
   "paper_text": "parameters (CPU and H100, agreement $4\\times10^{-15}$). \\item Rung 2 as well: the",
   "paper_line": 5880,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0035",
   "section": "Evidence grading",
   "claim": "number 12 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "Unfolding offsets, frozen & 12 & 12 & counts 12/12, stability",
   "paper_line": 5813,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0036",
   "section": "Evidence grading",
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   "paper_text": "Unfolding offsets, frozen & 12 & 12 & counts 12/12, stability",
   "paper_line": 5813,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0037",
   "section": "Evidence grading",
   "claim": "number 11 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "12 & counts 12/12, stability 11/12 \\\\ Shrimp-candidate regions",
   "paper_line": 5813,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0038",
   "section": "Evidence grading",
   "claim": "number 12 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "Unfolding offsets, frozen & 12 & 12 & counts 12/12, stability",
   "paper_line": 5813,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0039",
   "section": "Evidence grading",
   "claim": "number 13 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "period-5 orbit census (9 of 13 counts); the answer-level",
   "paper_text": "the predicted counts at 9 of 13 points and found two coexisting",
   "paper_line": 268,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0040",
   "section": "Evidence grading",
   "claim": "number 448 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "batch-layout comparison (448 cells, four comparisons);",
   "paper_text": "0.5B batch-layout comparison (448 cells, four comparisons) and",
   "paper_line": 5902,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0041",
   "section": "Evidence grading",
   "claim": "number 5353 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and crossover summaries (5353, 6837 and 24 cells); the",
   "paper_text": "of Section~\\ref{sec:theory} (5353, 6837 and 24 cells); the coefficients",
   "paper_line": 5903,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0042",
   "section": "Evidence grading",
   "claim": "number 6837 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "crossover summaries (5353, 6837 and 24 cells); the coefficients",
   "paper_text": "Section~\\ref{sec:theory} (5353, 6837 and 24 cells); the coefficients",
   "paper_line": 5903,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0043",
   "section": "Evidence grading",
   "claim": "number 24 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "summaries (5353, 6837 and 24 cells); the coefficients",
   "paper_text": "Section~\\ref{sec:theory} (5353, 6837 and 24 cells); the coefficients and",
   "paper_line": 5903,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0044",
   "section": "Evidence grading",
   "claim": "number 2700 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "both period selectors (all 2700 cells); the scalar conditions",
   "paper_text": "both period selectors (all 2700 cells); and the scalar conditions",
   "paper_line": 5905,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0045",
   "section": "Evidence grading",
   "claim": "number 10^{-12} in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "exactly, item-level part to \\(10^{-12}\\)). This reproduces the",
   "paper_text": "exactly, item-level part to $10^{-12}$) (Section~\\ref{sec:huginn}).",
   "paper_line": 5910,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0046",
   "section": "Evidence grading",
   "claim": "number 34 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of the raw data counted 34 distinct maps (987,308",
   "paper_text": "on 14 October 2026 counted 34 distinct maps (987\\,308 cells,",
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   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0047",
   "section": "Evidence grading",
   "claim": "number 987,308 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "counted 34 distinct maps (987,308 cells, 27 of them",
   "paper_text": "2026 counted 34 distinct maps (987\\,308 cells, 27 maps in float64)",
   "paper_line": 5778,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0048",
   "section": "Evidence grading",
   "claim": "number 27 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "distinct maps (987,308 cells, 27 of them",
   "paper_text": "distinct maps (987\\,308 cells, 27 maps in float64) in six models,",
   "paper_line": 5778,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0049",
   "section": "Evidence grading",
   "claim": "number 29 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "float64 maps) in six models; 29 of these maps and one partial",
   "paper_text": "one partial map. Of these, 29 maps and the partial one appear",
   "paper_line": 5779,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0050",
   "section": "Evidence grading",
   "claim": "number 2600 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "contain about 2600 periodic families of at",
   "paper_text": "labeled maps contain about 2600 periodic families of at least",
   "paper_line": 5782,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0051",
   "section": "Evidence grading",
   "claim": "number 26 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "least six cells. About 26 windows or",
   "paper_text": "per map. We singled out about 26 windows or families for float64",
   "paper_line": 5782,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0052",
   "section": "Evidence grading",
   "claim": "number 20 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "singled out for float64 work: 20 are reported in detail,",
   "paper_text": "families for float64 work: 20 are reported in detail, 2 only",
   "paper_line": 5783,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0053",
   "section": "Evidence grading",
   "claim": "number 54 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "within a bounded search). Of 54 Newton orbit attempts,",
   "paper_text": "within a bounded search). Of 54 Newton orbit attempts, 7 failed.",
   "paper_line": 5785,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0054",
   "section": "Evidence grading",
   "claim": "number 34 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Soft-token maps (distinct) | 34 | 29 | plus one partial",
   "paper_text": "Soft-token maps (distinct) & 34 & 29 & plus one partial map,",
   "paper_line": 5805,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0055",
   "section": "Evidence grading",
   "claim": "number 29 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "maps (distinct) | 34 | 29 | plus one partial map,",
   "paper_text": "Soft-token maps (distinct) & 34 & 29 & plus one partial map, reported",
   "paper_line": 5805,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0056",
   "section": "Evidence grading",
   "claim": "number 987,308 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| Cells of those maps | 987,308 | 893,868 | omitted: 5",
   "paper_text": "map, reported \\\\ \\quad cells & 987\\,308 & 893\\,868 & omitted: 5 discovery",
   "paper_line": 5805,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0057",
   "section": "Evidence grading",
   "claim": "number 893,868 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "those maps | 987,308 | 893,868 | omitted: 5 discovery",
   "paper_text": "\\\\ \\quad cells & 987\\,308 & 893\\,868 & omitted: 5 discovery or side",
   "paper_line": 5805,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0058",
   "section": "Evidence grading",
   "claim": "number 2600 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "least 6 cells) | about 2600 | | counted per labeled",
   "paper_text": "labeled maps contain about 2600 periodic families of at least",
   "paper_line": 5782,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0059",
   "section": "Evidence grading",
   "claim": "number 26 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "given float64 work | about 26 | 20 (+2) | +2: map features",
   "paper_text": "given float64 work & $\\approx26$ & 20 (+2) & +2: map features",
   "paper_line": 5810,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0060",
   "section": "Evidence grading",
   "claim": "number 20 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "float64 work | about 26 | 20 (+2) | +2: map features",
   "paper_text": "families for float64 work: 20 are reported in detail, 2 only",
   "paper_line": 5783,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0061",
   "section": "Evidence grading",
   "claim": "number 54 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Newton orbit attempts | 54 | | 7 failed |",
   "paper_text": "within a bounded search). Of 54 Newton orbit attempts, 7 failed.",
   "paper_line": 5785,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0062",
   "section": "Evidence grading",
   "claim": "number 12 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "offsets fixed in advance | 12 | 12 | counts 12 of 12,",
   "paper_text": "Unfolding offsets, frozen & 12 & 12 & counts 12/12, stability",
   "paper_line": 5813,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0063",
   "section": "Evidence grading",
   "claim": "number 12 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "fixed in advance | 12 | 12 | counts 12 of 12, stability",
   "paper_text": "Unfolding offsets, frozen & 12 & 12 & counts 12/12, stability",
   "paper_line": 5813,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0064",
   "section": "Evidence grading",
   "claim": "number 12 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "advance | 12 | 12 | counts 12 of 12, stability 11 of",
   "paper_text": "Unfolding offsets, frozen & 12 & 12 & counts 12/12, stability",
   "paper_line": 5813,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0065",
   "section": "Evidence grading",
   "claim": "number 12 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "12 | 12 | counts 12 of 12, stability 11 of 12 |",
   "paper_text": "Unfolding offsets, frozen & 12 & 12 & counts 12/12, stability",
   "paper_line": 5813,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0066",
   "section": "Evidence grading",
   "claim": "number 11 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "counts 12 of 12, stability 11 of 12 |",
   "paper_text": "12 & counts 12/12, stability 11/12 \\\\ Shrimp-candidate regions",
   "paper_line": 5813,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0067",
   "section": "Evidence grading",
   "claim": "number 12 in 'Evidence grading' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of 12, stability 11 of 12 |",
   "paper_text": "Unfolding offsets, frozen & 12 & 12 & counts 12/12, stability",
   "paper_line": 5813,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0068",
   "section": "Computer-assisted proof",
   "claim": "number 0.071674 in 'Computer-assisted proof' (generated: post phrase matched to the paper's source text)",
   "appears_as": "proof. At \\(\\alpha = 0.071674\\) and \\(\\log_{10}T = -0.115\\),",
   "paper_text": "Table~\\ref{tab:orbits}. At $\\alpha=0.071674$ and $\\log_{10}T=-0.115$, read",
   "paper_line": 5828,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0069",
   "section": "Computer-assisted proof",
   "claim": "number -0.115 in 'Computer-assisted proof' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.071674\\) and \\(\\log_{10}T = -0.115\\), read as exact",
   "paper_text": "$\\alpha=0.071674$ and $\\log_{10}T=-0.115$, read as exact binary64 rationals",
   "paper_line": 5828,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "methods-0070",
   "section": "Computer-assisted proof",
   "claim": "number 24 in 'Computer-assisted proof' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Qwen2.5-0.5B-Instruct checkpoint (all 24 layers, the full 151,936-token",
   "paper_text": "Qwen2.5-0.5B-Instruct checkpoint (all 24 layers, the full 151\\,936-token",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "methods-0071",
   "section": "Computer-assisted proof",
   "claim": "number 151,936 in 'Computer-assisted proof' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(all 24 layers, the full 151,936-token readout,",
   "paper_text": "checkpoint (all 24 layers, the full 151\\,936-token readout, the fixed 37-token",
   "paper_line": 5830,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "methods-0072",
   "section": "Computer-assisted proof",
   "claim": "number 37 in 'Computer-assisted proof' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the fixed 37-token prefix and the steering",
   "paper_text": "151\\,936-token readout, the fixed 37-token prefix, steering after",
   "paper_line": 5831,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "methods-0073",
   "section": "Computer-assisted proof",
   "claim": "number 12 in 'Computer-assisted proof' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and the steering at layer 12) has a primitive period-8",
   "paper_text": "steering after zero-based block 12) has a primitive period-8 orbit,",
   "paper_line": 5831,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "methods-0074",
   "section": "Computer-assisted proof",
   "claim": "number 10 in 'Computer-assisted proof' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\exp(\\ln 10\\cdot\\log_{10}T)\\) for that",
   "paper_text": "is the real number $\\exp(\\ln 10\\cdot\\log_{10}T)$ for that exact",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "methods-0075",
   "section": "Computer-assisted proof",
   "claim": "number 12 in 'Computer-assisted proof' (generated: post phrase matched to the paper's source text)",
   "appears_as": "steering is added after block 12 counted from zero.)",
   "paper_text": "steering after zero-based block 12) has a primitive period-8 orbit,",
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   "paper_file": "paper/llm/main.tex"
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   "id": "onepic-0000",
   "section": "One picture",
   "claim": "number 896 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "state has 896 dimensions by one-dimensional maps",
   "paper_text": "a network with 896-dimensional states shows the signatures of one-dimensional maps.",
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   "paper_file": "paper/llm/main.tex"
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   "id": "onepic-0001",
   "section": "One picture",
   "claim": "number 896 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "896-dimensional states shows the signatures of one-dimensional maps. Every",
   "paper_text": "a network with 896-dimensional states shows the signatures of one-dimensional maps.",
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   "paper_file": "paper/llm/main.tex"
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   "section": "One picture",
   "claim": "number 0.0630 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "between 0.06301 and 0.07773",
   "paper_text": "between 0.06301 and 0.07773",
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   "paper_file": "paper/llm/main.tex"
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   "id": "onepic-0003",
   "section": "One picture",
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   "paper_text": "between 0.06301 and 0.07773",
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   "paper_file": "paper/llm/main.tex"
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   "section": "One picture",
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   "paper_text": "between 0.06609 and 0.07006",
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   "paper_file": "paper/llm/main.tex"
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   "section": "One picture",
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   "paper_text": "between 0.06609 and 0.07006",
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   "id": "onepic-0006",
   "section": "One picture",
   "claim": "number 0.070 in 'One picture' (generated: post phrase matched to the paper's source text)",
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   "paper_file": "paper/llm/main.tex"
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   "section": "One picture",
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  {
   "id": "onepic-0008",
   "section": "One picture",
   "claim": "number 59 in 'One picture' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "from $\\log_{10}T=-2$ upward, 59 end on ``\\textbackslash n\\textbackslash",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "onepic-0009",
   "section": "One picture",
   "claim": "number 16 in 'One picture' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "n\\textbackslash nThe question'' and 16 on a period-4 loop that alternates",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "onepic-0010",
   "section": "One picture",
   "claim": "number 0.12 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "between 0 and 0.12 (in steps of 0.0005)",
   "paper_text": "between 0 and 0.12 (in steps of 0.0005)",
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   "paper_file": "paper/llm/main.tex"
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   "id": "onepic-0011",
   "section": "One picture",
   "claim": "number 0.070 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\alpha = 0.070\\) the 2-cycle loses stability",
   "paper_text": "both of its ends. At $\\alpha=0.070$ the 2-cycle is stable between",
   "paper_line": 3067,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "onepic-0012",
   "section": "One picture",
   "claim": "number -0.5147881 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "stability at \\(\\log_{10}T = -0.5147881\\),",
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   "paper_file": "paper/llm/main.tex"
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   "id": "onepic-0013",
   "section": "One picture",
   "claim": "number 0.070 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "weakens. At \\(\\alpha = 0.070\\) the",
   "paper_text": "At $\\alpha=0.070$ the 2-cycle is stable between",
   "paper_line": 3067,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0014",
   "section": "One picture",
   "claim": "number -0.1741065 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "disappears at \\(\\log_{10}T = -0.1741065\\), where a multiplier reaches",
   "paper_text": "alternates), and $\\log_{10}T=-0.1741065$, where a multiplier reaches",
   "paper_line": 3069,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0015",
   "section": "One picture",
   "claim": "number 0.065 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "extrapolated to \\(\\log_{10}T = -0.14536\\)",
   "paper_text": "extrapolated to $\\log_{10}T=-0.14536$",
   "paper_line": 3072,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0016",
   "section": "One picture",
   "claim": "number -0.14536 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "extrapolated to \\(\\log_{10}T = -0.14536\\)",
   "paper_text": "extrapolated to $\\log_{10}T=-0.14536$",
   "paper_line": 3072,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0017",
   "section": "One picture",
   "claim": "number -0.148 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the cut \\(\\log_{10}T = -0.148\\) it is born at a fold",
   "paper_text": "$0.0715$. On the cut $\\log_{10}T=-0.148$, the crescent's period-3 orbit",
   "paper_line": 3220,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0018",
   "section": "One picture",
   "claim": "number 0.06444 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\alpha = 0.06444\\) and flips at \\(\\alpha",
   "paper_text": "is born at a fold ($\\alpha=0.06444$) and flips at $\\alpha=0.06548$.",
   "paper_line": 3221,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0019",
   "section": "One picture",
   "claim": "number 0.06548 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and flips at \\(\\alpha = 0.06548\\) (Figure",
   "paper_text": "($\\alpha=0.06444$) and flips at $\\alpha=0.06548$. White circles: the census",
   "paper_line": 3221,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0020",
   "section": "One picture",
   "claim": "number 12 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "period 3 becomes 6, then 12, then 24, and the sequence",
   "paper_text": "showing the doublings $6\\to12\\to24\\to48$",
   "paper_line": 1894,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0021",
   "section": "One picture",
   "claim": "number 24 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "becomes 6, then 12, then 24, and the sequence",
   "paper_text": "showing the doublings $6\\to12\\to24\\to48$",
   "paper_line": 1894,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0022",
   "section": "One picture",
   "claim": "number -0.14 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = -0.14\\) is the first doubling",
   "paper_text": "the stripes near $\\log_{10}T=-0.14$ is the first doubling of the",
   "paper_line": 3081,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0023",
   "section": "One picture",
   "claim": "number 0.070 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\alpha\\). At \\(\\alpha = 0.070\\) it is bounded by two",
   "paper_text": "larger $\\alpha$. At $\\alpha=0.070$ it is bounded by two flips,",
   "paper_line": 3082,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0024",
   "section": "One picture",
   "claim": "number -0.1392937 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at \\(\\log_{10}T = -0.1392937\\) above and \\(-0.1414292\\)",
   "paper_text": "by two flips, at $\\log_{10}T=-0.1392937$ above and $-0.1414292$ below.",
   "paper_line": 3082,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0025",
   "section": "One picture",
   "claim": "number -0.1414292 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "-0.1392937\\) above and \\(-0.1414292\\) below. The two families",
   "paper_text": "$\\log_{10}T=-0.1392937$ above and $-0.1414292$ below. The two families cross",
   "paper_line": 3083,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0026",
   "section": "One picture",
   "claim": "number 896 in 'One picture' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "896 dimensions. Whether such simple laws can describe it",
   "paper_text": "a network with 896-dimensional states shows the signatures of one-dimensional maps.",
   "paper_line": 3047,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0027",
   "section": "One picture",
   "claim": "number 0.23 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "covariance \\(\\Sigma_p\\) is 0.23 to 0.87 of the first,",
   "paper_text": "readout covariance $\\Sigma_p$ is 0.23 to 0.87 of the first, and the",
   "paper_line": 3184,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0028",
   "section": "One picture",
   "claim": "number 0.87 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\Sigma_p\\) is 0.23 to 0.87 of the first,",
   "paper_text": "covariance $\\Sigma_p$ is 0.23 to 0.87 of the first, and the second",
   "paper_line": 3184,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0029",
   "section": "One picture",
   "claim": "number 0.12 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "step derivative is 0.11 to 0.90 of the",
   "paper_text": "step derivative is 0.11 to 0.90 of the first",
   "paper_line": 3185,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0030",
   "section": "One picture",
   "claim": "number 0.80 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "step derivative is 0.11 to 0.90 of the",
   "paper_text": "step derivative is 0.11 to 0.90 of the first",
   "paper_line": 3185,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0031",
   "section": "One picture",
   "claim": "number 0.081 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of the composed map is 0.081 for the 2-cycle, 0.092",
   "paper_text": "leading singular values is 0.081 for the 2-cycle, 0.092 for",
   "paper_line": 3186,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0032",
   "section": "One picture",
   "claim": "number 0.092 in 'One picture' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "values of the composed map is 0.081 for the 2-cycle, 0.092",
   "paper_text": "values is 0.081 for the 2-cycle, 0.092 for the period-3 loop and 0.26",
   "paper_line": 3186,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0033",
   "section": "One picture",
   "claim": "number 0.26 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "period-3 loop and 0.26 for the period-6 band.",
   "paper_text": "0.092 for the period-3 loop and 0.26 for the period-6 band; it falls",
   "paper_line": 3186,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0034",
   "section": "One picture",
   "claim": "number 3\\times10^{-4} in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "period-6 band. It falls to \\(3\\times10^{-4}\\) over",
   "paper_text": "period-6 band; it falls to $3\\times10^{-4}$ over twelve steps of the chaotic",
   "paper_line": 3187,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0035",
   "section": "One picture",
   "claim": "number 4\\times10^{-9} in 'One picture' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "chaotic crescent and to \\(4\\times10^{-9}\\) in the chaotic stripes",
   "paper_text": "the chaotic crescent and to $4\\times10^{-9}$ in the chaotic stripes. These ratios",
   "paper_line": 3187,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0036",
   "section": "One picture",
   "claim": "number 0.109 in 'One picture' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "600 steps their largest exponents are 0.109, 0.424 and 0.239 per step",
   "paper_text": "Over 600 steps their largest exponents are $0.109$, $0.424$ and $0.239$ per step",
   "paper_line": 3194,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0037",
   "section": "One picture",
   "claim": "number 0.424 in 'One picture' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "largest exponents are 0.109, 0.424 and 0.239 per step, and the next",
   "paper_text": "largest exponents are $0.109$, $0.424$ and $0.239$ per step, and the next three",
   "paper_line": 3194,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0038",
   "section": "One picture",
   "claim": "number 0.239 in 'One picture' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "exponents are 0.109, 0.424 and 0.239 per step, and the next",
   "paper_text": "exponents are $0.109$, $0.424$ and $0.239$ per step, and the next three are strongly negative",
   "paper_line": 3194,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0039",
   "section": "One picture",
   "claim": "number −0.82 in 'One picture' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "strongly negative, between −0.82 and −2.01",
   "paper_text": "strongly negative, between $-0.82$ and $-2.01$",
   "paper_line": 3195,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0040",
   "section": "One picture",
   "claim": "number −2.0 in 'One picture' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "three are strongly negative, between −0.82 and −2.01",
   "paper_text": "are strongly negative, between $-0.82$ and $-2.01$",
   "paper_line": 3195,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0041",
   "section": "One picture",
   "claim": "number 1.13 in 'One picture' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "The finite-time estimates are 1.13, 1.43 and 1.21 at the three",
   "paper_text": "the magnitude of the next, are 1.13, 1.43 and 1.21",
   "paper_line": 3196,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0042",
   "section": "One picture",
   "claim": "number 1.43 in 'One picture' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "shape. The finite-time estimates are 1.13, 1.43 and 1.21 at the three cells",
   "paper_text": "divided by the magnitude of the next, are 1.13, 1.43 and 1.21.",
   "paper_line": 3196,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0043",
   "section": "One picture",
   "claim": "number 1.21 in 'One picture' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "estimates are 1.13, 1.43 and 1.21 at the three cells",
   "paper_text": "are 1.13, 1.43 and 1.21. These estimates suggest",
   "paper_line": 3197,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0044",
   "section": "One picture",
   "claim": "number 600 in 'One picture' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "600 steps their largest exponents are 0.109",
   "paper_text": "Over 600 steps their largest exponents are",
   "paper_line": 3194,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0045",
   "section": "One picture",
   "claim": "number 3000 in 'One picture' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "3000 steps the largest exponents are",
   "paper_text": "(Over 3000 steps the largest exponents are",
   "paper_line": 3198,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0046",
   "section": "One picture",
   "claim": "number 0.098 in 'One picture' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "largest exponents are \\(0.098\\pm0.010\\), \\(0.437\\pm0.016\\)",
   "paper_text": "the largest exponents are $0.098\\pm0.010$, $0.437\\pm0.016$ and",
   "paper_line": 3198,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0047",
   "section": "One picture",
   "claim": "number 0.437 in 'One picture' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "are \\(0.098\\pm0.010\\), \\(0.437\\pm0.016\\) and",
   "paper_text": "exponents are $0.098\\pm0.010$, $0.437\\pm0.016$ and $0.196\\pm0.014$;",
   "paper_line": 3198,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0048",
   "section": "One picture",
   "claim": "number 0.196 in 'One picture' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "\\(0.196\\pm0.014\\), the values used",
   "paper_text": "$0.437\\pm0.016$ and $0.196\\pm0.014$; Section~\\ref{sec:dialogue}.)",
   "paper_line": 3199,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0049",
   "section": "One picture",
   "claim": "number -0.156 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = -0.156\\), places its first flip",
   "paper_text": "at $\\log_{10}T=-0.156$, places its first flip between",
   "paper_line": 3204,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0050",
   "section": "One picture",
   "claim": "number 0.06476 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "between \\(\\alpha = 0.0646\\) and 0.0648",
   "paper_text": "between $\\alpha=0.0646$ and 0.0648",
   "paper_line": 3205,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0051",
   "section": "One picture",
   "claim": "number 0.0644767 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.0644767 in the full map.",
   "paper_text": "against 0.0644767 in the full map",
   "paper_line": 3205,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0052",
   "section": "One picture",
   "claim": "number 12 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "philosophy direction, layer 12). <strong>(a) A compromise",
   "paper_text": "philosophy direction, layer 12). (a) Leading multiplier of",
   "paper_line": 3211,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0053",
   "section": "One picture",
   "claim": "number 0.070 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "temperature at \\(\\alpha = 0.070\\). The orbit is stable",
   "paper_text": "along temperature at $\\alpha=0.070$. It is stable (blue, inside",
   "paper_line": 3212,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0054",
   "section": "One picture",
   "claim": "number -0.5148 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the flip (\\(\\log_{10}T = -0.5148\\)), where the multiplier",
   "paper_text": "between the flip ($\\log_{10}T=-0.5148$) and the fold ($-0.1741$).",
   "paper_line": 3212,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0055",
   "section": "One picture",
   "claim": "number -0.1741 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "passes −1, and the fold (\\(-0.1741\\)), where it reaches +1;",
   "paper_text": "($\\log_{10}T=-0.5148$) and the fold ($-0.1741$). The boxes give the two blended",
   "paper_line": 3213,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0056",
   "section": "One picture",
   "claim": "number -0.115 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the row \\(\\log_{10}T = -0.115\\) of the \\(256\\times256\\)",
   "paper_text": "exponent along the row $\\log_{10}T=-0.115$ of the $256\\times256$ map.",
   "paper_line": 3214,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0057",
   "section": "One picture",
   "claim": "number 256 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = -0.115\\) of the \\(256\\times256\\) map. Past the",
   "paper_text": "$\\log_{10}T=-0.115$ of the $256\\times256$ map. Beyond the fold",
   "paper_line": 3214,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0058",
   "section": "One picture",
   "claim": "number 16 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "longer windows (periods 16 to 20) it grows linearly",
   "paper_text": "the longer windows (periods 16 to 20) it grows linearly with",
   "paper_line": 3217,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0059",
   "section": "One picture",
   "claim": "number 20 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "windows (periods 16 to 20) it grows linearly with",
   "paper_text": "longer windows (periods 16 to 20) it grows linearly with the",
   "paper_line": 3217,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0060",
   "section": "One picture",
   "claim": "number 0.069 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "located on cuts at \\(\\alpha = 0.069\\), 0.070 and 0.0715. On",
   "paper_text": "located on cuts at $\\alpha=0.069$, $0.070$ and $0.0715$. On",
   "paper_line": 3220,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0061",
   "section": "One picture",
   "claim": "number 0.070 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at \\(\\alpha = 0.069\\), 0.070 and 0.0715. On the cut",
   "paper_text": "on cuts at $\\alpha=0.069$, $0.070$ and $0.0715$. On the cut $\\log_{10}T=-0.148$,",
   "paper_line": 3220,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0062",
   "section": "One picture",
   "claim": "number 0.0715 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\alpha = 0.069\\), 0.070 and 0.0715. On the cut \\(\\log_{10}T",
   "paper_text": "$\\alpha=0.069$, $0.070$ and $0.0715$. On the cut $\\log_{10}T=-0.148$,",
   "paper_line": 3220,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0063",
   "section": "One picture",
   "claim": "number -0.148 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the cut \\(\\log_{10}T = -0.148\\), the crescent's period-3",
   "paper_text": "$0.0715$. On the cut $\\log_{10}T=-0.148$, the crescent's period-3 orbit",
   "paper_line": 3220,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0064",
   "section": "One picture",
   "claim": "number 0.06444 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "born at a fold (\\(\\alpha = 0.06444\\), green square) and flips",
   "paper_text": "is born at a fold ($\\alpha=0.06444$) and flips at $\\alpha=0.06548$.",
   "paper_line": 3221,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "onepic-0065",
   "section": "One picture",
   "claim": "number 0.06548 in 'One picture' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and flips at \\(\\alpha = 0.06548\\). White circles mark the",
   "paper_text": "($\\alpha=0.06444$) and flips at $\\alpha=0.06548$. White circles: the census",
   "paper_line": 3221,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "reason-0000",
   "section": "Reasoning models",
   "claim": "number 15 in 'Reasoning models' (generated: post phrase matched to the paper's source text)",
   "appears_as": "in concept tokens (the 15",
   "paper_text": "thinks in concept tokens (top 15, $T=0.6$) until its most probable",
   "paper_line": 1396,
   "paper_file": "paper/llm/main.tex"
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   "section": "Reasoning models",
   "claim": "number 0.6 in 'Reasoning models' (generated: post phrase matched to the paper's source text)",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
   "claim": "number 1536 in 'Reasoning models' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "the thinking block, or until 1536 steps. It then answers by sampling",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "reason-0004",
   "section": "Reasoning models",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "paper_text": "check set correctly, against 83\\,\\% with the correct tokenizer",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
   "claim": "number 81 in 'Reasoning models' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "correct tokenizer in bfloat16 and 81\\,\\% in float64",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "paper_file": "paper/llm/main.tex"
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   "paper_text": "soft-thinking answers (243 of 896; 95\\,\\% interval $[24.7,29.5]$),",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "appears_as": "soft-thinking answers (243 of 896; 95% interval [24.7, 29.5]),",
   "paper_text": "soft-thinking answers (243 of 896; 95\\,\\% interval $[24.7,29.5]$),",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "reason-0011",
   "section": "Reasoning models",
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   "appears_as": "(243 of 896; 95% interval [24.7, 29.5]), confirming the",
   "paper_text": "(243 of 896; 95\\,\\% interval $[24.7,29.5]$), confirming the prediction",
   "paper_line": 1405,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "reason-0012",
   "section": "Reasoning models",
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   "appears_as": "896; 95% interval [24.7, 29.5]), confirming the prediction",
   "paper_text": "896; 95\\,\\% interval $[24.7,29.5]$), confirming the prediction",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "paper_file": "paper/llm/main.tex"
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  {
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   "paper_text": "without both cells of this model (21.9\\,\\%)",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "paper_text": "DeepSeek-R1-Distill-Qwen-7B for 14.5\\,\\% of the problems ($[10.9,18.0]$)",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Reasoning models",
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   "paper_text": "14.5\\,\\% of the problems ($[10.9,18.0]$) at 88 to 90\\,\\% accuracy,",
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  {
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   "section": "Reasoning models",
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   "appears_as": "the problems ([10.9, 18.0]) at 88 to 90% accuracy,",
   "paper_text": "14.5\\,\\% of the problems ($[10.9,18.0]$) at 88 to 90\\,\\% accuracy,",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "appears_as": "problems ([10.9, 18.0]) at 88 to 90% accuracy, QwQ-32B",
   "paper_text": "problems ($[10.9,18.0]$) at 88 to 90\\,\\% accuracy, and QwQ-32B",
   "paper_line": 1411,
   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
   "claim": "number 90 in 'Reasoning models' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "problems ($[10.9,18.0]$) at 88 to 90\\,\\% accuracy, and QwQ-32B for",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "reason-0020",
   "section": "Reasoning models",
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   "appears_as": "90% accuracy, QwQ-32B for 19.5%",
   "paper_text": "90\\,\\% accuracy, and QwQ-32B for 19.5\\,\\% ($[16.4,22.3]$) at 86 to",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "paper_text": "and QwQ-32B for 19.5\\,\\% ($[16.4,22.3]$) at 86 to 87\\,\\%, and",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "appears_as": "([16.4, 22.3]) at 86 to 87%, and DeepSeek-R1-Distill-Llama-8B",
   "paper_text": "QwQ-32B for 19.5\\,\\% ($[16.4,22.3]$) at 86 to 87\\,\\%, and DeepSeek-R1-Distill-Llama-8B",
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   "paper_file": "paper/llm/main.tex"
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   "paper_text": "19.5\\,\\% ($[16.4,22.3]$) at 86 to 87\\,\\%, and DeepSeek-R1-Distill-Llama-8B",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Reasoning models",
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   "paper_text": "19.5\\,\\% ($[16.4,22.3]$) at 86 to 87\\,\\%, and DeepSeek-R1-Distill-Llama-8B",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "appears_as": "DeepSeek-R1-Distill-Llama-8B for 28.9%",
   "paper_text": "DeepSeek-R1-Distill-Llama-8B for 28.9\\,\\% ($[23.4,34.4]$) at 74 to",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "paper_text": "DeepSeek-R1-Distill-Llama-8B for 28.9\\,\\% ($[23.4,34.4]$) at 74 to 77\\,\\%. The",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "paper_text": "DeepSeek-R1-Distill-Llama-8B for 28.9\\,\\% ($[23.4,34.4]$) at 74 to 77\\,\\%. The two layouts",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "appears_as": "([23.4, 34.4]) at 74 to 77%. The two layouts disagreed",
   "paper_text": "28.9\\,\\% ($[23.4,34.4]$) at 74 to 77\\,\\%. The two layouts disagreed",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "paper_text": "28.9\\,\\% ($[23.4,34.4]$) at 74 to 77\\,\\%. The two layouts disagreed on correctness",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Reasoning models",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Reasoning models",
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   "paper_text": "DeepSeek-R1-Distill-Qwen-7B for 14.5\\,\\% of the problems ($[10.9,18.0]$)",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Reasoning models",
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   "paper_text": "layouts disagreed on correctness for 11.7, 14.5 and 18.0\\,\\% of the problems.",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Reasoning models",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Reasoning models",
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   "paper_text": "GSM8K the rates were 10.2, 19.9 and 21.5\\,\\% for the same three",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "appears_as": "changed 10.2, 19.9 and 21.5% of the answers for the",
   "paper_text": "the rates were 10.2, 19.9 and 21.5\\,\\% for the same three models.",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
   "claim": "number 7.4 in 'Reasoning models' (generated: post phrase matched to the paper's source text) (paper 318f8980)",
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   "paper_text": "Only in DeepSeek-R1-Distill-Llama-8B did soft thinking change more, by 7.4 points",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Reasoning models",
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   "section": "Reasoning models",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Reasoning models",
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   "paper_text": "by 7.4 points ($[1.9,12.9]$; exact McNemar $p=0.029$, not corrected for the five cells)",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Reasoning models",
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   "paper_text": "and it answered correctly 4.7 points less often",
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   "paper_file": "paper/llm/main.tex"
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   "paper_text": "often ($[-8.6,-0.8]$; McNemar $p=0.096$).",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "paper_text": "often ($[-8.6,-0.8]$; McNemar $p=0.096$).",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "paper_text": "often ($[-8.6,-0.8]$; McNemar $p=0.096$).",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "paper_text": "first model's soft rate was 11.7\\,\\% (difference 2.7 points,",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Reasoning models",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
   "claim": "number −1.6 in 'Reasoning models' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(difference 2.7 points, [−1.6, 6.6]), a separate replication",
   "paper_text": "11.7\\,\\% (difference 2.7 points, $[-1.6,6.6]$), a separate replication",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
   "claim": "number 6.6 in 'Reasoning models' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(difference 2.7 points, [−1.6, 6.6]), a separate replication",
   "paper_text": "(difference 2.7 points, $[-1.6,6.6]$), a separate replication",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "reason-0049",
   "section": "Reasoning models",
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   "appears_as": "DeepSeek-R1-Distill-Qwen-7B (44 to 48% correct) and 67%",
   "paper_text": "DeepSeek-R1-Distill-Qwen-7B (44 to 48\\,\\% correct) and 67\\,\\%",
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   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "reason-0050",
   "section": "Reasoning models",
   "claim": "number 48 in 'Reasoning models' (generated: post phrase matched to the paper's source text)",
   "appears_as": "DeepSeek-R1-Distill-Qwen-7B (44 to 48% correct) and 67% of those",
   "paper_text": "DeepSeek-R1-Distill-Qwen-7B (44 to 48\\,\\% correct) and 67\\,\\% of",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "appears_as": "(44 to 48% correct) and 67% of those of",
   "paper_text": "(44 to 48\\,\\% correct) and 67\\,\\% of those of DeepSeek-R1-Distill-Llama-8B",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
   "claim": "number 39 in 'Reasoning models' (generated: post phrase matched to the paper's source text) (paper 318f8980)",
   "appears_as": "DeepSeek-R1-Distill-Llama-8B (39 to 42% correct).",
   "paper_text": "DeepSeek-R1-Distill-Llama-8B (39 to 42\\,\\% correct).",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
   "claim": "number 42 in 'Reasoning models' (generated: post phrase matched to the paper's source text) (paper 318f8980)",
   "appears_as": "DeepSeek-R1-Distill-Llama-8B (39 to 42% correct).",
   "paper_text": "DeepSeek-R1-Distill-Llama-8B (39 to 42\\,\\% correct).",
   "paper_line": 1426,
   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
   "claim": "number 0.01 in 'Reasoning models' (generated: post phrase matched to the paper's source text)",
   "appears_as": "model is, has stayed below 0.01 nats",
   "paper_text": "the entropy has stayed below 0.01 nats for 256 steps. An exploratory",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "reason-0055",
   "section": "Reasoning models",
   "claim": "number 256 in 'Reasoning models' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "stayed below 0.01 nats for 256 steps. An exploratory rerun",
   "paper_line": 1434,
   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
   "claim": "number 4096 in 'Reasoning models' (generated: post phrase matched to the paper's source text)",
   "appears_as": "with a thinking budget of 4096 steps",
   "paper_text": "it, with a thinking budget of 4096 steps",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
   "claim": "number 1536 in 'Reasoning models' (generated: post phrase matched to the paper's source text)",
   "appears_as": "instead of 1536. Cold Stop ended thinking",
   "paper_text": "its own within the original 1536 steps was reproduced exactly",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "reason-0059",
   "section": "Reasoning models",
   "claim": "number 512 in 'Reasoning models' (generated: post phrase matched to the paper's source text)",
   "appears_as": "none of the 512 sampled rows: the models",
   "paper_text": "soft rows and in none of the 512 sampled rows; the models nearly",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "reason-0060",
   "section": "Reasoning models",
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   "appears_as": "DeepSeek-R1-Distill-Qwen-7B on 128 GSM8K problems: 8.6% (soft)",
   "paper_text": "DeepSeek-R1-Distill-Qwen-7B on 128 GSM8K problems, 50.0 and 54.7\\,\\%",
   "paper_line": 1438,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "reason-0061",
   "section": "Reasoning models",
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   "appears_as": "on 128 GSM8K problems: 8.6% (soft) and 17.2%",
   "paper_text": "still changed the answers: 8.6\\,\\% (soft) and 17.2\\,\\% (sampled)",
   "paper_line": 1437,
   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "appears_as": "problems: 8.6% (soft) and 17.2%",
   "paper_text": "answers: 8.6\\,\\% (soft) and 17.2\\,\\% (sampled) for DeepSeek-R1-Distill-Qwen-7B",
   "paper_line": 1437,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "reason-0063",
   "section": "Reasoning models",
   "claim": "number 50.0 in 'Reasoning models' (generated: post phrase matched to the paper's source text)",
   "appears_as": "same model on MATH-500: 50.0 and 54.7%;",
   "paper_text": "DeepSeek-R1-Distill-Qwen-7B on 128 GSM8K problems, 50.0 and 54.7\\,\\% for it on MATH-500,",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "paper_text": "128 GSM8K problems, 50.0 and 54.7\\,\\% for it on MATH-500, and",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "paper_text": "and 9.4\\,\\% for QwQ-32B on 64 GSM8K problems. The soft-minus-sampled",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "appears_as": "QwQ-32B on 64 GSM8K problems: 17.2 and 9.4%.",
   "paper_text": "54.7\\,\\% for it on MATH-500, and 17.2 and 9.4\\,\\% for QwQ-32B on",
   "paper_line": 1438,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "reason-0067",
   "section": "Reasoning models",
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   "appears_as": "GSM8K problems: 17.2 and 9.4%.",
   "paper_text": "it on MATH-500, and 17.2 and 9.4\\,\\% for QwQ-32B on 64 GSM8K",
   "paper_line": 1438,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "reason-0068",
   "section": "Reasoning models",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "reason-0070",
   "section": "Reasoning models",
   "claim": "number 90 in 'Reasoning models' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "reasoning models that answer 86 to 90\\,\\% of them correctly (DeepSeek-R1-Distill-Qwen-7B,",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "reason-0071",
   "section": "Reasoning models",
   "claim": "number 14.5 in 'Reasoning models' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "DeepSeek-R1-Distill-Qwen-7B for 14.5\\,\\% of the problems ($[10.9,18.0]$)",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "reason-0072",
   "section": "Reasoning models",
   "claim": "number 19.5 in 'Reasoning models' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "(DeepSeek-R1-Distill-Qwen-7B, QwQ-32B) changed 14.5 and 19.5\\,\\%, the two layouts disagreeing on correctness for",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Reasoning models",
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   "paper_text": "19.5\\,\\%, the two layouts disagreeing on correctness for 11.7 and 14.5\\,\\% of the problems.",
   "paper_line": 61,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "reason-0074",
   "section": "Reasoning models",
   "claim": "correctness disagreement of the two layouts, larger value, in 'Reasoning models'; range ends at their extremes, 11.7 and 14.5, since report f0a09f7f (paper 4e6e2ec6)",
   "appears_as": "the two layouts disagreeing on correctness for 11.7 and 14.5% of the problems, and",
   "paper_text": "disagreeing on correctness for 11.7 and 14.5\\,\\% of the problems. Ordinary",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "reason-0075",
   "section": "Reasoning models",
   "claim": "number 10^{-10} in 'Reasoning models' (generated: post phrase matched to the paper's source text)",
   "appears_as": "base row's by a relative \\(10^{-10}\\), far below any",
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   "section": "Reasoning models",
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   "paper_text": "DeepSeek-R1-Distill-Qwen-7B, 216 of 256 copies ended the thinking",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "paper_text": "DeepSeek-R1-Distill-Qwen-7B, 216 of 256 copies ended the thinking at",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "section": "Reasoning models",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Reasoning models",
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  {
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   "section": "Reasoning models",
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  {
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   "section": "Reasoning models",
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  {
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   "section": "Reasoning models",
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   "paper_text": "the median growth rates were 0.011 and 0.008 per step. The displacement",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "paper_text": "growth rates were 0.011 and 0.008 per step. The displacement",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "paper_text": "displacement alone changed 13.5 and 18.4\\,\\% of the answers,",
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  {
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   "section": "Reasoning models",
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   "paper_text": "displacement alone changed 13.5 and 18.4\\,\\% of the answers, respectively.",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Reasoning models",
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   "section": "Reasoning models",
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  {
   "id": "reason-0090",
   "section": "Reasoning models",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "reason-0091",
   "section": "Reasoning models",
   "claim": "number 96 in 'Reasoning models' (generated: post phrase matched to the paper's source text)",
   "appears_as": "smaller models and 96 for QwQ-32B.",
   "paper_text": "128 problems for each 7--8B model and 96 for QwQ-32B)",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Replication and size",
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   "paper_text": "Qwen2.5-1.5B (steering at layer 14 of 28), a coarse $64^2$ float64 map",
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   "paper_file": "paper/llm/main.tex"
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   "paper_file": "paper/llm/main.tex"
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   "section": "Replication and size",
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   "section": "Replication and size",
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   "id": "scale-0015",
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   "claim": "number -0.0019002 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(8\\times10^{-5}\\)), \\(-0.0019002\\) (16 → 32, next modulus",
   "paper_text": "modulus $8\\times10^{-5}$), $-0.0019002$ (period $16\\to32$, next modulus",
   "paper_line": 5287,
   "paper_file": "paper/llm/main.tex"
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   "id": "scale-0016",
   "section": "Replication and size",
   "claim": "number 16 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(8\\times10^{-5}\\)), \\(-0.0019002\\) (16 → 32, next modulus",
   "paper_text": "$0.014$), $-0.0021666$ (period $8\\to16$, next modulus $8\\times10^{-5}$),",
   "paper_line": 5287,
   "paper_file": "paper/llm/main.tex"
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   "id": "scale-0017",
   "section": "Replication and size",
   "claim": "number 32 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(8\\times10^{-5}\\)), \\(-0.0019002\\) (16 → 32, next modulus",
   "paper_text": "$-0.0019002$ (period $16\\to32$, next modulus $5\\times10^{-9}$)",
   "paper_line": 5288,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0018",
   "section": "Replication and size",
   "claim": "number 5\\times10^{-9} in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(5\\times10^{-9}\\)) and \\(-0.0018380\\) (32",
   "paper_text": "(period $16\\to32$, next modulus $5\\times10^{-9}$) and $-0.0018380$ (period",
   "paper_line": 5288,
   "paper_file": "paper/llm/main.tex"
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   "section": "Replication and size",
   "claim": "number -0.0018380 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(5\\times10^{-9}\\)) and \\(-0.0018380\\) (32 → 64). Along the",
   "paper_text": "modulus $5\\times10^{-9}$) and $-0.0018380$ (period $32\\to64$). Along",
   "paper_line": 5288,
   "paper_file": "paper/llm/main.tex"
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   "id": "scale-0020",
   "section": "Replication and size",
   "claim": "number 32 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(5\\times10^{-9}\\)) and \\(-0.0018380\\) (32 → 64). Along the way the",
   "paper_text": "$5\\times10^{-9}$) and $-0.0018380$ (period $32\\to64$). Along the way the exponent",
   "paper_line": 5288,
   "paper_file": "paper/llm/main.tex"
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   "id": "scale-0021",
   "section": "Replication and size",
   "claim": "number 64 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and \\(-0.0018380\\) (32 → 64). Along the way the exponent",
   "paper_text": "$-0.0018380$ (period $32\\to64$). Along the way the exponent",
   "paper_line": 5288,
   "paper_file": "paper/llm/main.tex"
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   "id": "scale-0022",
   "section": "Replication and size",
   "claim": "number 3.60 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "The interval ratios are 3.60, 4.28, 4.58,",
   "paper_text": "follows. The interval ratios are $3.60$, $4.28$, $4.58$, $4.648$ and",
   "paper_line": 5289,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0023",
   "section": "Replication and size",
   "claim": "number 4.28 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "interval ratios are 3.60, 4.28, 4.58,",
   "paper_text": "interval ratios are $3.60$, $4.28$, $4.58$, $4.648$ and $4.665$;",
   "paper_line": 5289,
   "paper_file": "paper/llm/main.tex"
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   "id": "scale-0024",
   "section": "Replication and size",
   "claim": "number 4.58 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "ratios are 3.60, 4.28, 4.58,",
   "paper_text": "ratios are $3.60$, $4.28$, $4.58$, $4.648$ and $4.665$; the",
   "paper_line": 5289,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "scale-0025",
   "section": "Replication and size",
   "claim": "number 4.648 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "4.648 and 4.665; the last three",
   "paper_text": "are $3.60$, $4.28$, $4.58$, $4.648$ and $4.665$; the last three",
   "paper_line": 5289,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "scale-0026",
   "section": "Replication and size",
   "claim": "number 4.665 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "4.648 and 4.665; the last three use the",
   "paper_text": "$4.28$, $4.58$, $4.648$ and $4.665$; the last three use the flips",
   "paper_line": 5290,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0027",
   "section": "Replication and size",
   "claim": "number -0.0018244 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "orbits at \\(\\log_{10}T = -0.0018244\\), \\(-0.00182151\\) and",
   "paper_text": "period-256 orbits at $\\log_{10}T=-0.0018244$, $-0.00182151$ and $-0.00182088$",
   "paper_line": 5290,
   "paper_file": "paper/llm/main.tex"
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   "id": "scale-0028",
   "section": "Replication and size",
   "claim": "number -0.00182151 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = -0.0018244\\), \\(-0.00182151\\) and",
   "paper_text": "at $\\log_{10}T=-0.0018244$, $-0.00182151$ and $-0.00182088$ (next moduli",
   "paper_line": 5291,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0029",
   "section": "Replication and size",
   "claim": "number -0.00182088 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-0.00182088\\) (next moduli below \\(3\\times10^{-14}\\)).",
   "paper_text": "$\\log_{10}T=-0.0018244$, $-0.00182151$ and $-0.00182088$ (next moduli below $3\\times10^{-14}$).",
   "paper_line": 5291,
   "paper_file": "paper/llm/main.tex"
  },
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   "id": "scale-0030",
   "section": "Replication and size",
   "claim": "number 3\\times10^{-14} in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-0.00182088\\) (next moduli below \\(3\\times10^{-14}\\)). The last ratio differs",
   "paper_text": "$-0.00182088$ (next moduli below $3\\times10^{-14}$). The last ratio differs from",
   "paper_line": 5291,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "scale-0031",
   "section": "Replication and size",
   "claim": "number 4.6692 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "from Feigenbaum's 4.6692 by 0.0044 (0.1%); the period-256",
   "paper_text": "differs from Feigenbaum's $4.6692$ by $0.0044$ (0.1\\,\\%); the",
   "paper_line": 5292,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "scale-0032",
   "section": "Replication and size",
   "claim": "number 0.0044 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Feigenbaum's 4.6692 by 0.0044 (0.1%); the period-256",
   "paper_text": "from Feigenbaum's $4.6692$ by $0.0044$ (0.1\\,\\%); the period-256",
   "paper_line": 5292,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0033",
   "section": "Replication and size",
   "claim": "number 0.1 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Feigenbaum's 4.6692 by 0.0044 (0.1%); the period-256 flip",
   "paper_text": "Feigenbaum's $4.6692$ by $0.0044$ (0.1\\,\\%); the period-256 flip is",
   "paper_line": 5292,
   "paper_file": "paper/llm/main.tex"
  },
  {
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   "section": "Replication and size",
   "claim": "number 3\\times10^{-14} in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(3\\times10^{-14}\\) in \\(\\log_{10}T\\), the",
   "paper_text": "period-256 flip is located to about $3\\times10^{-14}$ in $\\log_{10}T$, the floor",
   "paper_line": 5292,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0035",
   "section": "Replication and size",
   "claim": "number 2.84 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "early ratios range from 2.84 to 14.9.",
   "paper_text": "the early ratios range from $2.84$ to $14.9$ (Section~\\ref{sec:cascade}).",
   "paper_line": 5295,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0036",
   "section": "Replication and size",
   "claim": "number 14.9 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "ratios range from 2.84 to 14.9.",
   "paper_text": "ratios range from $2.84$ to $14.9$ (Section~\\ref{sec:cascade}).",
   "paper_line": 5295,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0037",
   "section": "Replication and size",
   "claim": "number 14 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "philosophy direction at layer 14, \\(256^2\\) float64 cells",
   "paper_text": "philosophy direction at layer 14, $256^2$ float64 cells over",
   "paper_line": 3270,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0038",
   "section": "Replication and size",
   "claim": "number 256 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "direction at layer 14, \\(256^2\\) float64 cells over",
   "paper_text": "philosophy direction at layer 14, $256^2$ float64 cells over $\\alpha\\in[0.03,0.12]$,",
   "paper_line": 3270,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0039",
   "section": "Replication and size",
   "claim": "number 0.03 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "cells over \\(\\alpha \\in [0.03, 0.12]\\), \\(\\log_{10}T",
   "paper_text": "float64 cells over $\\alpha\\in[0.03,0.12]$, $\\log_{10}T\\in[-0.2,0.2]$:",
   "paper_line": 3270,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0040",
   "section": "Replication and size",
   "claim": "number 0.12 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "over \\(\\alpha \\in [0.03, 0.12]\\), \\(\\log_{10}T \\in [-0.2,",
   "paper_text": "cells over $\\alpha\\in[0.03,0.12]$, $\\log_{10}T\\in[-0.2,0.2]$:",
   "paper_line": 3270,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0041",
   "section": "Replication and size",
   "claim": "number -0.2 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.12]\\), \\(\\log_{10}T \\in [-0.2, 0.2]\\): largest Lyapunov",
   "paper_text": "$\\alpha\\in[0.03,0.12]$, $\\log_{10}T\\in[-0.2,0.2]$: largest Lyapunov exponent",
   "paper_line": 3271,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0042",
   "section": "Replication and size",
   "claim": "number 0.2 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T \\in [-0.2, 0.2]\\): largest Lyapunov exponent",
   "paper_text": "$\\alpha\\in[0.03,0.12]$, $\\log_{10}T\\in[-0.2,0.2]$: largest Lyapunov exponent",
   "paper_line": 3271,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0043",
   "section": "Replication and size",
   "claim": "number 14 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "philosophy direction at layer 14, along \\(\\log_{10}T\\) at",
   "paper_text": "philosophy direction at layer 14, along $\\log_{10}T$ at $\\alpha=0.100$:",
   "paper_line": 5300,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0044",
   "section": "Replication and size",
   "claim": "number 0.100 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T\\) at \\(\\alpha = 0.100\\): period of the attractor",
   "paper_text": "along $\\log_{10}T$ at $\\alpha=0.100$: period of the attractor reached",
   "paper_line": 5300,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0045",
   "section": "Replication and size",
   "claim": "number 14 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "**Qwen2.5-7B** (steering at layer 14 of 28). Coarse \\(64^2\\)",
   "paper_text": "Qwen2.5-1.5B (steering at layer 14 of 28), a coarse $64^2$ float64",
   "paper_line": 5277,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0046",
   "section": "Replication and size",
   "claim": "number 28 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(steering at layer 14 of 28). Coarse \\(64^2\\) float64",
   "paper_text": "Qwen2.5-1.5B (steering at layer 14 of 28), a coarse $64^2$ float64 map",
   "paper_line": 5277,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0047",
   "section": "Replication and size",
   "claim": "number 64 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "layer 14 of 28). Coarse \\(64^2\\) float64 maps show the",
   "paper_text": "layer 14 of 28), a coarse $64^2$ float64 map over the range",
   "paper_line": 5277,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0048",
   "section": "Replication and size",
   "claim": "number 11 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "periods 2, 4, 3 and 11 dominate the periodic cells.",
   "paper_text": "exponent, and periods 2, 4, 3 and 11 dominate the periodic cells.",
   "paper_line": 5310,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0049",
   "section": "Replication and size",
   "claim": "number 0.12 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(\\(\\alpha \\in [0, 0.12]\\), \\(\\log_{10}T \\in [-0.3,",
   "paper_text": "hostility direction ($\\alpha\\in[0,0.12]$, $\\log_{10}T\\in[-0.3,0.3]$),",
   "paper_line": 5311,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0050",
   "section": "Replication and size",
   "claim": "number -0.3 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.12]\\), \\(\\log_{10}T \\in [-0.3, 0.3]\\)), 24% of cells",
   "paper_text": "($\\alpha\\in[0,0.12]$, $\\log_{10}T\\in[-0.3,0.3]$), 24\\,\\% of cells are",
   "paper_line": 5311,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0051",
   "section": "Replication and size",
   "claim": "number 0.3 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T \\in [-0.3, 0.3]\\)), 24% of cells are",
   "paper_text": "($\\alpha\\in[0,0.12]$, $\\log_{10}T\\in[-0.3,0.3]$), 24\\,\\% of cells are",
   "paper_line": 5311,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0052",
   "section": "Replication and size",
   "claim": "number 24 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T \\in [-0.3, 0.3]\\)), 24% of cells are",
   "paper_text": "$\\log_{10}T\\in[-0.3,0.3]$), 24\\,\\% of cells are chaotic. Bands",
   "paper_line": 5311,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0053",
   "section": "Replication and size",
   "claim": "number 0.1 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T \\approx 0.1\\), with high-entropy chaos",
   "paper_text": "sea below $\\log_{10}T\\approx0.1$, with high-entropy chaos above,",
   "paper_line": 5312,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0054",
   "section": "Replication and size",
   "claim": "number 0.09 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "steering (\\(\\alpha \\gtrsim 0.09\\)). The windows hold genuine",
   "paper_text": "strong steering ($\\alpha\\gtrsim0.09$). The windows hold genuine",
   "paper_line": 5313,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0055",
   "section": "Replication and size",
   "claim": "number -0.0143 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((\\log_{10}T, \\alpha) = (-0.0143, 0.0476)\\) (residual \\(2\\times10^{-14}\\);",
   "paper_text": "nOh'' at $(\\log_{10}T,\\alpha)=(-0.0143,0.0476)$ (residual $2\\times10^{-14}$;",
   "paper_line": 5315,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0056",
   "section": "Replication and size",
   "claim": "number 0.0476 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((\\log_{10}T, \\alpha) = (-0.0143, 0.0476)\\) (residual \\(2\\times10^{-14}\\);",
   "paper_text": "$(\\log_{10}T,\\alpha)=(-0.0143,0.0476)$ (residual $2\\times10^{-14}$;",
   "paper_line": 5315,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0057",
   "section": "Replication and size",
   "claim": "number 2\\times10^{-14} in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(-0.0143, 0.0476)\\) (residual \\(2\\times10^{-14}\\); spectral",
   "paper_text": "$(\\log_{10}T,\\alpha)=(-0.0143,0.0476)$ (residual $2\\times10^{-14}$; spectral radius $1.6\\times10^{-7}$,",
   "paper_line": 5315,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0058",
   "section": "Replication and size",
   "claim": "number 1.6\\times10^{-7} in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "radius \\(1.6\\times10^{-7}\\), nearly superstable),",
   "paper_text": "$2\\times10^{-14}$; spectral radius $1.6\\times10^{-7}$, nearly superstable), and",
   "paper_line": 5315,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0059",
   "section": "Replication and size",
   "claim": "number 0.2524 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "to a period-3 loop at \\((0.2524, 0.1143)\\) (residual \\(3\\times10^{-15}\\);",
   "paper_text": "cell to a period-3 loop at $(0.2524,0.1143)$ (residual $3\\times10^{-15}$;",
   "paper_line": 5316,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0060",
   "section": "Replication and size",
   "claim": "number 0.1143 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "period-3 loop at \\((0.2524, 0.1143)\\) (residual \\(3\\times10^{-15}\\);",
   "paper_text": "a period-3 loop at $(0.2524,0.1143)$ (residual $3\\times10^{-15}$;",
   "paper_line": 5316,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0061",
   "section": "Replication and size",
   "claim": "number 3\\times10^{-15} in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((0.2524, 0.1143)\\) (residual \\(3\\times10^{-15}\\);",
   "paper_text": "$(0.2524,0.1143)$ (residual $3\\times10^{-15}$; leading multiplier $-0.12$).",
   "paper_line": 5317,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0062",
   "section": "Replication and size",
   "claim": "number -0.12 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "leading multiplier \\(-0.12\\)). Where the coarse map",
   "paper_text": "\\item In Qwen2.5 it falls from $-0.12$ at 0.5B to $-1.99$ at 72B,",
   "paper_line": 3443,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0063",
   "section": "Replication and size",
   "claim": "number 0.0495 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "than\"` (between \\(\\alpha = 0.0495\\) and 0.0514 at",
   "paper_text": "better than'' (between $\\alpha=0.0495$ and $0.0514$ at $\\log_{10}T=-0.0143$),",
   "paper_line": 5320,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0064",
   "section": "Replication and size",
   "claim": "number 0.0514 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\alpha = 0.0495\\) and 0.0514 at",
   "paper_text": "(between $\\alpha=0.0495$ and $0.0514$ at $\\log_{10}T=-0.0143$),",
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   "section": "Replication and size",
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   "section": "Replication and size",
   "claim": "number 64 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
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   "section": "Replication and size",
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   "section": "Replication and size",
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   "section": "Replication and size",
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   "section": "Replication and size",
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   "section": "Replication and size",
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   "section": "Replication and size",
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   "section": "Replication and size",
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   "section": "Replication and size",
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   "section": "Replication and size",
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   "paper_text": "\\label{fig:llama} \\end{figure} Maps of $128^2$ cells (Figure~\\ref{fig:llamahires})",
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   "section": "Replication and size",
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   "paper_text": "and period (white: none up to 32).} \\label{fig:llamahires} \\end{figure}",
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   "appears_as": "| 65/512 (12.7%) | 6 | −1.0 to 1.2 | 0.226 | 0.249",
   "paper_text": "& 0.5 & 7/512 (1.4) & 1 & $-1.0$ to $0.3$ & 0.018 & 0.053 &",
   "paper_line": 3343,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0169",
   "section": "Replication and size",
   "claim": "number 1.2 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "65/512 (12.7%) | 6 | −1.0 to 1.2 | 0.226 | 0.249 | +0.88",
   "paper_text": "2/130 (1.5) & 0 & $-1.0$ to $1.2$ & 0.531 & 0.191 & $+0.85$",
   "paper_line": 3344,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0170",
   "section": "Replication and size",
   "claim": "number 0.226 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(12.7%) | 6 | −1.0 to 1.2 | 0.226 | 0.249 | +0.88 |",
   "paper_text": "(12.7) & 6 & $-1.0$ to $1.2$ & 0.226 & 0.249 & $+0.88$ \\\\ Qwen2.5-14B",
   "paper_line": 3346,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0171",
   "section": "Replication and size",
   "claim": "number 0.249 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| −1.0 to 1.2 | 0.226 | 0.249 | +0.88 |",
   "paper_text": "& $-1.0$ to $1.2$ & 0.226 & 0.249 & $+0.88$ \\\\ Qwen2.5-14B &",
   "paper_line": 3346,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0172",
   "section": "Replication and size",
   "claim": "number 0.88 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "1.2 | 0.226 | 0.249 | +0.88 |",
   "paper_text": "leading multiplier rises to $0.88$; both are explained by the",
   "paper_line": 4916,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0173",
   "section": "Replication and size",
   "claim": "number 14.7 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| Qwen2.5-14B | 14.7 | 0/130 (0.0%) | 0 | −1.0",
   "paper_text": "& $+0.88$ \\\\ Qwen2.5-14B & 14.7 & 0/130 (0.0) & 0 & $-1.0$",
   "paper_line": 3346,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0174",
   "section": "Replication and size",
   "claim": "number 0.0 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Qwen2.5-14B | 14.7 | 0/130 (0.0%) | 0 | −1.0 to 1.2 | 0.500",
   "paper_text": "\\\\ Qwen2.5-3B & 3.1 & 0/130 (0.0) & 0 & $-1.0$ to $1.2$ & 0.030",
   "paper_line": 3344,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0175",
   "section": "Replication and size",
   "claim": "number −1.0 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "14.7 | 0/130 (0.0%) | 0 | −1.0 to 1.2 | 0.500 | 0.191",
   "paper_text": "& 0.5 & 7/512 (1.4) & 1 & $-1.0$ to $0.3$ & 0.018 & 0.053 &",
   "paper_line": 3343,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0176",
   "section": "Replication and size",
   "claim": "number 1.2 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0/130 (0.0%) | 0 | −1.0 to 1.2 | 0.500 | 0.191 | +1.14",
   "paper_text": "2/130 (1.5) & 0 & $-1.0$ to $1.2$ & 0.531 & 0.191 & $+0.85$",
   "paper_line": 3344,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0177",
   "section": "Replication and size",
   "claim": "number 0.500 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(0.0%) | 0 | −1.0 to 1.2 | 0.500 | 0.191 | +1.14 |",
   "paper_text": "(0.0) & 0 & $-1.0$ to $1.2$ & 0.500 & 0.191 & $+1.14$ \\\\ Qwen2.5-32B",
   "paper_line": 3347,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0178",
   "section": "Replication and size",
   "claim": "number 0.191 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| −1.0 to 1.2 | 0.500 | 0.191 | +1.14 |",
   "paper_text": "& $-1.0$ to $1.2$ & 0.531 & 0.191 & $+0.85$ \\\\ Qwen2.5-3B & 3.1",
   "paper_line": 3344,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0179",
   "section": "Replication and size",
   "claim": "number 1.14 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "1.2 | 0.500 | 0.191 | +1.14 |",
   "paper_text": "to $1.2$ & 0.500 & 0.191 & $+1.14$ \\\\ Qwen2.5-32B & 32.8 & 0/130",
   "paper_line": 3347,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0180",
   "section": "Replication and size",
   "claim": "number 32.8 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| Qwen2.5-32B | 32.8 | 0/130 (0.0%) | 0 | −1.0",
   "paper_text": "& $+1.14$ \\\\ Qwen2.5-32B & 32.8 & 0/130 (0.0) & 0 & $-1.0$",
   "paper_line": 3347,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0181",
   "section": "Replication and size",
   "claim": "number 0.0 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Qwen2.5-32B | 32.8 | 0/130 (0.0%) | 0 | −1.0 to 1.2 | 0.010",
   "paper_text": "\\\\ Qwen2.5-3B & 3.1 & 0/130 (0.0) & 0 & $-1.0$ to $1.2$ & 0.030",
   "paper_line": 3344,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0182",
   "section": "Replication and size",
   "claim": "number −1.0 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "32.8 | 0/130 (0.0%) | 0 | −1.0 to 1.2 | 0.010 | 0.091",
   "paper_text": "& 0.5 & 7/512 (1.4) & 1 & $-1.0$ to $0.3$ & 0.018 & 0.053 &",
   "paper_line": 3343,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0183",
   "section": "Replication and size",
   "claim": "number 1.2 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0/130 (0.0%) | 0 | −1.0 to 1.2 | 0.010 | 0.091 | +0.36",
   "paper_text": "2/130 (1.5) & 0 & $-1.0$ to $1.2$ & 0.531 & 0.191 & $+0.85$",
   "paper_line": 3344,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0184",
   "section": "Replication and size",
   "claim": "number 0.010 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(0.0%) | 0 | −1.0 to 1.2 | 0.010 | 0.091 | +0.36 |",
   "paper_text": "(0.0) & 0 & $-1.0$ to $1.2$ & 0.010 & 0.091 & $+0.36$ \\\\ Qwen2.5-72B",
   "paper_line": 3348,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0185",
   "section": "Replication and size",
   "claim": "number 0.091 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| −1.0 to 1.2 | 0.010 | 0.091 | +0.36 |",
   "paper_text": "& $-1.0$ to $1.2$ & 0.010 & 0.091 & $+0.36$ \\\\ Qwen2.5-72B &",
   "paper_line": 3348,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0186",
   "section": "Replication and size",
   "claim": "number 0.36 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "1.2 | 0.010 | 0.091 | +0.36 |",
   "paper_text": "to $1.2$ & 0.010 & 0.091 & $+0.36$ \\\\ Qwen2.5-72B & 72.7 & 0/128",
   "paper_line": 3348,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0187",
   "section": "Replication and size",
   "claim": "number 72.7 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| Qwen2.5-72B | 72.7 | 0/128 (0.0%) | 0 | −1.0",
   "paper_text": "& $+0.36$ \\\\ Qwen2.5-72B & 72.7 & 0/128 (0.0) & 0 & $-1.0$",
   "paper_line": 3348,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0188",
   "section": "Replication and size",
   "claim": "number 0.0 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Qwen2.5-72B | 72.7 | 0/128 (0.0%) | 0 | −1.0 to 1.2 | 0.000",
   "paper_text": "\\\\ Qwen2.5-3B & 3.1 & 0/130 (0.0) & 0 & $-1.0$ to $1.2$ & 0.030",
   "paper_line": 3344,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0189",
   "section": "Replication and size",
   "claim": "number −1.0 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "72.7 | 0/128 (0.0%) | 0 | −1.0 to 1.2 | 0.000 | 0.014",
   "paper_text": "& 0.5 & 7/512 (1.4) & 1 & $-1.0$ to $0.3$ & 0.018 & 0.053 &",
   "paper_line": 3343,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0190",
   "section": "Replication and size",
   "claim": "number 1.2 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0/128 (0.0%) | 0 | −1.0 to 1.2 | 0.000 | 0.014 | −0.45",
   "paper_text": "2/130 (1.5) & 0 & $-1.0$ to $1.2$ & 0.531 & 0.191 & $+0.85$",
   "paper_line": 3344,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0191",
   "section": "Replication and size",
   "claim": "number 0.000 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(0.0%) | 0 | −1.0 to 1.2 | 0.000 | 0.014 | −0.45 |",
   "paper_text": "(0.0) & 0 & $-1.0$ to $1.2$ & 0.000 & 0.014 & $-0.45$ \\\\ Llama-3.1-8B",
   "paper_line": 3349,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0192",
   "section": "Replication and size",
   "claim": "number 0.014 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| −1.0 to 1.2 | 0.000 | 0.014 | −0.45 |",
   "paper_text": "& $-1.0$ to $1.2$ & 0.000 & 0.014 & $-0.45$ \\\\ Llama-3.1-8B &",
   "paper_line": 3349,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0193",
   "section": "Replication and size",
   "claim": "number −0.45 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "to 1.2 | 0.000 | 0.014 | −0.45 |",
   "paper_text": "to $1.2$ & 0.000 & 0.014 & $-0.45$ \\\\ Llama-3.1-8B & 8.0 & 96/512",
   "paper_line": 3349,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0194",
   "section": "Replication and size",
   "claim": "number 8.0 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| Llama-3.1-8B | 8.0 | 96/512 (18.8%) | 2 |",
   "paper_text": "& $-0.45$ \\\\ Llama-3.1-8B & 8.0 & 96/512 (18.8) & 2 & $-1.0$",
   "paper_line": 3349,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0195",
   "section": "Replication and size",
   "claim": "number 96 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| Llama-3.1-8B | 8.0 | 96/512 (18.8%) | 2 | −1.0",
   "paper_text": "$-0.45$ \\\\ Llama-3.1-8B & 8.0 & 96/512 (18.8) & 2 & $-1.0$ to",
   "paper_line": 3349,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0196",
   "section": "Replication and size",
   "claim": "number 18.8 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Llama-3.1-8B | 8.0 | 96/512 (18.8%) | 2 | −1.0 to 1.2 | 0.241",
   "paper_text": "Llama-3.1-8B & 8.0 & 96/512 (18.8) & 2 & $-1.0$ to $1.2$ & 0.241",
   "paper_line": 3350,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0197",
   "section": "Replication and size",
   "claim": "number −1.0 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 96/512 (18.8%) | 2 | −1.0 to 1.2 | 0.241 | 0.634",
   "paper_text": "& 72.7 & 0/128 (0.0) & 0 & $-1.0$ to $1.2$ & 0.000 & 0.014 &",
   "paper_line": 3349,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0198",
   "section": "Replication and size",
   "claim": "number 1.2 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "96/512 (18.8%) | 2 | −1.0 to 1.2 | 0.241 | 0.634 | +0.66",
   "paper_text": "0/128 (0.0) & 0 & $-1.0$ to $1.2$ & 0.000 & 0.014 & $-0.45$",
   "paper_line": 3349,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0199",
   "section": "Replication and size",
   "claim": "number 0.241 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(18.8%) | 2 | −1.0 to 1.2 | 0.241 | 0.634 | +0.66 |",
   "paper_text": "(18.8) & 2 & $-1.0$ to $1.2$ & 0.241 & 0.634 & $+0.66$ \\\\ Llama-3.1-70B",
   "paper_line": 3350,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0200",
   "section": "Replication and size",
   "claim": "number 0.634 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| −1.0 to 1.2 | 0.241 | 0.634 | +0.66 |",
   "paper_text": "& $-1.0$ to $1.2$ & 0.241 & 0.634 & $+0.66$ \\\\ Llama-3.1-70B",
   "paper_line": 3350,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0201",
   "section": "Replication and size",
   "claim": "number 0.66 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "1.2 | 0.241 | 0.634 | +0.66 |",
   "paper_text": "to $1.2$ & 0.241 & 0.634 & $+0.66$ \\\\ Llama-3.1-70B & 70.6 &",
   "paper_line": 3350,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0202",
   "section": "Replication and size",
   "claim": "number 70.6 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| Llama-3.1-70B | 70.6 | 3/128 (2.3%) | 28 | −1.0",
   "paper_text": "$+0.66$ \\\\ Llama-3.1-70B & 70.6 & 3/128 (2.3) & 28 & $-1.0$",
   "paper_line": 3350,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0203",
   "section": "Replication and size",
   "claim": "number 2.3 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Llama-3.1-70B | 70.6 | 3/128 (2.3%) | 28 | −1.0 to 0.3 |",
   "paper_text": "Llama-3.1-70B & 70.6 & 3/128 (2.3) & 28 & $-1.0$ to $0.3$ & 0.031",
   "paper_line": 3351,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "scale-0204",
   "section": "Replication and size",
   "claim": "number 28 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 70.6 | 3/128 (2.3%) | 28 | −1.0 to 0.3 | 0.031 |",
   "paper_text": "Llama-3.1-70B & 70.6 & 3/128 (2.3) & 28 & $-1.0$ to $0.3$ & 0.031 &",
   "paper_line": 3351,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0205",
   "section": "Replication and size",
   "claim": "number −1.0 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "70.6 | 3/128 (2.3%) | 28 | −1.0 to 0.3 | 0.031 | 0.307",
   "paper_text": "& 72.7 & 0/128 (0.0) & 0 & $-1.0$ to $1.2$ & 0.000 & 0.014 &",
   "paper_line": 3349,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0206",
   "section": "Replication and size",
   "claim": "number 0.3 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "3/128 (2.3%) | 28 | −1.0 to 0.3 | 0.031 | 0.307 | +0.41",
   "paper_text": "3/128 (2.3) & 28 & $-1.0$ to $0.3$ & 0.031 & 0.307 & $+0.41$",
   "paper_line": 3351,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0207",
   "section": "Replication and size",
   "claim": "number 0.031 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(2.3%) | 28 | −1.0 to 0.3 | 0.031 | 0.307 | +0.41 |",
   "paper_text": "(2.3) & 28 & $-1.0$ to $0.3$ & 0.031 & 0.307 & $+0.41$ \\\\ Llama-3.3-70B",
   "paper_line": 3351,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0208",
   "section": "Replication and size",
   "claim": "number 0.307 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| −1.0 to 0.3 | 0.031 | 0.307 | +0.41 |",
   "paper_text": "& $-1.0$ to $0.3$ & 0.031 & 0.307 & $+0.41$ \\\\ Llama-3.3-70B",
   "paper_line": 3351,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0209",
   "section": "Replication and size",
   "claim": "number 0.41 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.3 | 0.031 | 0.307 | +0.41 |",
   "paper_text": "to $0.3$ & 0.031 & 0.307 & $+0.41$ \\\\ Llama-3.3-70B & 70.6 &",
   "paper_line": 3351,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0210",
   "section": "Replication and size",
   "claim": "number 70.6 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| Llama-3.3-70B | 70.6 | 0/128 (0.0%) | 19 | −1.0",
   "paper_text": "$+0.66$ \\\\ Llama-3.1-70B & 70.6 & 3/128 (2.3) & 28 & $-1.0$",
   "paper_line": 3350,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0211",
   "section": "Replication and size",
   "claim": "number 0.0 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Llama-3.3-70B | 70.6 | 0/128 (0.0%) | 19 | −1.0 to 0.3 |",
   "paper_text": "Qwen2.5-72B & 72.7 & 0/128 (0.0) & 0 & $-1.0$ to $1.2$ & 0.000",
   "paper_line": 3349,
   "paper_file": "paper/llm/main.tex"
  },
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   "id": "scale-0212",
   "section": "Replication and size",
   "claim": "number 19 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 70.6 | 0/128 (0.0%) | 19 | −1.0 to 0.3 | 0.000 |",
   "paper_text": "Llama-3.3-70B & 70.6 & 0/128 (0.0) & 19 & $-1.0$ to $0.3$ & 0.000 &",
   "paper_line": 3352,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0213",
   "section": "Replication and size",
   "claim": "number −1.0 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "70.6 | 0/128 (0.0%) | 19 | −1.0 to 0.3 | 0.000 | 0.225",
   "paper_text": "& 72.7 & 0/128 (0.0) & 0 & $-1.0$ to $1.2$ & 0.000 & 0.014 &",
   "paper_line": 3349,
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   "paper_text": "(0.0) & 0 & $-1.0$ to $1.2$ & 0.000 & 0.014 & $-0.45$ \\\\ Llama-3.1-8B",
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   "paper_text": "organization recurs in Qwen2.5-1.5B (Figure~\\ref{fig:qwen15})",
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   "paper_line": 3353,
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   "paper_line": 3355,
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   "paper_line": 3352,
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   "paper_line": 3353,
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   "paper_line": 3356,
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   "paper_line": 3352,
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   "section": "Replication and size",
   "claim": "number 0.21 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.35 against \\(-0.01\\) to 0.21).",
   "paper_text": "($\\log_{10}T=0.10$--$0.35$ against $-0.01$--$0.21$). \\begin{table}[H] \\centering\\footnotesize\\setlength{\\tabcolsep}{4pt}",
   "paper_line": 3336,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0315",
   "section": "Replication and size",
   "claim": "number 48 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "chaotic temperatures among 48 over \\(\\log_{10}T \\in [-0.4,",
   "paper_text": "chaotic temperatures among 48 over $\\log_{10}T\\in[-0.4,0.9]$,",
   "paper_line": 5487,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0316",
   "section": "Replication and size",
   "claim": "number -0.4 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "over \\(\\log_{10}T \\in [-0.4, 0.9]\\), the primary endpoint.",
   "paper_text": "among 48 over $\\log_{10}T\\in[-0.4,0.9]$, the primary endpoint.",
   "paper_line": 5487,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0317",
   "section": "Replication and size",
   "claim": "number 0.9 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T \\in [-0.4, 0.9]\\), the primary endpoint.",
   "paper_text": "48 over $\\log_{10}T\\in[-0.4,0.9]$, the primary endpoint. Right:",
   "paper_line": 5487,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0318",
   "section": "Replication and size",
   "claim": "number 10^{-3} in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Chaotic: exponents above \\(10^{-3}\\) at both twin offsets",
   "paper_text": "(shading). Chaotic: exponents above $10^{-3}$ at both twin offsets ($10^{-5}$,",
   "paper_line": 5489,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0319",
   "section": "Replication and size",
   "claim": "number 10^{-5} in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at both twin offsets (\\(10^{-5}\\), \\(10^{-7}\\)) and no",
   "paper_text": "$10^{-3}$ at both twin offsets ($10^{-5}$, $10^{-7}$) and no period",
   "paper_line": 5489,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0320",
   "section": "Replication and size",
   "claim": "number 10^{-7} in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "offsets (\\(10^{-5}\\), \\(10^{-7}\\)) and no period up to",
   "paper_text": "both twin offsets ($10^{-5}$, $10^{-7}$) and no period up to 64; 1000",
   "paper_line": 5489,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0321",
   "section": "Replication and size",
   "claim": "number 64 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(10^{-7}\\)) and no period up to 64; 1000 transient and 2000",
   "paper_text": "$10^{-7}$) and no period up to 64; 1000 transient and 2000 measured",
   "paper_line": 5489,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0322",
   "section": "Replication and size",
   "claim": "number 1000 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and no period up to 64; 1000 transient and 2000 measured",
   "paper_text": "$10^{-7}$) and no period up to 64; 1000 transient and 2000 measured",
   "paper_line": 5489,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0323",
   "section": "Replication and size",
   "claim": "number 2000 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "64; 1000 transient and 2000 measured steps, float64.",
   "paper_text": "Appendix~\\ref{sec:methods} (1000 transient and 2000 measured steps in float64;",
   "paper_line": 3282,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0324",
   "section": "Replication and size",
   "claim": "number 48 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "chaotic at fewer of the 48 temperatures",
   "paper_text": "be chaotic at fewer of the 48 temperatures than the 14B on",
   "paper_line": 3518,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0325",
   "section": "Replication and size",
   "claim": "number 14 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of them, against 14, 9, 11 and 15, so the prediction",
   "paper_text": "1, 0 and 0 of them, against 14, 9, 11 and 15, so the prediction",
   "paper_line": 3519,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0326",
   "section": "Replication and size",
   "claim": "number 11 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of them, against 14, 9, 11 and 15, so the prediction",
   "paper_text": "and 0 of them, against 14, 9, 11 and 15, so the prediction holds",
   "paper_line": 3519,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0327",
   "section": "Replication and size",
   "claim": "number 15 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "them, against 14, 9, 11 and 15, so the prediction holds",
   "paper_text": "them, against 14, 9, 11 and 15, so the prediction holds on",
   "paper_line": 3519,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0328",
   "section": "Replication and size",
   "claim": "number 0.319 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "temperature (\\(\\log_{10}T = 0.319\\), exponents 0.35 and 0.34)",
   "paper_text": "chaotic temperature ($\\log_{10}T=0.319$, exponents 0.35 and 0.34)",
   "paper_line": 3521,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0329",
   "section": "Replication and size",
   "claim": "number 0.35 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(\\(\\log_{10}T = 0.319\\), exponents 0.35 and 0.34) is chaotic",
   "paper_text": "($\\log_{10}T=0.319$, exponents 0.35 and 0.34) is chaotic again",
   "paper_line": 3522,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0330",
   "section": "Replication and size",
   "claim": "number 0.34 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.319\\), exponents 0.35 and 0.34) is chaotic",
   "paper_text": "($\\log_{10}T=0.319$, exponents 0.35 and 0.34) is chaotic again when recomputed",
   "paper_line": 3522,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0331",
   "section": "Replication and size",
   "claim": "number 0.34 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "automatic-differentiation tangent exponent of 0.34.",
   "paper_text": "an automatic-differentiation tangent exponent of 0.34. With the paper's prompt, where",
   "paper_line": 3523,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0332",
   "section": "Replication and size",
   "claim": "number 1.2 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = 1.2\\), that makes five prompts",
   "paper_text": "robust chaos up to $\\log_{10}T=1.2$, that makes five prompts on",
   "paper_line": 3523,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0333",
   "section": "Replication and size",
   "claim": "number 0.03 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "than the grid spacing (0.03 decades), so a narrow chaotic",
   "paper_text": "less than the grid spacing (0.03 decades), so a narrow chaotic",
   "paper_line": 3524,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0334",
   "section": "Replication and size",
   "claim": "number 0.02 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "fourth a band of chaos about 0.02 decades",
   "paper_text": "fourth a band of chaos about 0.02 decades wide just above the",
   "paper_line": 3527,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0335",
   "section": "Replication and size",
   "claim": "number 0.319 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the jump (\\(\\log_{10}T = 0.319\\) to 0.336; exponents up",
   "paper_text": "above the jump ($\\log_{10}T=0.319$--$0.336$; exponents up to",
   "paper_line": 3528,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0336",
   "section": "Replication and size",
   "claim": "number 0.336 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(\\(\\log_{10}T = 0.319\\) to 0.336; exponents up to 0.40,",
   "paper_text": "jump ($\\log_{10}T=0.319$--$0.336$; exponents up to 0.40, which",
   "paper_line": 3528,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0337",
   "section": "Replication and size",
   "claim": "number 0.40 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.336; exponents up to 0.40,",
   "paper_text": "($\\log_{10}T=0.319$--$0.336$; exponents up to 0.40, which twins at $10^{-5}$ to",
   "paper_line": 3528,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0338",
   "section": "Replication and size",
   "claim": "number 10^{-5} in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "which twins at \\(10^{-5}\\) to \\(10^{-7}\\) reproduce",
   "paper_text": "up to 0.40, which twins at $10^{-5}$ to $10^{-7}$ reproduce within",
   "paper_line": 3528,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0339",
   "section": "Replication and size",
   "claim": "number 10^{-7} in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "twins at \\(10^{-5}\\) to \\(10^{-7}\\) reproduce within 0.004),",
   "paper_text": "which twins at $10^{-5}$ to $10^{-7}$ reproduce within 0.004), at",
   "paper_line": 3528,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0340",
   "section": "Replication and size",
   "claim": "number 0.004 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(10^{-7}\\) reproduce within 0.004), at nearly uniform",
   "paper_text": "$10^{-7}$ reproduce within 0.004), at nearly uniform distributions,",
   "paper_line": 3528,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0341",
   "section": "Replication and size",
   "claim": "number 191 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "positive exponent at any of 191 temperatures between \\(\\log_{10}T",
   "paper_text": "positive exponent at any of 191 temperatures between $\\log_{10}T=-1$",
   "paper_line": 5503,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0342",
   "section": "Replication and size",
   "claim": "number 1.2 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "1.2, Llama-3.3-70B none in",
   "paper_text": "between $\\log_{10}T=-1$ and $1.2$, Llama-3.3-70B none in $[-1,0.3]$,",
   "paper_line": 5503,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0343",
   "section": "Replication and size",
   "claim": "number 0.3 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Llama-3.3-70B none in \\([-1, 0.3]\\), and Llama-3.1-70B three",
   "paper_text": "Llama-3.3-70B none in $[-1,0.3]$, and Llama-3.1-70B three",
   "paper_line": 5504,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0344",
   "section": "Replication and size",
   "claim": "number 0.3 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\([-1, 0.3]\\). Finer lines found candidates:",
   "paper_text": "three temperatures in $[-1,0.3]$. Finer lines found candidates:",
   "paper_line": 5504,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0345",
   "section": "Replication and size",
   "claim": "number 0.3728 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "entropy jump (\\(\\log_{10}T = 0.3728\\) to 0.376) and two isolated",
   "paper_text": "Qwen2.5-72B's entropy jump ($\\log_{10}T=0.3728$--$0.376$) and two isolated",
   "paper_line": 5505,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0346",
   "section": "Replication and size",
   "claim": "number 0.376 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(\\(\\log_{10}T = 0.3728\\) to 0.376) and two isolated",
   "paper_text": "jump ($\\log_{10}T=0.3728$--$0.376$) and two isolated temperatures",
   "paper_line": 5505,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0347",
   "section": "Replication and size",
   "claim": "number 0.250 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "temperatures of Llama-3.3-70B (0.250, 0.306), all at the single",
   "paper_text": "temperatures of Llama-3.3-70B ($0.250$, $0.306$), all at the single",
   "paper_line": 5506,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0348",
   "section": "Replication and size",
   "claim": "number 0.306 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of Llama-3.3-70B (0.250, 0.306), all at the single twin",
   "paper_text": "of Llama-3.3-70B ($0.250$, $0.306$), all at the single twin offset",
   "paper_line": 5506,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0349",
   "section": "Replication and size",
   "claim": "number 10^{-6} in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(10^{-6}\\). The window failed a",
   "paper_text": "at the single twin offset $10^{-6}$. The window failed a three-offset",
   "paper_line": 5506,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0350",
   "section": "Replication and size",
   "claim": "number 64 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "exponent is negative at all 64",
   "paper_text": "exponent is negative at all 64 temperatures of the window",
   "paper_line": 5507,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0351",
   "section": "Replication and size",
   "claim": "number 10^{-5} in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "temperatures of the window at \\(10^{-5}\\), near zero at \\(10^{-6}\\),",
   "paper_text": "temperatures of the window at $10^{-5}$, near zero at $10^{-6}$, and",
   "paper_line": 5507,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0352",
   "section": "Replication and size",
   "claim": "number 10^{-6} in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(10^{-5}\\), near zero at \\(10^{-6}\\), and positive at",
   "paper_text": "at $10^{-5}$, near zero at $10^{-6}$, and positive at 60 of the",
   "paper_line": 5508,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0353",
   "section": "Replication and size",
   "claim": "number 60 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "60 of the 64 at \\(10^{-7}\\),",
   "paper_text": "$10^{-6}$, and positive at 60 of the 64 at $10^{-7}$, including",
   "paper_line": 5508,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0354",
   "section": "Replication and size",
   "claim": "number 64 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "60 of the 64 at \\(10^{-7}\\), including",
   "paper_text": "$10^{-6}$, and positive at 60 of the 64 at $10^{-7}$, including four",
   "paper_line": 5508,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0355",
   "section": "Replication and size",
   "claim": "number 10^{-7} in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "60 of the 64 at \\(10^{-7}\\), including four temperatures",
   "paper_text": "positive at 60 of the 64 at $10^{-7}$, including four temperatures",
   "paper_line": 5508,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0356",
   "section": "Replication and size",
   "claim": "number 10^{-4} in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "all four offsets from \\(10^{-4}\\) to \\(10^{-7}\\) and for",
   "paper_text": "negative at all four offsets from $10^{-4}$ to $10^{-7}$ and for an automatic-differentiation",
   "paper_line": 5513,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0357",
   "section": "Replication and size",
   "claim": "number 10^{-7} in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "offsets from \\(10^{-4}\\) to \\(10^{-7}\\) and for an automatic-differentiation",
   "paper_text": "offsets from $10^{-4}$ to $10^{-7}$ and for an automatic-differentiation tangent vector",
   "paper_line": 5513,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0358",
   "section": "Replication and size",
   "claim": "number 0.015 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "twin exponents lie within 0.015 of the tangent exponent",
   "paper_text": "four twin exponents lie within 0.015 of the tangent exponent at",
   "paper_line": 5515,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0359",
   "section": "Replication and size",
   "claim": "number 0.374 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "2 to 4 (\\(\\log_{10}T = 0.374\\)). The same test on Llama-3.1-70B's",
   "paper_text": "doubles from 2 to 4 ($\\log_{10}T=0.374$). The selected cells below",
   "paper_line": 5517,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0360",
   "section": "Replication and size",
   "claim": "number 0.136 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of them (\\(\\log_{10}T = 0.136\\) and 0.198;",
   "paper_text": "confirms two of them ($\\log_{10}T=0.136$ and $0.198$; exponents 0.23",
   "paper_line": 5522,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0361",
   "section": "Replication and size",
   "claim": "number 0.198 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(\\(\\log_{10}T = 0.136\\) and 0.198;",
   "paper_text": "them ($\\log_{10}T=0.136$ and $0.198$; exponents 0.23 to 0.26 and",
   "paper_line": 5522,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0362",
   "section": "Replication and size",
   "claim": "number 0.23 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "exponents 0.23 to 0.26 and 0.40 to 0.41",
   "paper_text": "($\\log_{10}T=0.136$ and $0.198$; exponents 0.23 to 0.26 and 0.40 to 0.41 at",
   "paper_line": 5523,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0363",
   "section": "Replication and size",
   "claim": "number 0.26 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "exponents 0.23 to 0.26 and 0.40 to 0.41 at the",
   "paper_text": "$0.198$; exponents 0.23 to 0.26 and 0.40 to 0.41 at the three",
   "paper_line": 5523,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0364",
   "section": "Replication and size",
   "claim": "number 0.40 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "exponents 0.23 to 0.26 and 0.40 to 0.41 at the three offsets)",
   "paper_text": "exponents 0.23 to 0.26 and 0.40 to 0.41 at the three offsets)",
   "paper_line": 5523,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0365",
   "section": "Replication and size",
   "claim": "number 0.41 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.23 to 0.26 and 0.40 to 0.41 at the three offsets) and",
   "paper_text": "exponents 0.23 to 0.26 and 0.40 to 0.41 at the three offsets) and rejects",
   "paper_line": 5523,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0366",
   "section": "Replication and size",
   "claim": "number 0.116 in 'Replication and size' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(0.116; positive only at \\(10^{-6}\\)),",
   "paper_text": "offsets) and rejects the weakest ($0.116$; positive only at $10^{-6}$),",
   "paper_line": 5523,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0367",
   "section": "Replication and size",
   "claim": "number 10^{-6} in 'Replication and size' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "model is chaotic at 10, 73 and 161 (0.48, 0.68 and 0.75; Figure~\\ref{fig:moe}).",
   "paper_line": 5445,
   "paper_file": "paper/llm/main.tex"
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   "section": "Mixtures of experts",
   "claim": "number 0.48 in 'Mixtures of experts' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "chaotic at 10, 73 and 161 (0.48, 0.68 and 0.75; Figure~\\ref{fig:moe}).",
   "paper_line": 5446,
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   "section": "Mixtures of experts",
   "claim": "number 0.68 in 'Mixtures of experts' (generated: post phrase matched to the paper's source text)",
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   "paper_line": 5446,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "scale-0480",
   "section": "Mixtures of experts",
   "claim": "number 0.75 in 'Mixtures of experts' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and 161 (0.48, 0.68 and 0.75). The hybrid attention",
   "paper_text": "73 and 161 (0.48, 0.68 and 0.75; Figure~\\ref{fig:moe}). The",
   "paper_line": 5446,
   "paper_file": "paper/llm/main.tex"
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   "section": "Mixtures of experts",
   "claim": "number 128 in 'Mixtures of experts' (generated: post phrase matched to the paper's source text)",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Mixtures of experts",
   "claim": "number 0.3 in 'Mixtures of experts' (generated: post phrase matched to the paper's source text)",
   "appears_as": "network factor between 0.3 and 6 nats is \\(-1.90\\),",
   "paper_text": "median network factor between 0.3 and 6 nats is $-1.90$, against",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Mixtures of experts",
   "claim": "number -1.90 in 'Mixtures of experts' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "between 0.3 and 6 nats is $-1.90$, against $+0.05$ and $-1.41$",
   "paper_line": 3507,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0484",
   "section": "Mixtures of experts",
   "claim": "number 0.05 in 'Mixtures of experts' (generated: post phrase matched to the paper's source text)",
   "appears_as": "against \\(+0.05\\) and \\(-1.41\\) for the",
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   "paper_line": 3507,
   "paper_file": "paper/llm/main.tex"
  },
  {
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   "section": "Mixtures of experts",
   "claim": "number -1.41 in 'Mixtures of experts' (generated: post phrase matched to the paper's source text)",
   "appears_as": "against \\(+0.05\\) and \\(-1.41\\) for the two dense models",
   "paper_text": "$-1.90$, against $+0.05$ and $-1.41$ for the two dense models and",
   "paper_line": 3507,
   "paper_file": "paper/llm/main.tex"
  },
  {
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   "section": "Mixtures of experts",
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   "appears_as": "two dense models and \\(-1.73\\) for the dense",
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   "paper_line": 3508,
   "paper_file": "paper/llm/main.tex"
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   "id": "scale-0487",
   "section": "Mixtures of experts",
   "claim": "number 1.27 in 'Mixtures of experts' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "lowers the network factor by 1.27 (4B), 1.33 (9B) and 0.76 nats",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "scale-0488",
   "section": "Mixtures of experts",
   "claim": "number 1.33 in 'Mixtures of experts' (generated: post phrase matched to the paper's source text)",
   "appears_as": "1.33 (9B) and 0.76 nats (the",
   "paper_text": "network factor by 1.27 (4B), 1.33 (9B) and 0.76 nats (the mixture",
   "paper_line": 5451,
   "paper_file": "paper/llm/main.tex"
  },
  {
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   "section": "Mixtures of experts",
   "claim": "number 0.76 in 'Mixtures of experts' (generated: post phrase matched to the paper's source text)",
   "appears_as": "1.33 (9B) and 0.76 nats (the mixture of experts).",
   "paper_text": "by 1.27 (4B), 1.33 (9B) and 0.76 nats (the mixture of experts).",
   "paper_line": 5451,
   "paper_file": "paper/llm/main.tex"
  },
  {
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   "section": "Mixtures of experts",
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   "appears_as": "median network factor (\\(-0.36\\)) between",
   "paper_text": "factor between 0.3 and 6 nats ($-0.36$) lies between those of the",
   "paper_line": 5459,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0491",
   "section": "Mixtures of experts",
   "claim": "number 0.11 in 'Mixtures of experts' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the dense OLMo-2-1B (\\(+0.11\\)) and OLMo-2-7B (\\(-0.52\\)),",
   "paper_text": "those of the dense OLMo-2-1B ($+0.11$) and OLMo-2-7B ($-0.52$).",
   "paper_line": 5459,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0492",
   "section": "Mixtures of experts",
   "claim": "number -0.52 in 'Mixtures of experts' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(\\(+0.11\\)) and OLMo-2-7B (\\(-0.52\\)), but that pair",
   "paper_text": "OLMo-2-1B ($+0.11$) and OLMo-2-7B ($-0.52$). OLMoE normalizes before",
   "paper_line": 5459,
   "paper_file": "paper/llm/main.tex"
  },
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   "section": "Mixtures of experts",
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   "paper_text": "the orbit, unsteered loop, 24 temperatures per model, float64",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Mixtures of experts",
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   "appears_as": "in the unsteered sweep (128 temperatures, \\(\\log_{10}T",
   "paper_text": "Appendix~\\ref{sec:methods}) in the unsteered sweep (128 temperatures, $\\log_{10}T\\in[-1,0.3]$)",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "scale-0495",
   "section": "Mixtures of experts",
   "claim": "number 0.3 in 'Mixtures of experts' (generated: post phrase matched to the paper's source text)",
   "appears_as": "temperatures, \\(\\log_{10}T \\in [-1, 0.3]\\)) and in 32 × 32 maps",
   "paper_text": "temperatures, $\\log_{10}T\\in[-1,0.3]$) and in $32\\times32$ maps",
   "paper_line": 5468,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0496",
   "section": "Mixtures of experts",
   "claim": "number 32 in 'Mixtures of experts' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\in [-1, 0.3]\\)) and in 32 × 32 maps steered along",
   "paper_text": "$\\log_{10}T\\in[-1,0.3]$) and in $32\\times32$ maps steered along philosophy",
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   "paper_file": "paper/llm/main.tex"
  },
  {
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   "section": "Mixtures of experts",
   "claim": "number 32 in 'Mixtures of experts' (generated: post phrase matched to the paper's source text)",
   "appears_as": "[-1, 0.3]\\)) and in 32 × 32 maps steered along philosophy",
   "paper_text": "$\\log_{10}T\\in[-1,0.3]$) and in $32\\times32$ maps steered along philosophy",
   "paper_line": 5469,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0498",
   "section": "Mixtures of experts",
   "claim": "number 24 in 'Mixtures of experts' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "Qwen3.5-35B-A3B and OLMoE-1B-7B (24 temperatures each, as in (a)):",
   "paper_line": 5471,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0499",
   "section": "Mixtures of experts",
   "claim": "number 10^{-7} in 'Mixtures of experts' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "A twin at relative offset $10^{-7}$ never switched an expert.} \\label{fig:moe}",
   "paper_line": 5475,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0500",
   "section": "Predictor and 70B steering",
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   "paper_line": 5539,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "scale-0501",
   "section": "Predictor and 70B steering",
   "claim": "number 0.014 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and 10 nats, ranges from 0.014",
   "paper_text": "1 and 10 nats, ranges from 0.014 (Qwen2.5-72B) to 0.69 (OLMo-2-32B).",
   "paper_line": 5539,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0502",
   "section": "Predictor and 70B steering",
   "claim": "number 0.69 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(Qwen2.5-72B) to 0.69 (OLMo-2-32B). It orders",
   "paper_text": "from 0.014 (Qwen2.5-72B) to 0.69 (OLMo-2-32B). It orders the",
   "paper_line": 5539,
   "paper_file": "paper/llm/main.tex"
  },
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   "id": "scale-0503",
   "section": "Predictor and 70B steering",
   "claim": "number 0.55 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(Spearman +0.55) somewhat better than their",
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   "paper_file": "paper/llm/main.tex"
  },
  {
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   "section": "Predictor and 70B steering",
   "claim": "number −0.44 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
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   "paper_line": 5540,
   "paper_file": "paper/llm/main.tex"
  },
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   "section": "Predictor and 70B steering",
   "claim": "number 10 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "distributions, above its 10-nat bound. This analysis",
   "paper_text": "uniform distributions, above its 10-nat bound. This analysis was",
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   "paper_file": "paper/llm/main.tex"
  },
  {
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   "section": "Predictor and 70B steering",
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   "paper_line": 5546,
   "paper_file": "paper/llm/main.tex"
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   "section": "Predictor and 70B steering",
   "claim": "number 0.5 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
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   "section": "Predictor and 70B steering",
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   "section": "Predictor and 70B steering",
   "claim": "number 0.06 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Predictor and 70B steering",
   "claim": "number 0.44 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "weakens on the expanded sweeps ($+0.44$), and the one-step gain at",
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  },
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   "section": "Predictor and 70B steering",
   "claim": "number −0.5 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
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   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0512",
   "section": "Predictor and 70B steering",
   "claim": "number −3.4 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "chaotic ones included ($-0.5$ to $-3.4$ per step), and orders nothing",
   "paper_line": 5549,
   "paper_file": "paper/llm/main.tex"
  },
  {
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   "section": "Predictor and 70B steering",
   "claim": "number −0.32 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(−0.32). These features ran on",
   "paper_text": "step), and orders nothing ($-0.32$). These features ran on two",
   "paper_line": 5549,
   "paper_file": "paper/llm/main.tex"
  },
  {
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   "section": "Predictor and 70B steering",
   "claim": "number 10^{-7} in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "only at about the \\(10^{-7}\\) level. No reliable predictor",
   "paper_text": "changes them only at about the $10^{-7}$ level. We have not established",
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   "paper_file": "paper/llm/main.tex"
  },
  {
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   "section": "Predictor and 70B steering",
   "claim": "number 10^{-6} in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "labels at the single offset $10^{-6}$, which the plateau test above",
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   "paper_file": "paper/llm/main.tex"
  },
  {
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   "section": "Predictor and 70B steering",
   "claim": "number 4.3 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "model and at equal norm, 4.3% of cells are labeled chaotic",
   "paper_text": "70B SAE and at equal norm, 4.3\\,\\% of cells are labeled chaotic",
   "paper_line": 5557,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0517",
   "section": "Predictor and 70B steering",
   "claim": "number 3.5 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "3.5% along the autoencoder's",
   "paper_text": "chaotic along the concept vector, 3.5\\,\\% along the frozen-rule hostility",
   "paper_line": 5557,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0518",
   "section": "Predictor and 70B steering",
   "claim": "number 1.1 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "1.1% along a Gaussian direction",
   "paper_text": "frozen-rule hostility feature, 1.1\\,\\% along a Gaussian direction",
   "paper_line": 5558,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0519",
   "section": "Predictor and 70B steering",
   "claim": "number 0.2 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Gaussian direction and 0.2% along a random live feature,",
   "paper_text": "along a Gaussian direction and 0.2\\,\\% along a random live feature,",
   "paper_line": 5558,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0520",
   "section": "Predictor and 70B steering",
   "claim": "number 28 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "random live feature, against 28, 29,",
   "paper_text": "random live feature, against 28, 29, 39 and 27\\,\\% for the",
   "paper_line": 5559,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0521",
   "section": "Predictor and 70B steering",
   "claim": "number 29 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "live feature, against 28, 29,",
   "paper_text": "random live feature, against 28, 29, 39 and 27\\,\\% for the same",
   "paper_line": 5559,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0522",
   "section": "Predictor and 70B steering",
   "claim": "number 39 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "39 and 27% for the same four",
   "paper_text": "live feature, against 28, 29, 39 and 27\\,\\% for the same four",
   "paper_line": 5559,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0523",
   "section": "Predictor and 70B steering",
   "claim": "number 27 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "39 and 27% for the same four directions",
   "paper_text": "feature, against 28, 29, 39 and 27\\,\\% for the same four directions",
   "paper_line": 5559,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0524",
   "section": "Predictor and 70B steering",
   "claim": "share and number of chaos-labeled cells of the 1024 in the steered Qwen2.5-72B map (hostility) (paper 4e6e2ec6)",
   "appears_as": "gives 0.8%: eight of its 1024 cells, all at \\(\\log_{10}T",
   "paper_text": "Qwen2.5-72B along hostility gives 0.8\\,\\%: eight of its 1024 cells, all at $\\log_{10}T=0.26$--$0.30$.",
   "paper_line": 5560,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0525",
   "section": "Predictor and 70B steering",
   "claim": "temperatures of the eight chaos-labeled cells of the steered Qwen2.5-72B map (paper 4e6e2ec6)",
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   "paper_text": "eight of its 1024 cells, all at $\\log_{10}T=0.26$--$0.30$. Recomputed in float64",
   "paper_line": 5560,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0526",
   "section": "Predictor and 70B steering",
   "claim": "number 0.30 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = 0.26\\) to 0.30. Recomputed in float64",
   "paper_text": "all at $\\log_{10}T=0.26$--$0.30$. Recomputed in float64 throughout,",
   "paper_line": 5560,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0527",
   "section": "Predictor and 70B steering",
   "claim": "number 0.23 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "automatic-differentiation tangent exponents of 0.23 to",
   "paper_text": "automatic-differentiation tangent exponents of 0.23 to 0.36 that the twins at all",
   "paper_line": 5561,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0528",
   "section": "Predictor and 70B steering",
   "claim": "number 0.36 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.36 that the twins at all four",
   "paper_text": "tangent exponents of 0.23 to 0.36 that the twins at all four",
   "paper_line": 5561,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0529",
   "section": "Predictor and 70B steering",
   "claim": "number 10^{-4} in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "all four offsets from \\(10^{-4}\\) to \\(10^{-7}\\) reproduce",
   "paper_text": "twins at all four offsets from $10^{-4}$ to $10^{-7}$ reproduce within",
   "paper_line": 5561,
   "paper_file": "paper/llm/main.tex"
  },
  {
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   "section": "Predictor and 70B steering",
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   "paper_text": "offsets from $10^{-4}$ to $10^{-7}$ reproduce within 0.01; five",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Predictor and 70B steering",
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   "paper_text": "$10^{-7}$ reproduce within 0.01; five have nearly uniform next-token",
   "paper_line": 5562,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "scale-0532",
   "section": "Predictor and 70B steering",
   "claim": "number 11.0 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "next-token distributions (11.0 to 11.1 nats) and",
   "paper_text": "uniform next-token distributions (11.0 to 11.1 nats) and one alternates",
   "paper_line": 5562,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "scale-0533",
   "section": "Predictor and 70B steering",
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   "appears_as": "distributions (11.0 to 11.1 nats) and",
   "paper_text": "next-token distributions (11.0 to 11.1 nats) and one alternates between",
   "paper_line": 5562,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "scale-0534",
   "section": "Predictor and 70B steering",
   "claim": "number −3.8 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "with exponents between −3.8 and",
   "paper_text": "orbits with exponents between $-3.8$ and $-3.6$, and the steered",
   "paper_line": 5564,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0535",
   "section": "Predictor and 70B steering",
   "claim": "number −3.6 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "−3.6, and the steered cells",
   "paper_text": "exponents between $-3.8$ and $-3.6$, and the steered cells above",
   "paper_line": 5564,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0536",
   "section": "Predictor and 70B steering",
   "claim": "number 0.325 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "cells above \\(\\log_{10}T = 0.325\\) are near-uniform fixed",
   "paper_text": "steered cells above $\\log_{10}T=0.325$ are near-uniform fixed points,",
   "paper_line": 5564,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0537",
   "section": "Predictor and 70B steering",
   "claim": "number 0.3 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T \\approx 0.3\\) to 0.1. A \\(128 \\times",
   "paper_text": "moves from $\\log_{10}T\\approx0.3$ to $0.1$. A $128\\times128$",
   "paper_line": 5566,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0538",
   "section": "Predictor and 70B steering",
   "claim": "number 0.1 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T \\approx 0.3\\) to 0.1. A \\(128 \\times 128\\) zoom",
   "paper_text": "$\\log_{10}T\\approx0.3$ to $0.1$. A $128\\times128$ zoom of",
   "paper_line": 5566,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0539",
   "section": "Predictor and 70B steering",
   "claim": "number 128 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\approx 0.3\\) to 0.1. A \\(128 \\times 128\\) zoom of the",
   "paper_text": "$\\log_{10}T\\approx0.3$ to $0.1$. A $128\\times128$ zoom of the concept",
   "paper_line": 5566,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0540",
   "section": "Predictor and 70B steering",
   "claim": "number 128 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "to 0.1. A \\(128 \\times 128\\) zoom of the concept plane,",
   "paper_text": "$\\log_{10}T\\approx0.3$ to $0.1$. A $128\\times128$ zoom of the concept",
   "paper_line": 5566,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0541",
   "section": "Predictor and 70B steering",
   "claim": "number 3410 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "it: a chaotic band (3410 of the 16,384 cells, 20.8%;",
   "paper_text": "resolves it: a chaotic band (3410 of the 16{,}384 cells, 20.8\\,\\%;",
   "paper_line": 5568,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0542",
   "section": "Predictor and 70B steering",
   "claim": "number 16,384 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "chaotic band (3410 of the 16,384 cells, 20.8%; largest exponent",
   "paper_text": "a chaotic band (3410 of the 16{,}384 cells, 20.8\\,\\%; largest exponent",
   "paper_line": 5568,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0543",
   "section": "Predictor and 70B steering",
   "claim": "number 20.8 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(3410 of the 16,384 cells, 20.8%; largest exponent 0.64),",
   "paper_text": "(3410 of the 16{,}384 cells, 20.8\\,\\%; largest exponent 0.64),",
   "paper_line": 5568,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0544",
   "section": "Predictor and 70B steering",
   "claim": "number 0.64 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "20.8%; largest exponent 0.64), threaded",
   "paper_text": "20.8\\,\\%; largest exponent 0.64), threaded by periodic windows,",
   "paper_line": 5569,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0545",
   "section": "Predictor and 70B steering",
   "claim": "number 0.23 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "from \\(\\log_{10}T \\approx 0.23\\) at",
   "paper_text": "moves from $\\log_{10}T\\approx0.23$ at $\\alpha=0.06$ to $\\approx0.19$",
   "paper_line": 5569,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0546",
   "section": "Predictor and 70B steering",
   "claim": "number 0.06 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\alpha = 0.06\\) to about 0.19 at \\(\\alpha",
   "paper_text": "descending along $\\alpha\\approx0.06$ and periodic windows inside",
   "paper_line": 5279,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0547",
   "section": "Predictor and 70B steering",
   "claim": "number 0.19 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\alpha = 0.06\\) to about 0.19 at \\(\\alpha = 0.12\\). A",
   "paper_text": "at $\\alpha=0.06$ to $\\approx0.19$ at $\\alpha=0.12$, and periodic",
   "paper_line": 3553,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0548",
   "section": "Predictor and 70B steering",
   "claim": "number 0.12 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "about 0.19 at \\(\\alpha = 0.12\\). A plateau test of 24",
   "paper_text": "$296\\times512$ cells over $\\alpha\\in[-0.12,0.12]$, $\\log_{10}T\\in[-0.45,0.3]$;",
   "paper_line": 819,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0549",
   "section": "Predictor and 70B steering",
   "claim": "number 24 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.12\\). A plateau test of 24 cells drawn",
   "paper_text": "exponent. A plateau test of 24 cells drawn by a rule fixed",
   "paper_line": 5572,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0550",
   "section": "Predictor and 70B steering",
   "claim": "number 12 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "rule fixed in advance (12 chaotic, 6 periodic, 6",
   "paper_text": "by a rule fixed in advance (12 chaotic, 6 periodic, 6 unresolved;",
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   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0551",
   "section": "Predictor and 70B steering",
   "claim": "number 11 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "automatic-differentiation tangent) confirms 11 of the 12 chaotic labels,",
   "paper_text": "an automatic-differentiation tangent) confirms 11 of the 12 chaotic labels, whose",
   "paper_line": 5573,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "scale-0552",
   "section": "Predictor and 70B steering",
   "claim": "number 12 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "tangent) confirms 11 of the 12 chaotic labels, whose four",
   "paper_text": "tangent) confirms 11 of the 12 chaotic labels, whose four",
   "paper_line": 5573,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0553",
   "section": "Predictor and 70B steering",
   "claim": "number 0.012 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "within 0.012, and 5 of the 6 periodic",
   "paper_text": "four exponents agree within 0.012, and 5 of the 6 periodic ones.",
   "paper_line": 5574,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0554",
   "section": "Predictor and 70B steering",
   "claim": "number 0.20 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "near \\(\\log_{10}T = 0.20\\) where a long, weakly",
   "paper_text": "neighboring cells near $\\log_{10}T=0.20$ where a long, weakly attracting",
   "paper_line": 5575,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0555",
   "section": "Predictor and 70B steering",
   "claim": "number 15 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "attracting loop (periods 15 and 16)",
   "paper_text": "weakly attracting loop (periods 15 and 16) and chaos are reached",
   "paper_line": 5575,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0556",
   "section": "Predictor and 70B steering",
   "claim": "number 16 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "attracting loop (periods 15 and 16)",
   "paper_text": "attracting loop (periods 15 and 16) and chaos are reached from",
   "paper_line": 5575,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0557",
   "section": "Predictor and 70B steering",
   "claim": "number −0.005 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "small negative exponents (−0.005 to −0.03) and no period",
   "paper_text": "small negative exponents ($-0.005$ to $-0.03$) and no period",
   "paper_line": 5577,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0558",
   "section": "Predictor and 70B steering",
   "claim": "number −0.03 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "negative exponents (−0.005 to −0.03) and no period up to 32.",
   "paper_text": "negative exponents ($-0.005$ to $-0.03$) and no period up to 32. An",
   "paper_line": 5577,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0559",
   "section": "Predictor and 70B steering",
   "claim": "number 32 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "−0.03) and no period up to 32. An",
   "paper_text": "$-0.03$) and no period up to 32. An earlier $64\\times64$ zoom",
   "paper_line": 5577,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0560",
   "section": "Predictor and 70B steering",
   "claim": "number 64 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "earlier \\(64 \\times 64\\) zoom of the",
   "paper_text": "period up to 32. An earlier $64\\times64$ zoom of the same window,",
   "paper_line": 5578,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0561",
   "section": "Predictor and 70B steering",
   "claim": "number 64 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "earlier \\(64 \\times 64\\) zoom of the same window,",
   "paper_text": "to 32. An earlier $64\\times64$ zoom of the same window, computed",
   "paper_line": 5578,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0562",
   "section": "Predictor and 70B steering",
   "claim": "number 44 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "computed before the fix, had 44% such",
   "paper_text": "computed before the fix, had 44\\,\\% such cells and, above the",
   "paper_line": 5578,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0563",
   "section": "Predictor and 70B steering",
   "claim": "number 515 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "cells and, above the band, 515 cells with periods from",
   "paper_text": "cells and, above the band, 515 cells with periods from 3 to",
   "paper_line": 5578,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0564",
   "section": "Predictor and 70B steering",
   "claim": "number 32 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "with periods from 3 to 32 but a constant leading",
   "paper_text": "cells with periods from 3 to 32 but a constant leading token,",
   "paper_line": 5579,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0565",
   "section": "Predictor and 70B steering",
   "claim": "number 128 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(128 \\times 128\\) zoom supersedes",
   "paper_text": "N-shaped: a bimodal map. A $128\\times128$ zoom around another,",
   "paper_line": 4900,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0566",
   "section": "Predictor and 70B steering",
   "claim": "number 128 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(128 \\times 128\\) zoom supersedes it.",
   "paper_text": "N-shaped: a bimodal map. A $128\\times128$ zoom around another,",
   "paper_line": 4900,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0567",
   "section": "Predictor and 70B steering",
   "claim": "number 32 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Llama-3.3-70B-Instruct soft-token maps (\\(32^2\\) float64 cells, 300",
   "paper_text": "Llama-3.3-70B-Instruct soft-token maps ($32^2$ float64 cells, 300 transient",
   "paper_line": 5584,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0568",
   "section": "Predictor and 70B steering",
   "claim": "number 300 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(\\(32^2\\) float64 cells, 300 transient and 300 measured",
   "paper_text": "maps ($32^2$ float64 cells, 300 transient and 300 measured",
   "paper_line": 5584,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0569",
   "section": "Predictor and 70B steering",
   "claim": "number 300 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "cells, 300 transient and 300 measured steps, maximum",
   "paper_text": "float64 cells, 300 transient and 300 measured steps, maximum period",
   "paper_line": 5584,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0570",
   "section": "Predictor and 70B steering",
   "claim": "number 32 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "measured steps, maximum period 32) steered after block 50",
   "paper_text": "measured steps, maximum period 32) steered after zero-based block",
   "paper_line": 5585,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0571",
   "section": "Predictor and 70B steering",
   "claim": "number 50 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "32) steered after block 50 counted from zero, the",
   "paper_text": "steered after zero-based block 50, the hook point of Goodfire's",
   "paper_line": 5585,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0572",
   "section": "Predictor and 70B steering",
   "claim": "number 44 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "same norm. Chaotic cells: 44, 36, 2 and 11 of 1024 (concept,",
   "paper_text": "the same norm. Chaotic cells: 44, 36, 2 and 11 of 1024 (concept,",
   "paper_line": 5588,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0573",
   "section": "Predictor and 70B steering",
   "claim": "number 36 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "norm. Chaotic cells: 44, 36, 2 and 11 of 1024 (concept,",
   "paper_text": "same norm. Chaotic cells: 44, 36, 2 and 11 of 1024 (concept,",
   "paper_line": 5588,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0574",
   "section": "Predictor and 70B steering",
   "claim": "number 11 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Chaotic cells: 44, 36, 2 and 11 of 1024 (concept, feature,",
   "paper_text": "Chaotic cells: 44, 36, 2 and 11 of 1024 (concept, feature,",
   "paper_line": 5588,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0575",
   "section": "Predictor and 70B steering",
   "claim": "number 1024 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "cells: 44, 36, 2 and 11 of 1024 (concept, feature, random",
   "paper_text": "cells: 44, 36, 2 and 11 of 1024 (concept, feature, random feature,",
   "paper_line": 5588,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0576",
   "section": "Predictor and 70B steering",
   "claim": "number 468 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "nor a positive exponent: 468, 358, 223 and 424. Source:",
   "paper_text": "period nor a positive exponent: 468, 358, 223 and 424.} \\label{fig:controls70}",
   "paper_line": 5589,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0577",
   "section": "Predictor and 70B steering",
   "claim": "number 358 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "positive exponent: 468, 358, 223 and 424. Source: byte-identical",
   "paper_text": "nor a positive exponent: 468, 358, 223 and 424.} \\label{fig:controls70}",
   "paper_line": 5589,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0578",
   "section": "Predictor and 70B steering",
   "claim": "number 223 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "positive exponent: 468, 358, 223 and 424. Source: byte-identical",
   "paper_text": "positive exponent: 468, 358, 223 and 424.} \\label{fig:controls70}",
   "paper_line": 5589,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "scale-0579",
   "section": "Predictor and 70B steering",
   "claim": "number 424 in 'Predictor and 70B steering' (generated: post phrase matched to the paper's source text)",
   "appears_as": "exponent: 468, 358, 223 and 424. Source: byte-identical",
   "paper_text": "exponent: 468, 358, 223 and 424.} \\label{fig:controls70} \\end{figure}",
   "paper_line": 5589,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0000",
   "section": "Feigenbaum ratios",
   "claim": "number 1978 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "is chaotic. In 1978 Mitchell Feigenbaum found",
   "paper_text": "low-dimensional maps \\cite{feigenbaum1978quantitative,gallas1993structure}",
   "paper_line": 157,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0001",
   "section": "Feigenbaum ratios",
   "claim": "number 4.6692 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "shrink by a common factor, \\(\\delta = 4.6692\\ldots\\),",
   "paper_text": "Feigenbaum's constant is $\\delta=4.6692\\ldots$ \\cite{feigenbaum1978quantitative};",
   "paper_line": 1989,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0002",
   "section": "Feigenbaum ratios",
   "claim": "number 12 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "existence\"` doubles to periods 6, 12, 24 and onward. Along the",
   "paper_text": "of ``is it'' (periods 10 and 12), and along the band's flip",
   "paper_line": 918,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0003",
   "section": "Feigenbaum ratios",
   "claim": "number 24 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "doubles to periods 6, 12, 24 and onward. Along the cut",
   "paper_text": "Brackets for periods 12 and 24 are the closest points where",
   "paper_line": 1920,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0004",
   "section": "Feigenbaum ratios",
   "claim": "number 4.6688 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "from below; the last one, 4.6688, lies within 0.008% of",
   "paper_text": "$\\delta$ from below, the last ($4.6688$) within $0.008\\,\\%$ of it,",
   "paper_line": 1880,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0005",
   "section": "Feigenbaum ratios",
   "claim": "number 0.008 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "one, 4.6688, lies within 0.008% of it. The first",
   "paper_text": "the last ($4.6688$) within $0.008\\,\\%$ of it, and within $0.015\\,\\%$",
   "paper_line": 1880,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0006",
   "section": "Feigenbaum ratios",
   "claim": "number -0.14798 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "cut.** Along \\(\\log_{10}T = -0.14798\\) the map's cells show",
   "paper_text": "inward. Along the cut $\\log_{10}T=-0.14798$, the map's cells show period",
   "paper_line": 1846,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0007",
   "section": "Feigenbaum ratios",
   "claim": "number 25 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "over 25 columns, period 6 over",
   "paper_text": "map's cells show period 3 over 25 columns, period 6 over about",
   "paper_line": 1846,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0008",
   "section": "Feigenbaum ratios",
   "claim": "number 14 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "columns, period 6 over about 14, period 12 over 4 and period",
   "paper_text": "columns, period 6 over about 14, period 12 over 4 and period",
   "paper_line": 1847,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0009",
   "section": "Feigenbaum ratios",
   "claim": "number 12 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "6 over about 14, period 12 over 4 and period 24 in",
   "paper_text": "period 6 over about 14, period 12 over 4 and period 24 in one",
   "paper_line": 1847,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0010",
   "section": "Feigenbaum ratios",
   "claim": "number 24 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "period 12 over 4 and period 24 in one",
   "paper_text": "period 12 over 4 and period 24 in one column, followed by",
   "paper_line": 1847,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0011",
   "section": "Feigenbaum ratios",
   "claim": "number 2.844 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "two ratios, \\(\\delta_2 = 2.844\\) and",
   "paper_text": "first two ratios, $\\delta_2=2.844$ and $\\delta_3=2.859$ (indexed",
   "paper_line": 1850,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0012",
   "section": "Feigenbaum ratios",
   "claim": "number 2.859 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\delta_3 = 2.859\\), are far from Feigenbaum's",
   "paper_text": "$\\delta_2=2.844$ and $\\delta_3=2.859$ (indexed as in Table~\\ref{tab:cascade}),",
   "paper_line": 1850,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0013",
   "section": "Feigenbaum ratios",
   "claim": "number 4.6692 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "are far from Feigenbaum's 4.6692, even though from the",
   "paper_text": "are far from Feigenbaum's $4.6692$, even though from the second",
   "paper_line": 1851,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0014",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0023 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "second flip on the orbits' linear relaxation is dominated by one direction (next modulus 0.0023,",
   "paper_text": "dominated in their linear relaxation by one direction (next modulus $0.0023$, $2\\times10^{-6}$, $2\\times10^{-12}$)",
   "paper_line": 1852,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0015",
   "section": "Feigenbaum ratios",
   "claim": "number 2\\times10^{-6} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(2\\times10^{-6}\\), \\(2\\times10^{-12}\\)).",
   "paper_text": "dominated in their linear relaxation by one direction (next modulus $0.0023$, $2\\times10^{-6}$, $2\\times10^{-12}$)",
   "paper_line": 1852,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0016",
   "section": "Feigenbaum ratios",
   "claim": "number 2\\times10^{-12} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(2\\times10^{-6}\\), \\(2\\times10^{-12}\\)). The next ratio, \\(\\delta_4",
   "paper_text": "$0.0023$, $2\\times10^{-6}$, $2\\times10^{-12}$). The next ratio, $\\delta_4=3.781$,",
   "paper_line": 1852,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0017",
   "section": "Feigenbaum ratios",
   "claim": "number 3.781 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "next ratio, \\(\\delta_4 = 3.781\\), is",
   "paper_text": "$2\\times10^{-12}$). The next ratio, $\\delta_4=3.781$, is markedly larger. The first",
   "paper_line": 1852,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0018",
   "section": "Feigenbaum ratios",
   "claim": "number 4\\times10^{-15} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "a CPU and an H100 to \\(4\\times10^{-15}\\).",
   "paper_text": "computations on a CPU and an H100 to $4\\times10^{-15}$. Continuing a just-born doubled",
   "paper_line": 1853,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0019",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0654807769499 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 1 | 3 → 6 | 0.0654807769499 | 0.088 | |",
   "paper_text": "\\\\ \\midrule 1 & $3\\to6$ & $0.0654807769499$ & $0.088$ & \\\\ 2 & $6\\to12$",
   "paper_line": 1967,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0020",
   "section": "Feigenbaum ratios",
   "claim": "number 0.088 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "→ 6 | 0.0654807769499 | 0.088 | |",
   "paper_text": "$3\\to6$ & $0.0654807769499$ & $0.088$ & \\\\ 2 & $6\\to12$ & $0.0659055406325$",
   "paper_line": 1969,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0021",
   "section": "Feigenbaum ratios",
   "claim": "number 12 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 2 | 6 → 12 | 0.0659055406325 | 0.0023",
   "paper_text": "philosophy direction at layer 12), at increasing distance from",
   "paper_line": 1762,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0022",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0659055406325 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 2 | 6 → 12 | 0.0659055406325 | 0.0023 | 2.844 |",
   "paper_text": "$0.088$ & \\\\ 2 & $6\\to12$ & $0.0659055406325$ & $0.0023$ & $2.844$ \\\\ 3",
   "paper_line": 1969,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0023",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0023 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "12 | 0.0659055406325 | 0.0023 | 2.844 |",
   "paper_text": "dominated in their linear relaxation by one direction (next modulus $0.0023$, $2\\times10^{-6}$, $2\\times10^{-12}$)",
   "paper_line": 1852,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0024",
   "section": "Feigenbaum ratios",
   "claim": "number 2.844 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.0659055406325 | 0.0023 | 2.844 |",
   "paper_text": "first two ratios, $\\delta_2=2.844$ and $\\delta_3=2.859$ (indexed",
   "paper_line": 1850,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0025",
   "section": "Feigenbaum ratios",
   "claim": "number 12 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 3 | 12 → 24 | 0.0660549041785",
   "paper_text": "$2\\times10^{-6}$, $2\\times10^{-12}$). The next ratio, $\\delta_4=3.781$,",
   "paper_line": 1852,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0026",
   "section": "Feigenbaum ratios",
   "claim": "number 24 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 3 | 12 → 24 | 0.0660549041785 | \\(2.4\\times10^{-6}\\)",
   "paper_text": "the root, so $s_{12}$ and $s_{24}$ are known only within brackets",
   "paper_line": 1867,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0027",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0660549041785 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 3 | 12 → 24 | 0.0660549041785 | \\(2.4\\times10^{-6}\\)",
   "paper_text": "$2.844$ \\\\ 3 & $12\\to24$ & $0.0660549041785$ & $2.4\\times10^{-6}$ & $2.859$",
   "paper_line": 1970,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0028",
   "section": "Feigenbaum ratios",
   "claim": "number 2.4\\times10^{-6} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "24 | 0.0660549041785 | \\(2.4\\times10^{-6}\\) | 2.859 |",
   "paper_text": "$12\\to24$ & $0.0660549041785$ & $2.4\\times10^{-6}$ & $2.859$ \\\\ 4 & $24\\to48$",
   "paper_line": 1971,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0029",
   "section": "Feigenbaum ratios",
   "claim": "number 2.859 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(2.4\\times10^{-6}\\) | 2.859 |",
   "paper_text": "$0.0660549041785$ & $2.4\\times10^{-6}$ & $2.859$ \\\\ 4 & $24\\to48$ & $0.0661071412523$",
   "paper_line": 1971,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0030",
   "section": "Feigenbaum ratios",
   "claim": "number 24 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 4 | 24 → 48 | 0.0661071412523",
   "paper_text": "the root, so $s_{12}$ and $s_{24}$ are known only within brackets",
   "paper_line": 1867,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0031",
   "section": "Feigenbaum ratios",
   "claim": "number 48 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 4 | 24 → 48 | 0.0661071412523 | \\(2.3\\times10^{-12}\\)",
   "paper_text": "just-born doubled orbit past period 48 failed: Newton's method slides",
   "paper_line": 1856,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0032",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0661071412523 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 4 | 24 → 48 | 0.0661071412523 | \\(2.3\\times10^{-12}\\)",
   "paper_text": "$2.859$ \\\\ 4 & $24\\to48$ & $0.0661071412523$ & $2.3\\times10^{-12}$ & $3.781$",
   "paper_line": 1971,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0033",
   "section": "Feigenbaum ratios",
   "claim": "number 2.3\\times10^{-12} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "48 | 0.0661071412523 | \\(2.3\\times10^{-12}\\) | 3.781 |",
   "paper_text": "$24\\to48$ & $0.0661071412523$ & $2.3\\times10^{-12}$ & $3.781$ \\\\ 5 & $48\\to96$",
   "paper_line": 1972,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0034",
   "section": "Feigenbaum ratios",
   "claim": "number 3.781 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(2.3\\times10^{-12}\\) | 3.781 |",
   "paper_text": "$2\\times10^{-12}$). The next ratio, $\\delta_4=3.781$, is markedly larger. The first",
   "paper_line": 1852,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0035",
   "section": "Feigenbaum ratios",
   "claim": "number 48 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 5 | 48 → 96 | 0.0661209563174",
   "paper_text": "within one iterate of 42 of 48 passages; all six misses are",
   "paper_line": 1821,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0036",
   "section": "Feigenbaum ratios",
   "claim": "number 96 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 5 | 48 → 96 | 0.0661209563174 | \\(<10^{-13}\\)",
   "paper_text": "runs started inside the period-96 band, which located the flips",
   "paper_line": 1864,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0037",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0661209563174 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 5 | 48 → 96 | 0.0661209563174 | \\(<10^{-13}\\) | 4.365",
   "paper_text": "$3.781$ \\\\ 5 & $48\\to96$ & $0.0661209563174$ & $<10^{-13}$ & $4.365$ \\\\",
   "paper_line": 1972,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0038",
   "section": "Feigenbaum ratios",
   "claim": "number 10^{-13} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 0.0661209563174 | \\(<10^{-13}\\) | 4.365 |",
   "paper_text": "Newton residuals below $3\\times10^{-13}$ and the other computed Ritz",
   "paper_line": 1918,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0039",
   "section": "Feigenbaum ratios",
   "claim": "number 4.365 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.0661209563174 | \\(<10^{-13}\\) | 4.365 |",
   "paper_text": "$0.0661209563174$ & $<10^{-13}$ & $4.365$ \\\\ 6 & $96\\to192$ & $0.0661241213732$",
   "paper_line": 1973,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0040",
   "section": "Feigenbaum ratios",
   "claim": "number 96 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 6 | 96 → 192 | 0.0661241213732",
   "paper_text": "runs started inside the period-96 band, which located the flips",
   "paper_line": 1864,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0041",
   "section": "Feigenbaum ratios",
   "claim": "number 192 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 6 | 96 → 192 | 0.0661241213732 | \\(<10^{-13}\\)",
   "paper_text": "located the flips of periods 96, 192 and 384 directly. The accumulation",
   "paper_line": 1864,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0042",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0661241213732 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 6 | 96 → 192 | 0.0661241213732 | \\(<10^{-13}\\) | 4.596",
   "paper_text": "$4.365$ \\\\ 6 & $96\\to192$ & $0.0661241213732$ & $<10^{-13}$ & $4.596$ \\\\",
   "paper_line": 1973,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0043",
   "section": "Feigenbaum ratios",
   "claim": "number 10^{-13} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 0.0661241213732 | \\(<10^{-13}\\) | 4.596 |",
   "paper_text": "Newton residuals below $3\\times10^{-13}$ and the other computed Ritz",
   "paper_line": 1918,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0044",
   "section": "Feigenbaum ratios",
   "claim": "number 4.596 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.0661241213732 | \\(<10^{-13}\\) | 4.596 |",
   "paper_text": "$0.0661241213732$ & $<10^{-13}$ & $4.596$ \\\\ 7 & $192\\to384$ & $0.0661248100141$",
   "paper_line": 1974,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0045",
   "section": "Feigenbaum ratios",
   "claim": "number 192 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 7 | 192 → 384 | 0.0661248100141",
   "paper_text": "located the flips of periods 96, 192 and 384 directly. The accumulation",
   "paper_line": 1864,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0046",
   "section": "Feigenbaum ratios",
   "claim": "number 384 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 7 | 192 → 384 | 0.0661248100141 | \\(<10^{-13}\\)",
   "paper_text": "flips of periods 96, 192 and 384 directly. The accumulation",
   "paper_line": 1864,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0047",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0661248100141 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 7 | 192 → 384 | 0.0661248100141 | \\(<10^{-13}\\) | 4.653",
   "paper_text": "$4.596$ \\\\ 7 & $192\\to384$ & $0.0661248100141$ & $<10^{-13}$ & $4.653$ \\\\",
   "paper_line": 1974,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0048",
   "section": "Feigenbaum ratios",
   "claim": "number 10^{-13} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 0.0661248100141 | \\(<10^{-13}\\) | 4.653 |",
   "paper_text": "Newton residuals below $3\\times10^{-13}$ and the other computed Ritz",
   "paper_line": 1918,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0049",
   "section": "Feigenbaum ratios",
   "claim": "number 4.653 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.0661248100141 | \\(<10^{-13}\\) | 4.653 |",
   "paper_text": "$0.0661248100141$ & $<10^{-13}$ & $4.653$ \\\\",
   "paper_line": 1975,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0050",
   "section": "Feigenbaum ratios",
   "claim": "number 384 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 8 | 384 → 768 | 0.0661249580173",
   "paper_text": "flips of periods 96, 192 and 384 directly. The accumulation",
   "paper_line": 1864,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0051",
   "section": "Feigenbaum ratios",
   "claim": "number 768 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 8 | 384 → 768 | 0.0661249580173 | \\(<10^{-13}\\)",
   "paper_text": "half-period parent. Through period 768 the superstable ratios are",
   "paper_line": 1859,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0052",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0661249580173 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 8 | 384 → 768 | 0.0661249580173 | \\(<10^{-13}\\) | |",
   "paper_text": "$4.653$ \\\\ 8 & $384\\to768$ & $0.0661249580173$ & $<10^{-13}$ & \\\\ \\bottomrule",
   "paper_line": 1975,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0053",
   "section": "Feigenbaum ratios",
   "claim": "number 10^{-13} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 0.0661249580173 | \\(<10^{-13}\\) | |",
   "paper_text": "Newton residuals below $3\\times10^{-13}$ and the other computed Ritz",
   "paper_line": 1918,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0054",
   "section": "Feigenbaum ratios",
   "claim": "number -0.14798 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "sequence along \\(\\log_{10}T = -0.14798\\) (Qwen2.5-0.5B-Instruct,",
   "paper_text": "sequence along $\\log_{10}T=-0.14798$. For the first five flips",
   "paper_line": 1979,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0055",
   "section": "Feigenbaum ratios",
   "claim": "number 12 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "philosophy direction at layer 12, float64). For the first",
   "paper_text": "(philosophy direction, layer 12), from flips and from superstable",
   "paper_line": 1873,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0056",
   "section": "Feigenbaum ratios",
   "claim": "number 4\\times10^{-10} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "from \\(-1\\) by at most \\(4\\times10^{-10}\\), with Newton residuals",
   "paper_text": "differs from $-1$ by at most $4\\times10^{-10}$, the Newton residuals are",
   "paper_line": 1980,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0057",
   "section": "Feigenbaum ratios",
   "claim": "number 4\\times10^{-13} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Newton residuals below \\(4\\times10^{-13}\\). The sixth flip was located",
   "paper_text": "Newton residuals are below $4\\times10^{-13}$, and the other computed Ritz",
   "paper_line": 1980,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0058",
   "section": "Feigenbaum ratios",
   "claim": "number 5.7\\times10^{-7} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "multiplier (critical value \\(5.7\\times10^{-7}\\) from \\(-1\\)); its location",
   "paper_text": "value differs from $-1$ by $5.7\\times10^{-7}$, its scatter between bracket",
   "paper_line": 1982,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0059",
   "section": "Feigenbaum ratios",
   "claim": "number 2\\times10^{-12} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "is uncertain by about \\(2\\times10^{-12}\\), which changes \\(\\delta_5\\)",
   "paper_text": "location is uncertain by about $2\\times10^{-12}$, which changes $\\delta_5$",
   "paper_line": 1984,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0060",
   "section": "Feigenbaum ratios",
   "claim": "number 10^{-5} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\delta_5\\) by less than \\(10^{-5}\\). The seventh is clean",
   "paper_text": "changes $\\delta_5$ by less than $10^{-5}$. The seventh flip is clean",
   "paper_line": 1984,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0061",
   "section": "Feigenbaum ratios",
   "claim": "number -1.000000016 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "clean (critical value \\(-1.000000016\\)). The eighth was accepted",
   "paper_text": "flip is clean (critical value $-1.000000016$, Newton residual $2.8\\times10^{-12}$).",
   "paper_line": 1984,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0062",
   "section": "Feigenbaum ratios",
   "claim": "number 5.3\\times10^{-5} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "period-384 multiplier (\\(5.3\\times10^{-5}\\) from \\(-1\\), acceptance",
   "paper_text": "value differs from $-1$ by $5.3\\times10^{-5}$ (acceptance threshold $10^{-4}$),",
   "paper_line": 1986,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0063",
   "section": "Feigenbaum ratios",
   "claim": "number 10^{-4} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "acceptance threshold \\(10^{-4}\\)); its location is uncertain",
   "paper_text": "$5.3\\times10^{-5}$ (acceptance threshold $10^{-4}$), bracket evaluations within",
   "paper_line": 1986,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0064",
   "section": "Feigenbaum ratios",
   "claim": "number 4\\times10^{-12} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "is uncertain by about \\(4\\times10^{-12}\\), which changes \\(\\delta_7\\)",
   "paper_text": "location is uncertain by about $4\\times10^{-12}$, which changes $\\delta_7$",
   "paper_line": 1988,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0065",
   "section": "Feigenbaum ratios",
   "claim": "number 10^{-4} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\delta_7\\) by about \\(10^{-4}\\). For the logistic map",
   "paper_text": "$4\\times10^{-12}$ of it scatter by about $10^{-4}$ in that difference, and the",
   "paper_line": 1987,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0066",
   "section": "Feigenbaum ratios",
   "claim": "number 4.751 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "map the first ratios are 4.751, 4.656 and 4.668. Source:",
   "paper_text": "logistic map the first ratios are $4.751$, $4.656$, $4.668$. The first",
   "paper_line": 1990,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0067",
   "section": "Feigenbaum ratios",
   "claim": "number 4.656 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "first ratios are 4.751, 4.656 and 4.668. Source: the",
   "paper_text": "first ratios are $4.751$, $4.656$, $4.668$. The first four parameters",
   "paper_line": 1990,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0068",
   "section": "Feigenbaum ratios",
   "claim": "number 4.668 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "ratios are 4.751, 4.656 and 4.668. Source: the report's cascade",
   "paper_text": "ratios are $4.751$, $4.656$, $4.668$. The first four parameters",
   "paper_line": 1990,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0069",
   "section": "Feigenbaum ratios",
   "claim": "number 48 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "long periods: past period 48, Newton's method, asked",
   "paper_text": "just-born doubled orbit past period 48 failed: Newton's method slides",
   "paper_line": 1856,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0070",
   "section": "Feigenbaum ratios",
   "claim": "number 768 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "period 768 the superstable ratios",
   "paper_text": "half-period parent. Through period 768 the superstable ratios are",
   "paper_line": 1859,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0071",
   "section": "Feigenbaum ratios",
   "claim": "number 3.19 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "superstable ratios are 3.19, 4.02, 4.478, 4.625 and",
   "paper_text": "the superstable ratios are $3.19$, $4.02$, $4.478$, $4.625$",
   "paper_line": 1859,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0072",
   "section": "Feigenbaum ratios",
   "claim": "number 4.02 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "superstable ratios are 3.19, 4.02, 4.478, 4.625 and 4.660",
   "paper_text": "superstable ratios are $3.19$, $4.02$, $4.478$, $4.625$ and $4.660$.",
   "paper_line": 1859,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0073",
   "section": "Feigenbaum ratios",
   "claim": "number 4.478 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "ratios are 3.19, 4.02, 4.478, 4.625 and 4.660 (Table",
   "paper_text": "ratios are $3.19$, $4.02$, $4.478$, $4.625$ and $4.660$. The",
   "paper_line": 1860,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0074",
   "section": "Feigenbaum ratios",
   "claim": "number 4.625 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "are 3.19, 4.02, 4.478, 4.625 and 4.660 (Table",
   "paper_text": "are $3.19$, $4.02$, $4.478$, $4.625$ and $4.660$. The last three",
   "paper_line": 1860,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0075",
   "section": "Feigenbaum ratios",
   "claim": "number 4.660 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "4.02, 4.478, 4.625 and 4.660 (Table",
   "paper_text": "$4.02$, $4.478$, $4.625$ and $4.660$. The last three come from",
   "paper_line": 1860,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0076",
   "section": "Feigenbaum ratios",
   "claim": "number 10^{-14} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(10^{-14}\\) and differ from Feigenbaum's",
   "paper_text": "from parameters resolved to $10^{-14}$ and differ from Feigenbaum's",
   "paper_line": 1860,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0077",
   "section": "Feigenbaum ratios",
   "claim": "number 0.19 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "from Feigenbaum's value by 0.19, 0.044 and 0.0097; from",
   "paper_text": "from Feigenbaum's value by $0.19$, $0.044$ and $0.0097$; from",
   "paper_line": 1861,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0078",
   "section": "Feigenbaum ratios",
   "claim": "number 0.044 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Feigenbaum's value by 0.19, 0.044 and 0.0097; from",
   "paper_text": "Feigenbaum's value by $0.19$, $0.044$ and $0.0097$; from $4.02$",
   "paper_line": 1861,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0079",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0097 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "value by 0.19, 0.044 and 0.0097; from",
   "paper_text": "value by $0.19$, $0.044$ and $0.0097$; from $4.02$ on, the distance",
   "paper_line": 1861,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0080",
   "section": "Feigenbaum ratios",
   "claim": "number 4.02 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "4.02 on, the distance shrinks",
   "paper_text": "$0.044$ and $0.0097$; from $4.02$ on, the distance shrinks by",
   "paper_line": 1861,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0081",
   "section": "Feigenbaum ratios",
   "claim": "number 3.4 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "distance shrinks by factors of 3.4, 4.3 and 4.6. The flip",
   "paper_text": "distance shrinks by factors of $3.4$, $4.3$ and $4.6$. The flip",
   "paper_line": 1861,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0082",
   "section": "Feigenbaum ratios",
   "claim": "number 4.3 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "shrinks by factors of 3.4, 4.3 and 4.6. The flip ratios",
   "paper_text": "shrinks by factors of $3.4$, $4.3$ and $4.6$. The flip ratios",
   "paper_line": 1861,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0083",
   "section": "Feigenbaum ratios",
   "claim": "number 4.6 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "factors of 3.4, 4.3 and 4.6. The flip ratios",
   "paper_text": "factors of $3.4$, $4.3$ and $4.6$. The flip ratios $2.84$, $2.86$,",
   "paper_line": 1861,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0084",
   "section": "Feigenbaum ratios",
   "claim": "number 2.84 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "2.84, 2.86, 3.78, 4.36, 4.60",
   "paper_text": "and $4.6$. The flip ratios $2.84$, $2.86$, $3.78$, $4.36$, $4.60$",
   "paper_line": 1862,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0085",
   "section": "Feigenbaum ratios",
   "claim": "number 2.86 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "2.84, 2.86, 3.78, 4.36, 4.60 and 4.65",
   "paper_text": "$4.6$. The flip ratios $2.84$, $2.86$, $3.78$, $4.36$, $4.60$ and",
   "paper_line": 1862,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0086",
   "section": "Feigenbaum ratios",
   "claim": "number 3.78 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "2.84, 2.86, 3.78, 4.36, 4.60 and 4.65 rise",
   "paper_text": "flip ratios $2.84$, $2.86$, $3.78$, $4.36$, $4.60$ and $4.65$",
   "paper_line": 1863,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0087",
   "section": "Feigenbaum ratios",
   "claim": "number 4.36 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "2.84, 2.86, 3.78, 4.36, 4.60 and 4.65 rise in",
   "paper_text": "ratios $2.84$, $2.86$, $3.78$, $4.36$, $4.60$ and $4.65$ rise in",
   "paper_line": 1863,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0088",
   "section": "Feigenbaum ratios",
   "claim": "number 4.60 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "2.84, 2.86, 3.78, 4.36, 4.60 and 4.65 rise in step (Figure",
   "paper_text": "$2.84$, $2.86$, $3.78$, $4.36$, $4.60$ and $4.65$ rise in step (Figure~\\ref{fig:feigenbaum});",
   "paper_line": 1863,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0089",
   "section": "Feigenbaum ratios",
   "claim": "number 4.65 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "2.86, 3.78, 4.36, 4.60 and 4.65 rise in step (Figure",
   "paper_text": "$3.78$, $4.36$, $4.60$ and $4.65$ rise in step (Figure~\\ref{fig:feigenbaum});",
   "paper_line": 1863,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0090",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0661250 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\alpha_\\infty \\approx 0.0661250\\). The early superstable",
   "paper_text": "lies near $\\alpha_\\infty\\approx0.0661250$. The early superstable values",
   "paper_line": 1865,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0091",
   "section": "Feigenbaum ratios",
   "claim": "number 1.24\\times10^{-5} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "only within brackets of \\(1.24\\times10^{-5}\\)",
   "paper_text": "known only within brackets of $1.24\\times10^{-5}$ and $6.9\\times10^{-7}$, and",
   "paper_line": 1867,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0092",
   "section": "Feigenbaum ratios",
   "claim": "number 6.9\\times10^{-7} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and \\(6.9\\times10^{-7}\\), and the ratios 3.19",
   "paper_text": "of $1.24\\times10^{-5}$ and $6.9\\times10^{-7}$, and the ratios $3.19$ and",
   "paper_line": 1867,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0093",
   "section": "Feigenbaum ratios",
   "claim": "number 3.19 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(6.9\\times10^{-7}\\), and the ratios 3.19 and 4.019 have worst-case",
   "paper_text": "$6.9\\times10^{-7}$, and the ratios $3.19$ and $4.019$ have worst-case",
   "paper_line": 1868,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0094",
   "section": "Feigenbaum ratios",
   "claim": "number 4.019 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and the ratios 3.19 and 4.019 have worst-case ranges",
   "paper_text": "and the ratios $3.19$ and $4.019$ have worst-case ranges $[2.895,3.338]$",
   "paper_line": 1868,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0095",
   "section": "Feigenbaum ratios",
   "claim": "number 2.895 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "[2.895, 3.338] and [4.019, 4.101].",
   "paper_text": "$4.019$ have worst-case ranges $[2.895,3.338]$ and $[4.019,4.101]$.",
   "paper_line": 1868,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0096",
   "section": "Feigenbaum ratios",
   "claim": "number 3.338 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "[2.895, 3.338] and [4.019, 4.101].",
   "paper_text": "have worst-case ranges $[2.895,3.338]$ and $[4.019,4.101]$. $s_6$",
   "paper_line": 1868,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0097",
   "section": "Feigenbaum ratios",
   "claim": "number 4.019 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "[2.895, 3.338] and [4.019, 4.101].",
   "paper_text": "and the ratios $3.19$ and $4.019$ have worst-case ranges $[2.895,3.338]$",
   "paper_line": 1868,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0098",
   "section": "Feigenbaum ratios",
   "claim": "number 4.101 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "[2.895, 3.338] and [4.019, 4.101].",
   "paper_text": "$[2.895,3.338]$ and $[4.019,4.101]$. $s_6$ is less precise still,",
   "paper_line": 1868,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0099",
   "section": "Feigenbaum ratios",
   "claim": "number 12 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 12 | 0.0659717 | \\(1.24\\times10^{-5}\\)",
   "paper_text": "$2\\times10^{-6}$, $2\\times10^{-12}$). The next ratio, $\\delta_4=3.781$,",
   "paper_line": 1852,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0100",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0659717 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 12 | 0.0659717 | \\(1.24\\times10^{-5}\\)",
   "paper_text": "$\\frac{s_p-s_{p/2}}{s_{2p}-s_p}$ \\\\ \\midrule 12 & $0.0659717$ & $1.24\\times10^{-5}$ & \\\\",
   "paper_line": 1906,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0101",
   "section": "Feigenbaum ratios",
   "claim": "number 1.24\\times10^{-5} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 12 | 0.0659717 | \\(1.24\\times10^{-5}\\) | |",
   "paper_text": "known only within brackets of $1.24\\times10^{-5}$ and $6.9\\times10^{-7}$, and",
   "paper_line": 1867,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0102",
   "section": "Feigenbaum ratios",
   "claim": "number 24 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 24 | 0.06608014 | \\(6.9\\times10^{-7}\\)",
   "paper_text": "the root, so $s_{12}$ and $s_{24}$ are known only within brackets",
   "paper_line": 1867,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0103",
   "section": "Feigenbaum ratios",
   "claim": "number 0.06608014 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 24 | 0.06608014 | \\(6.9\\times10^{-7}\\)",
   "paper_text": "$1.24\\times10^{-5}$ & \\\\ 24 & $0.06608014$ & $6.9\\times10^{-7}$ & $3.19$",
   "paper_line": 1908,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0104",
   "section": "Feigenbaum ratios",
   "claim": "number 6.9\\times10^{-7} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 24 | 0.06608014 | \\(6.9\\times10^{-7}\\) | 3.19 |",
   "paper_text": "of $1.24\\times10^{-5}$ and $6.9\\times10^{-7}$, and the ratios $3.19$ and",
   "paper_line": 1867,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0105",
   "section": "Feigenbaum ratios",
   "claim": "number 3.19 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(6.9\\times10^{-7}\\) | 3.19 |",
   "paper_text": "$6.9\\times10^{-7}$, and the ratios $3.19$ and $4.019$ have worst-case",
   "paper_line": 1868,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0106",
   "section": "Feigenbaum ratios",
   "claim": "number 48 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 48 | 0.066114132784466 | \\(3.3\\times10^{-15}\\)",
   "paper_text": "just-born doubled orbit past period 48 failed: Newton's method slides",
   "paper_line": 1856,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0107",
   "section": "Feigenbaum ratios",
   "claim": "number 0.066114132784466 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 48 | 0.066114132784466 | \\(3.3\\times10^{-15}\\)",
   "paper_text": "$6.9\\times10^{-7}$ & $3.19$ \\\\ 48 & $0.066114132784466$ & $3.3\\times10^{-15}$ & $4.019$",
   "paper_line": 1909,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0108",
   "section": "Feigenbaum ratios",
   "claim": "number 3.3\\times10^{-15} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 0.066114132784466 | \\(3.3\\times10^{-15}\\) | 4.019 |",
   "paper_text": "48 & $0.066114132784466$ & $3.3\\times10^{-15}$ & $4.019$ \\\\ 96 & $0.066122589892689$",
   "paper_line": 1910,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0109",
   "section": "Feigenbaum ratios",
   "claim": "number 4.019 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(3.3\\times10^{-15}\\) | 4.019 |",
   "paper_text": "and the ratios $3.19$ and $4.019$ have worst-case ranges $[2.895,3.338]$",
   "paper_line": 1868,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0110",
   "section": "Feigenbaum ratios",
   "claim": "number 96 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 96 | 0.066122589892689 | \\(7\\times10^{-15}\\)",
   "paper_text": "$3.3\\times10^{-15}$ & $4.019$ \\\\ 96 & $0.066122589892689$ & $7\\times10^{-15}$",
   "paper_line": 1910,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0111",
   "section": "Feigenbaum ratios",
   "claim": "number 0.066122589892689 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 96 | 0.066122589892689 | \\(7\\times10^{-15}\\) |",
   "paper_text": "$3.3\\times10^{-15}$ & $4.019$ \\\\ 96 & $0.066122589892689$ & $7\\times10^{-15}$ & $4.4779$",
   "paper_line": 1910,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0112",
   "section": "Feigenbaum ratios",
   "claim": "number 7\\times10^{-15} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 0.066122589892689 | \\(7\\times10^{-15}\\) | 4.4779 |",
   "paper_text": "96 & $0.066122589892689$ & $7\\times10^{-15}$ & $4.4779$ \\\\ 192 & $0.066124478510077$",
   "paper_line": 1911,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0113",
   "section": "Feigenbaum ratios",
   "claim": "number 4.4779 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| \\(7\\times10^{-15}\\) | 4.4779 |",
   "paper_text": "$0.066122589892689$ & $7\\times10^{-15}$ & $4.4779$ \\\\ 192 & $0.066124478510077$",
   "paper_line": 1911,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0114",
   "section": "Feigenbaum ratios",
   "claim": "number 192 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 192 | 0.066124478510077 | \\(6.4\\times10^{-15}\\)",
   "paper_text": "$7\\times10^{-15}$ & $4.4779$ \\\\ 192 & $0.066124478510077$ & $6.4\\times10^{-15}$",
   "paper_line": 1911,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0115",
   "section": "Feigenbaum ratios",
   "claim": "number 0.066124478510077 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 192 | 0.066124478510077 | \\(6.4\\times10^{-15}\\)",
   "paper_text": "$7\\times10^{-15}$ & $4.4779$ \\\\ 192 & $0.066124478510077$ & $6.4\\times10^{-15}$ & $4.6251$",
   "paper_line": 1911,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0116",
   "section": "Feigenbaum ratios",
   "claim": "number 6.4\\times10^{-15} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 0.066124478510077 | \\(6.4\\times10^{-15}\\) | 4.6251 |",
   "paper_text": "192 & $0.066124478510077$ & $6.4\\times10^{-15}$ & $4.6251$ \\\\ 384 & $0.066124886853811$",
   "paper_line": 1912,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0117",
   "section": "Feigenbaum ratios",
   "claim": "number 4.6251 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(6.4\\times10^{-15}\\) | 4.6251 |",
   "paper_text": "$0.066124478510077$ & $6.4\\times10^{-15}$ & $4.6251$ \\\\ 384 & $0.066124886853811$",
   "paper_line": 1912,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0118",
   "section": "Feigenbaum ratios",
   "claim": "number 384 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 384 | 0.066124886853811 | \\(5\\times10^{-15}\\)",
   "paper_text": "$6.4\\times10^{-15}$ & $4.6251$ \\\\ 384 & $0.066124886853811$ & $5\\times10^{-15}$",
   "paper_line": 1912,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0119",
   "section": "Feigenbaum ratios",
   "claim": "number 0.066124886853811 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 384 | 0.066124886853811 | \\(5\\times10^{-15}\\) |",
   "paper_text": "$6.4\\times10^{-15}$ & $4.6251$ \\\\ 384 & $0.066124886853811$ & $5\\times10^{-15}$ & $4.6595$",
   "paper_line": 1912,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0120",
   "section": "Feigenbaum ratios",
   "claim": "number 5\\times10^{-15} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 0.066124886853811 | \\(5\\times10^{-15}\\) | 4.6595 |",
   "paper_text": "384 & $0.066124886853811$ & $5\\times10^{-15}$ & $4.6595$ \\\\ 768 & $0.066124974490236$",
   "paper_line": 1913,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0121",
   "section": "Feigenbaum ratios",
   "claim": "number 4.6595 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| \\(5\\times10^{-15}\\) | 4.6595 |",
   "paper_text": "$0.066124886853811$ & $5\\times10^{-15}$ & $4.6595$ \\\\ 768 & $0.066124974490236$",
   "paper_line": 1913,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0122",
   "section": "Feigenbaum ratios",
   "claim": "number 768 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 768 | 0.066124974490236 | \\(4.1\\times10^{-15}\\)",
   "paper_text": "$5\\times10^{-15}$ & $4.6595$ \\\\ 768 & $0.066124974490236$ & $4.1\\times10^{-15}$",
   "paper_line": 1913,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0123",
   "section": "Feigenbaum ratios",
   "claim": "number 0.066124974490236 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 768 | 0.066124974490236 | \\(4.1\\times10^{-15}\\)",
   "paper_text": "$5\\times10^{-15}$ & $4.6595$ \\\\ 768 & $0.066124974490236$ & $4.1\\times10^{-15}$ & \\\\",
   "paper_line": 1913,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0124",
   "section": "Feigenbaum ratios",
   "claim": "number 4.1\\times10^{-15} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 0.066124974490236 | \\(4.1\\times10^{-15}\\) | |",
   "paper_text": "768 & $0.066124974490236$ & $4.1\\times10^{-15}$ & \\\\ \\bottomrule \\end{tabular}",
   "paper_line": 1914,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0125",
   "section": "Feigenbaum ratios",
   "claim": "number -0.14798 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "sequence along \\(\\log_{10}T = -0.14798\\). The ratio in each row",
   "paper_text": "sequence along $\\log_{10}T=-0.14798$: the critical multiplier of",
   "paper_line": 1917,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0126",
   "section": "Feigenbaum ratios",
   "claim": "number 3\\times10^{-13} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Newton residuals below \\(3\\times10^{-13}\\); at period 768 the residual",
   "paper_text": "with Newton residuals below $3\\times10^{-13}$ and the other computed Ritz",
   "paper_line": 1918,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0127",
   "section": "Feigenbaum ratios",
   "claim": "number 768 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(3\\times10^{-13}\\); at period 768 the residual is \\(1.2\\times10^{-12}\\).",
   "paper_text": "period 96 to 384; at period 768 the residual is $1.2\\times10^{-12}$",
   "paper_line": 1919,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0128",
   "section": "Feigenbaum ratios",
   "claim": "number 1.2\\times10^{-12} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "period 768 the residual is \\(1.2\\times10^{-12}\\). Brackets for periods",
   "paper_text": "period 768 the residual is $1.2\\times10^{-12}$ and the other moduli are below",
   "paper_line": 1919,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0129",
   "section": "Feigenbaum ratios",
   "claim": "number 12 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(1.2\\times10^{-12}\\). Brackets for periods 12 and 24 are the closest",
   "paper_text": "$3\\times10^{-20}$. Brackets for periods 12 and 24 are the closest points",
   "paper_line": 1920,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0130",
   "section": "Feigenbaum ratios",
   "claim": "number 24 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Brackets for periods 12 and 24 are the closest points",
   "paper_text": "Brackets for periods 12 and 24 are the closest points where",
   "paper_line": 1920,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0131",
   "section": "Feigenbaum ratios",
   "claim": "number 12 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(philosophy direction, layer 12), from flips and from superstable",
   "paper_text": "(philosophy direction, layer 12), from flips and from superstable",
   "paper_line": 1873,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0132",
   "section": "Feigenbaum ratios",
   "claim": "number 14 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(philosophy direction, layer 14), from flips. A superstable",
   "paper_text": "(philosophy direction, layer 14; Figure~\\ref{fig:qwen15route}),",
   "paper_line": 1875,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0133",
   "section": "Feigenbaum ratios",
   "claim": "number -0.148 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(s_{24}\\). At \\(\\log_{10}T = -0.148\\), and in the 1.5B model,",
   "paper_text": "and $s_{24}$. At $\\log_{10}T=-0.148$, and in the 1.5B model, the",
   "paper_line": 1878,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0134",
   "section": "Feigenbaum ratios",
   "claim": "number -0.148 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "superstable ratio at \\(-0.148\\) is within 0.21% of it,",
   "paper_text": "last superstable ratio at $-0.148$ is within 0.21\\,\\% of it,",
   "paper_line": 1879,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0135",
   "section": "Feigenbaum ratios",
   "claim": "number 0.21 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at \\(-0.148\\) is within 0.21% of it, and the last 1.5B",
   "paper_text": "ratio at $-0.148$ is within 0.21\\,\\% of it, and the last 1.5B",
   "paper_line": 1879,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0136",
   "section": "Feigenbaum ratios",
   "claim": "number 4.665 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and the last 1.5B ratio (4.665) within 0.1%. At \\(\\log_{10}T",
   "paper_text": "it, and the last 1.5B ratio ($4.665$) within 0.1\\,\\%. At $\\log_{10}T=-0.156$",
   "paper_line": 1879,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0137",
   "section": "Feigenbaum ratios",
   "claim": "number 0.1 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "1.5B ratio (4.665) within 0.1%. At \\(\\log_{10}T = -0.156\\)",
   "paper_text": "1.5B ratio ($4.665$) within 0.1\\,\\%. At $\\log_{10}T=-0.156$",
   "paper_line": 1879,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0138",
   "section": "Feigenbaum ratios",
   "claim": "number -0.156 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.1%. At \\(\\log_{10}T = -0.156\\) the first ratio, 14.9,",
   "paper_text": "within 0.1\\,\\%. At $\\log_{10}T=-0.156$ the first ratio, $14.9$, lies",
   "paper_line": 1879,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0139",
   "section": "Feigenbaum ratios",
   "claim": "number 14.9 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "-0.156\\) the first ratio, 14.9, lies off the scale (arrow),",
   "paper_text": "$\\log_{10}T=-0.156$ the first ratio, $14.9$, lies off the scale (arrow),",
   "paper_line": 1879,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0140",
   "section": "Feigenbaum ratios",
   "claim": "number 4.6688 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\delta\\) from below, the last (4.6688) within 0.008% of it, and",
   "paper_text": "$\\delta$ from below, the last ($4.6688$) within $0.008\\,\\%$ of it,",
   "paper_line": 1880,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0141",
   "section": "Feigenbaum ratios",
   "claim": "number 0.008 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the last (4.6688) within 0.008% of it, and within 0.015%",
   "paper_text": "the last ($4.6688$) within $0.008\\,\\%$ of it, and within $0.015\\,\\%$",
   "paper_line": 1880,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0142",
   "section": "Feigenbaum ratios",
   "claim": "number 0.015 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.008% of it, and within 0.015% over the location uncertainty",
   "paper_text": "$0.008\\,\\%$ of it, and within $0.015\\,\\%$ over the location uncertainty",
   "paper_line": 1880,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0143",
   "section": "Feigenbaum ratios",
   "claim": "number 3.40 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(s_{12}\\) and \\(s_{24}\\) allow [3.40, 29.3] and [1.01, 4.65].",
   "paper_text": "$s_{12}$ and $s_{24}$ allow $[3.40,29.3]$ and $[1.01,4.65]$. Each",
   "paper_line": 1881,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0144",
   "section": "Feigenbaum ratios",
   "claim": "number 29.3 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(s_{24}\\) allow [3.40, 29.3] and [1.01, 4.65]. Each",
   "paper_text": "$s_{12}$ and $s_{24}$ allow $[3.40,29.3]$ and $[1.01,4.65]$. Each sequence",
   "paper_line": 1881,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0145",
   "section": "Feigenbaum ratios",
   "claim": "number 1.01 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "allow [3.40, 29.3] and [1.01, 4.65]. Each sequence ends",
   "paper_text": "$s_{24}$ allow $[3.40,29.3]$ and $[1.01,4.65]$. Each sequence ends",
   "paper_line": 1881,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0146",
   "section": "Feigenbaum ratios",
   "claim": "number 4.65 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "[3.40, 29.3] and [1.01, 4.65]. Each sequence ends at",
   "paper_text": "allow $[3.40,29.3]$ and $[1.01,4.65]$. Each sequence ends at the",
   "paper_line": 1881,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0147",
   "section": "Feigenbaum ratios",
   "claim": "number -0.148 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "computed: the flips at \\(-0.148\\) at period 384, the superstable",
   "paper_text": "level computed: the flips at $-0.148$ at period 384, the superstable",
   "paper_line": 1882,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0148",
   "section": "Feigenbaum ratios",
   "claim": "number 384 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at \\(-0.148\\) at period 384, the superstable points",
   "paper_text": "flips at $-0.148$ at period 384, the superstable points at",
   "paper_line": 1882,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0149",
   "section": "Feigenbaum ratios",
   "claim": "number 768 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "the superstable points at period 768 at \\(-0.148\\) and at period 384 at \\(-0.156\\)",
   "paper_text": "the superstable points at period 768 at $-0.148$ and at period 384 at $-0.156$",
   "paper_line": 1882,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0150",
   "section": "Feigenbaum ratios",
   "claim": "number 256 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "the 1.5B route at period 256, and the cut at \\(-0.156\\),",
   "paper_text": "the 1.5B route at period 256, and the cut at $-0.156$, which",
   "paper_line": 1882,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0151",
   "section": "Feigenbaum ratios",
   "claim": "number -0.156 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "period 256, and the cut at \\(-0.156\\), which we followed furthest,",
   "paper_text": "period 256, and the cut at $-0.156$, which we followed furthest,",
   "paper_line": 1882,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0152",
   "section": "Feigenbaum ratios",
   "claim": "number 768 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "followed furthest, at the 768 → 1536 flip. Source: byte-identical",
   "paper_text": "followed furthest, at the $768\\to1536$ flip. } \\label{fig:feigenbaum}",
   "paper_line": 1883,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0153",
   "section": "Feigenbaum ratios",
   "claim": "number 1536 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "furthest, at the 768 → 1536 flip. Source: byte-identical",
   "paper_text": "followed furthest, at the $768\\to1536$ flip. } \\label{fig:feigenbaum}",
   "paper_line": 1883,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0154",
   "section": "Feigenbaum ratios",
   "claim": "number -0.156 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = -0.156\\) the first ratio is 14.93,",
   "paper_text": "and it fails. At $\\log_{10}T=-0.156$ the first ratio is $14.93$,",
   "paper_line": 1928,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0155",
   "section": "Feigenbaum ratios",
   "claim": "number 14.93 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "-0.156\\) the first ratio is 14.93, five times its value at",
   "paper_text": "$\\log_{10}T=-0.156$ the first ratio is $14.93$, five times its value at $-0.148$",
   "paper_line": 1928,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0156",
   "section": "Feigenbaum ratios",
   "claim": "number -0.148 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-0.148\\) (Table",
   "paper_text": "$14.93$, five times its value at $-0.148$ (Table~\\ref{tab:cascade156}).",
   "paper_line": 1928,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0157",
   "section": "Feigenbaum ratios",
   "claim": "number -0.152 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "). At \\(-0.152\\) the continued period-12",
   "paper_text": "(Table~\\ref{tab:cascade156}). At $-0.152$ the continued period-12 solution",
   "paper_line": 1929,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0158",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0657 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "parent near \\(\\alpha \\approx 0.0657\\), and",
   "paper_text": "period-6 parent near $\\alpha\\approx0.0657$, and the forward search found",
   "paper_line": 1929,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0159",
   "section": "Feigenbaum ratios",
   "claim": "number -0.156 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "ratios at \\(\\log_{10}T = -0.156\\) behave",
   "paper_text": "period 256, and the cut at $-0.156$, which we followed furthest,",
   "paper_line": 1882,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0160",
   "section": "Feigenbaum ratios",
   "claim": "number 3.124 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "universality requires: 3.124, 4.4988, 4.6208, 4.6618,",
   "paper_text": "requires. The next ratios are $3.124$, $4.4988$, $4.6208$, $4.6618$,",
   "paper_line": 1933,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0161",
   "section": "Feigenbaum ratios",
   "claim": "number 4.4988 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "universality requires: 3.124, 4.4988, 4.6208, 4.6618, 4.6673",
   "paper_text": "The next ratios are $3.124$, $4.4988$, $4.6208$, $4.6618$, $4.6673$",
   "paper_line": 1933,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0162",
   "section": "Feigenbaum ratios",
   "claim": "number 4.6208 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "requires: 3.124, 4.4988, 4.6208, 4.6618, 4.6673 and 4.6688.",
   "paper_text": "ratios are $3.124$, $4.4988$, $4.6208$, $4.6618$, $4.6673$ and $4.6688$.",
   "paper_line": 1933,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0163",
   "section": "Feigenbaum ratios",
   "claim": "number 4.6618 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "3.124, 4.4988, 4.6208, 4.6618, 4.6673 and 4.6688. Their",
   "paper_text": "$3.124$, $4.4988$, $4.6208$, $4.6618$, $4.6673$ and $4.6688$. Their",
   "paper_line": 1933,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0164",
   "section": "Feigenbaum ratios",
   "claim": "number 4.6673 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "4.4988, 4.6208, 4.6618, 4.6673 and 4.6688. Their",
   "paper_text": "$4.4988$, $4.6208$, $4.6618$, $4.6673$ and $4.6688$. Their deviations",
   "paper_line": 1933,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0165",
   "section": "Feigenbaum ratios",
   "claim": "number 4.6688 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "4.6208, 4.6618, 4.6673 and 4.6688. Their",
   "paper_text": "$4.6208$, $4.6618$, $4.6673$ and $4.6688$. Their deviations from $\\delta=4.6692$",
   "paper_line": 1933,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0166",
   "section": "Feigenbaum ratios",
   "claim": "number -1.55 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "deviations from \\(\\delta\\) are \\(-1.55\\), \\(-0.17\\), \\(-0.048\\),",
   "paper_text": "deviations from $\\delta=4.6692$ are $-1.55$, $-0.17$, $-0.048$, $-0.0074$,",
   "paper_line": 1934,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0167",
   "section": "Feigenbaum ratios",
   "claim": "number -0.17 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\delta\\) are \\(-1.55\\), \\(-0.17\\), \\(-0.048\\), \\(-0.0074\\),",
   "paper_text": "$\\delta=4.6692$ are $-1.55$, $-0.17$, $-0.048$, $-0.0074$, $-0.0019$",
   "paper_line": 1934,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0168",
   "section": "Feigenbaum ratios",
   "claim": "number -0.048 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-1.55\\), \\(-0.17\\), \\(-0.048\\), \\(-0.0074\\),",
   "paper_text": "$\\delta=4.6692$ are $-1.55$, $-0.17$, $-0.048$, $-0.0074$, $-0.0019$ and",
   "paper_line": 1934,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0169",
   "section": "Feigenbaum ratios",
   "claim": "number -0.0074 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-0.17\\), \\(-0.048\\), \\(-0.0074\\),",
   "paper_text": "$-1.55$, $-0.17$, $-0.048$, $-0.0074$, $-0.0019$ and $-0.00036$;",
   "paper_line": 1934,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0170",
   "section": "Feigenbaum ratios",
   "claim": "number -0.0019 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-0.0019\\) and \\(-0.00036\\). They",
   "paper_text": "$-0.17$, $-0.048$, $-0.0074$, $-0.0019$ and $-0.00036$; they keep",
   "paper_line": 1934,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0171",
   "section": "Feigenbaum ratios",
   "claim": "number -0.00036 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-0.0019\\) and \\(-0.00036\\). They keep one sign,",
   "paper_text": "$-0.048$, $-0.0074$, $-0.0019$ and $-0.00036$; they keep one sign, from",
   "paper_line": 1934,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0172",
   "section": "Feigenbaum ratios",
   "claim": "number 3.5 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "closes the gap by a factor of 3.5 to 6.5 (the location",
   "paper_text": "closes the gap by a factor of 3.5 to 6.5 (the location uncertainty of the period-384",
   "paper_line": 1935,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0173",
   "section": "Feigenbaum ratios",
   "claim": "number 6.5 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "gap by a factor of 3.5 to 6.5 (the location uncertainty of the",
   "paper_text": "the gap by a factor of 3.5 to 6.5 (the location uncertainty of the period-384 flip",
   "paper_line": 1935,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0174",
   "section": "Feigenbaum ratios",
   "claim": "number 4.6694 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "sequence) gives 4.6694. The last ratio uses the",
   "paper_text": "the last three ratios gives $4.6694$. Universality of this kind",
   "paper_line": 1936,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0175",
   "section": "Feigenbaum ratios",
   "claim": "number 4.1\\times10^{-7} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "with \\(\\lvert\\mu+1\\rvert = 4.1\\times10^{-7}\\). The penultimate flip,",
   "paper_text": "flip), located with $|\\mu+1|=4.1\\times10^{-7}$. The penultimate flip, of",
   "paper_line": 1941,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0176",
   "section": "Feigenbaum ratios",
   "claim": "number 384 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "384 step Jacobians. On an H100",
   "paper_text": "its multiplier, a product of 384 step Jacobians. On an H100",
   "paper_line": 1942,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0177",
   "section": "Feigenbaum ratios",
   "claim": "number 1.8\\times10^{-5} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(1.8\\times10^{-5}\\) about a straight line",
   "paper_text": "computed $\\mu+1$ scatters by $1.8\\times10^{-5}$ about a straight line near",
   "paper_line": 1942,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0178",
   "section": "Feigenbaum ratios",
   "claim": "number 0.06510347354866666 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "located it at \\(\\alpha = 0.06510347354866666\\), with",
   "paper_text": "workstation GPU located it at $\\alpha=0.06510347354866666$ with $|\\mu+1|=4\\times10^{-9}$,",
   "paper_line": 1945,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0179",
   "section": "Feigenbaum ratios",
   "claim": "number 4\\times10^{-9} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lvert\\mu+1\\rvert = 4\\times10^{-9}\\), \\(9\\times10^{-14}\\)",
   "paper_text": "$\\alpha=0.06510347354866666$ with $|\\mu+1|=4\\times10^{-9}$, $9\\times10^{-14}$ from the",
   "paper_line": 1946,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0180",
   "section": "Feigenbaum ratios",
   "claim": "number 9\\times10^{-14} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lvert\\mu+1\\rvert = 4\\times10^{-9}\\), \\(9\\times10^{-14}\\) from the H100",
   "paper_text": "$|\\mu+1|=4\\times10^{-9}$, $9\\times10^{-14}$ from the H100 estimate. Over",
   "paper_line": 1946,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0181",
   "section": "Feigenbaum ratios",
   "claim": "number 4.6672 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\delta_7\\) lies between 4.6672 and 4.6674, the last",
   "paper_text": "ratio $\\delta_7$ lies between $4.6672$ and $4.6674$, $\\delta_8$,",
   "paper_line": 1947,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0182",
   "section": "Feigenbaum ratios",
   "claim": "number 4.6674 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "lies between 4.6672 and 4.6674, the last",
   "paper_text": "lies between $4.6672$ and $4.6674$, $\\delta_8$, the last ratio,",
   "paper_line": 1947,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0183",
   "section": "Feigenbaum ratios",
   "claim": "number 4.6685 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "ratio \\(\\delta_8\\) between 4.6685 and 4.6692, and the extrapolated",
   "paper_text": "$\\delta_8$, the last ratio, between $4.6685$ and $4.6692$, and the extrapolated",
   "paper_line": 1947,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0184",
   "section": "Feigenbaum ratios",
   "claim": "number 4.6692 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\delta_8\\) between 4.6685 and 4.6692, and the extrapolated value",
   "paper_text": "ratio, between $4.6685$ and $4.6692$, and the extrapolated value",
   "paper_line": 1947,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0185",
   "section": "Feigenbaum ratios",
   "claim": "number 4.6688 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "4.6688 and 4.6702, an interval",
   "paper_text": "extrapolated value between $4.6688$ and $4.6702$, an interval",
   "paper_line": 1948,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0186",
   "section": "Feigenbaum ratios",
   "claim": "number 4.6702 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "4.6688 and 4.6702, an interval that contains",
   "paper_text": "value between $4.6688$ and $4.6702$, an interval that contains",
   "paper_line": 1948,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0187",
   "section": "Feigenbaum ratios",
   "claim": "number 384 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "same cut, through period 384, give the ratios",
   "paper_text": "the same cut, through period 384, give the ratios $10.21$, $3.713$,",
   "paper_line": 1949,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0188",
   "section": "Feigenbaum ratios",
   "claim": "number 10.21 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "10.21, 3.713, 4.572, 4.643 and",
   "paper_text": "period 384, give the ratios $10.21$, $3.713$, $4.572$, $4.643$",
   "paper_line": 1949,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0189",
   "section": "Feigenbaum ratios",
   "claim": "number 3.713 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "10.21, 3.713, 4.572, 4.643 and 4.6646.",
   "paper_text": "384, give the ratios $10.21$, $3.713$, $4.572$, $4.643$ and $4.6646$.",
   "paper_line": 1949,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0190",
   "section": "Feigenbaum ratios",
   "claim": "number 4.572 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "10.21, 3.713, 4.572, 4.643 and 4.6646. Before",
   "paper_text": "the ratios $10.21$, $3.713$, $4.572$, $4.643$ and $4.6646$. Before",
   "paper_line": 1949,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0191",
   "section": "Feigenbaum ratios",
   "claim": "number 4.643 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "10.21, 3.713, 4.572, 4.643 and 4.6646. Before computing",
   "paper_text": "$10.21$, $3.713$, $4.572$, $4.643$ and $4.6646$. Before computing",
   "paper_line": 1949,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0192",
   "section": "Feigenbaum ratios",
   "claim": "number 4.6646 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "3.713, 4.572, 4.643 and 4.6646. Before computing them",
   "paper_text": "$3.713$, $4.572$, $4.643$ and $4.6646$. Before computing them we",
   "paper_line": 1949,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0193",
   "section": "Feigenbaum ratios",
   "claim": "number 4.436 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "within 5% of \\(\\delta\\), in [4.436, 4.902]. Through period",
   "paper_text": "within 5\\,\\% of $\\delta$, in $[4.436,4.902]$. At the original readout,",
   "paper_line": 1951,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0194",
   "section": "Feigenbaum ratios",
   "claim": "number 4.902 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\delta\\), in [4.436, 4.902]. Through period 192 the",
   "paper_text": "5\\,\\% of $\\delta$, in $[4.436,4.902]$. At the original readout,",
   "paper_line": 1951,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0195",
   "section": "Feigenbaum ratios",
   "claim": "number 192 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "4.902]. Through period 192 the point estimates",
   "paper_text": "original readout, through period 192, the point estimates $4.572$",
   "paper_line": 1951,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0196",
   "section": "Feigenbaum ratios",
   "claim": "number 4.572 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "4.572 and 4.643 met it, but the",
   "paper_text": "period 192, the point estimates $4.572$ and $4.643$ met it, but the",
   "paper_line": 1951,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0197",
   "section": "Feigenbaum ratios",
   "claim": "number 4.643 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "4.572 and 4.643 met it, but the bracket",
   "paper_text": "point estimates $4.572$ and $4.643$ met it, but the bracket envelope",
   "paper_line": 1951,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0198",
   "section": "Feigenbaum ratios",
   "claim": "number 4.572 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the bracket envelope of 4.572 did not; extending the",
   "paper_text": "but the bracket envelope of $4.572$ did not; extending the computation",
   "paper_line": 1952,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0199",
   "section": "Feigenbaum ratios",
   "claim": "number 384 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "computation to period 384 later gave the pair 4.643",
   "paper_text": "extending the computation to period 384 later gave the pair $4.643$",
   "paper_line": 1952,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0200",
   "section": "Feigenbaum ratios",
   "claim": "number 4.643 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "384 later gave the pair 4.643 and 4.6646, both inside",
   "paper_text": "period 384 later gave the pair $4.643$ and $4.6646$, both inside",
   "paper_line": 1952,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0201",
   "section": "Feigenbaum ratios",
   "claim": "number 4.6646 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "gave the pair 4.643 and 4.6646, both inside the",
   "paper_text": "gave the pair $4.643$ and $4.6646$, both inside the interval.",
   "paper_line": 1953,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0202",
   "section": "Feigenbaum ratios",
   "claim": "number 4.6646 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "interval. The last, 4.6646, rests on parameters resolved",
   "paper_text": "inside the interval. The last, $4.6646$, rests on parameters resolved",
   "paper_line": 1953,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0203",
   "section": "Feigenbaum ratios",
   "claim": "number 5\\times10^{-15} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "parameters resolved to \\(5\\times10^{-15}\\)",
   "paper_text": "on parameters resolved to $5\\times10^{-15}$ and differs from $\\delta$",
   "paper_line": 1953,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0204",
   "section": "Feigenbaum ratios",
   "claim": "number 0.1 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "differs from \\(\\delta\\) by 0.1%. Finite-order ratios also",
   "paper_text": "and differs from $\\delta$ by $0.1\\,\\%$. Over the corners of the",
   "paper_line": 1953,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0205",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0644766567385 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 1 | 3 → 6 | 0.0644766567385 | 0.12 | |",
   "paper_text": "\\\\ \\midrule 1 & $3\\to6$ & $0.0644766567385$ & $0.12$ & \\\\ 2 & $6\\to12$",
   "paper_line": 2000,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0206",
   "section": "Feigenbaum ratios",
   "claim": "number 0.12 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "→ 6 | 0.0644766567385 | 0.12 | |",
   "paper_text": "only $-0.07$ (interval $[-0.23,0.12]$); a logit bias alone, with",
   "paper_line": 249,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0207",
   "section": "Feigenbaum ratios",
   "claim": "number 12 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 2 | 6 → 12 | 0.0650493555308 | 0.045",
   "paper_text": "philosophy direction at layer 12), at increasing distance from",
   "paper_line": 1762,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0208",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0650493555308 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 2 | 6 → 12 | 0.0650493555308 | 0.045 | 14.93 |",
   "paper_text": "$0.12$ & \\\\ 2 & $6\\to12$ & $0.0650493555308$ & $0.045$ & $14.93$ \\\\ 3 &",
   "paper_line": 2002,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0209",
   "section": "Feigenbaum ratios",
   "claim": "number 0.045 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "12 | 0.0650493555308 | 0.045 | 14.93 |",
   "paper_text": "$6\\to12$ & $0.0650493555308$ & $0.045$ & $14.93$ \\\\ 3 & $12\\to24$",
   "paper_line": 2003,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0210",
   "section": "Feigenbaum ratios",
   "claim": "number 14.93 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.0650493555308 | 0.045 | 14.93 |",
   "paper_text": "$\\log_{10}T=-0.156$ the first ratio is $14.93$, five times its value at $-0.148$",
   "paper_line": 1928,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0211",
   "section": "Feigenbaum ratios",
   "claim": "number 12 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 3 | 12 → 24 | 0.0650877194158",
   "paper_text": "$2\\times10^{-6}$, $2\\times10^{-12}$). The next ratio, $\\delta_4=3.781$,",
   "paper_line": 1852,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0212",
   "section": "Feigenbaum ratios",
   "claim": "number 24 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 3 | 12 → 24 | 0.0650877194158 | \\(7.0\\times10^{-5}\\)",
   "paper_text": "the root, so $s_{12}$ and $s_{24}$ are known only within brackets",
   "paper_line": 1867,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0213",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0650877194158 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 3 | 12 → 24 | 0.0650877194158 | \\(7.0\\times10^{-5}\\)",
   "paper_text": "$14.93$ \\\\ 3 & $12\\to24$ & $0.0650877194158$ & $7.0\\times10^{-5}$ & $3.124$",
   "paper_line": 2003,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0214",
   "section": "Feigenbaum ratios",
   "claim": "number 7.0\\times10^{-5} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "24 | 0.0650877194158 | \\(7.0\\times10^{-5}\\) | 3.124 |",
   "paper_text": "$12\\to24$ & $0.0650877194158$ & $7.0\\times10^{-5}$ & $3.124$ \\\\ 4 & $24\\to48$",
   "paper_line": 2004,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0215",
   "section": "Feigenbaum ratios",
   "claim": "number 3.124 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(7.0\\times10^{-5}\\) | 3.124 |",
   "paper_text": "$0.0650877194158$ & $7.0\\times10^{-5}$ & $3.124$ \\\\ 4 & $24\\to48$ & $0.0650999993318$",
   "paper_line": 2004,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0216",
   "section": "Feigenbaum ratios",
   "claim": "number 24 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 4 | 24 → 48 | 0.0650999993318",
   "paper_text": "the root, so $s_{12}$ and $s_{24}$ are known only within brackets",
   "paper_line": 1867,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0217",
   "section": "Feigenbaum ratios",
   "claim": "number 48 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 4 | 24 → 48 | 0.0650999993318 | \\(4.3\\times10^{-7}\\)",
   "paper_text": "just-born doubled orbit past period 48 failed: Newton's method slides",
   "paper_line": 1856,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0218",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0650999993318 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 4 | 24 → 48 | 0.0650999993318 | \\(4.3\\times10^{-7}\\)",
   "paper_text": "$3.124$ \\\\ 4 & $24\\to48$ & $0.0650999993318$ & $4.3\\times10^{-7}$ & $4.4988$",
   "paper_line": 2004,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0219",
   "section": "Feigenbaum ratios",
   "claim": "number 4.3\\times10^{-7} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "48 | 0.0650999993318 | \\(4.3\\times10^{-7}\\) | 4.4988 |",
   "paper_text": "$24\\to48$ & $0.0650999993318$ & $4.3\\times10^{-7}$ & $4.4988$ \\\\ 5 & $48\\to96$",
   "paper_line": 2005,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0220",
   "section": "Feigenbaum ratios",
   "claim": "number 4.4988 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(4.3\\times10^{-7}\\) | 4.4988 |",
   "paper_text": "$0.0650999993318$ & $4.3\\times10^{-7}$ & $4.4988$ \\\\ 5 & $48\\to96$ & $0.0651027289524$",
   "paper_line": 2005,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0221",
   "section": "Feigenbaum ratios",
   "claim": "number 48 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 5 | 48 → 96 | 0.0651027289524",
   "paper_text": "just-born doubled orbit past period 48 failed: Newton's method slides",
   "paper_line": 1856,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0222",
   "section": "Feigenbaum ratios",
   "claim": "number 96 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 5 | 48 → 96 | 0.0651027289524 | \\(1.8\\times10^{-13}\\)",
   "paper_text": "$3.3\\times10^{-15}$ & $4.019$ \\\\ 96 & $0.066122589892689$ & $7\\times10^{-15}$",
   "paper_line": 1910,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0223",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0651027289524 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 5 | 48 → 96 | 0.0651027289524 | \\(1.8\\times10^{-13}\\)",
   "paper_text": "$4.4988$ \\\\ 5 & $48\\to96$ & $0.0651027289524$ & $1.8\\times10^{-13}$ & $4.6208$",
   "paper_line": 2005,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0224",
   "section": "Feigenbaum ratios",
   "claim": "number 1.8\\times10^{-13} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "96 | 0.0651027289524 | \\(1.8\\times10^{-13}\\) | 4.6208 |",
   "paper_text": "$48\\to96$ & $0.0651027289524$ & $1.8\\times10^{-13}$ & $4.6208$ \\\\ 6 & $96\\to192$",
   "paper_line": 2006,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0225",
   "section": "Feigenbaum ratios",
   "claim": "number 4.6208 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(1.8\\times10^{-13}\\) | 4.6208 |",
   "paper_text": "$0.0651027289524$ & $1.8\\times10^{-13}$ & $4.6208$ \\\\ 6 & $96\\to192$ & $0.0651033196816$",
   "paper_line": 2006,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0226",
   "section": "Feigenbaum ratios",
   "claim": "number 96 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 6 | 96 → 192 | 0.0651033196816",
   "paper_text": "$3.3\\times10^{-15}$ & $4.019$ \\\\ 96 & $0.066122589892689$ & $7\\times10^{-15}$",
   "paper_line": 1910,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0227",
   "section": "Feigenbaum ratios",
   "claim": "number 192 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 6 | 96 → 192 | 0.0651033196816 | \\(2.9\\times10^{-14}\\)",
   "paper_text": "$7\\times10^{-15}$ & $4.4779$ \\\\ 192 & $0.066124478510077$ & $6.4\\times10^{-15}$",
   "paper_line": 1911,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0228",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0651033196816 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 6 | 96 → 192 | 0.0651033196816 | \\(2.9\\times10^{-14}\\)",
   "paper_text": "$4.6208$ \\\\ 6 & $96\\to192$ & $0.0651033196816$ & $2.9\\times10^{-14}$ & $4.6618$",
   "paper_line": 2006,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0229",
   "section": "Feigenbaum ratios",
   "claim": "number 2.9\\times10^{-14} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "192 | 0.0651033196816 | \\(2.9\\times10^{-14}\\) | 4.6618 |",
   "paper_text": "$96\\to192$ & $0.0651033196816$ & $2.9\\times10^{-14}$ & $4.6618$ \\\\ 7 & $192\\to384$",
   "paper_line": 2007,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0230",
   "section": "Feigenbaum ratios",
   "claim": "number 4.6618 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(2.9\\times10^{-14}\\) | 4.6618 |",
   "paper_text": "$0.0651033196816$ & $2.9\\times10^{-14}$ & $4.6618$ \\\\ 7 & $192\\to384$ & $0.0651034463988$",
   "paper_line": 2007,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0231",
   "section": "Feigenbaum ratios",
   "claim": "number 192 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 7 | 192 → 384 | 0.0651034463988",
   "paper_text": "$7\\times10^{-15}$ & $4.4779$ \\\\ 192 & $0.066124478510077$ & $6.4\\times10^{-15}$",
   "paper_line": 1911,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0232",
   "section": "Feigenbaum ratios",
   "claim": "number 384 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 7 | 192 → 384 | 0.0651034463988 | \\(1.5\\times10^{-14}\\)",
   "paper_text": "$6.4\\times10^{-15}$ & $4.6251$ \\\\ 384 & $0.066124886853811$ & $5\\times10^{-15}$",
   "paper_line": 1912,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0233",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0651034463988 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 7 | 192 → 384 | 0.0651034463988 | \\(1.5\\times10^{-14}\\)",
   "paper_text": "$4.6618$ \\\\ 7 & $192\\to384$ & $0.0651034463988$ & $1.5\\times10^{-14}$ & $4.6673$",
   "paper_line": 2007,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0234",
   "section": "Feigenbaum ratios",
   "claim": "number 1.5\\times10^{-14} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "384 | 0.0651034463988 | \\(1.5\\times10^{-14}\\) | 4.6673 |",
   "paper_text": "$192\\to384$ & $0.0651034463988$ & $1.5\\times10^{-14}$ & $4.6673$ \\\\ 8 & $384\\to768$",
   "paper_line": 2008,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0235",
   "section": "Feigenbaum ratios",
   "claim": "number 4.6673 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(1.5\\times10^{-14}\\) | 4.6673 |",
   "paper_text": "$0.0651034463988$ & $1.5\\times10^{-14}$ & $4.6673$ \\\\ 8 & $384\\to768$ & $0.0651034735487$",
   "paper_line": 2008,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0236",
   "section": "Feigenbaum ratios",
   "claim": "number 384 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 8 | 384 → 768 | 0.0651034735487",
   "paper_text": "$6.4\\times10^{-15}$ & $4.6251$ \\\\ 384 & $0.066124886853811$ & $5\\times10^{-15}$",
   "paper_line": 1912,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0237",
   "section": "Feigenbaum ratios",
   "claim": "number 768 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 8 | 384 → 768 | 0.0651034735487 | \\(3.2\\times10^{-13}\\)",
   "paper_text": "$5\\times10^{-15}$ & $4.6595$ \\\\ 768 & $0.066124974490236$ & $4.1\\times10^{-15}$",
   "paper_line": 1913,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0238",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0651034735487 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 8 | 384 → 768 | 0.0651034735487 | \\(3.2\\times10^{-13}\\)",
   "paper_text": "$4.6673$ \\\\ 8 & $384\\to768$ & $0.0651034735487$ & $3.2\\times10^{-13}$ & $4.6688$",
   "paper_line": 2008,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0239",
   "section": "Feigenbaum ratios",
   "claim": "number 3.2\\times10^{-13} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "768 | 0.0651034735487 | \\(3.2\\times10^{-13}\\) | 4.6688 |",
   "paper_text": "$384\\to768$ & $0.0651034735487$ & $3.2\\times10^{-13}$ & $4.6688$ \\\\ 9 & $768\\to1536$",
   "paper_line": 2009,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0240",
   "section": "Feigenbaum ratios",
   "claim": "number 4.6688 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(3.2\\times10^{-13}\\) | 4.6688 |",
   "paper_text": "$0.0651034735487$ & $3.2\\times10^{-13}$ & $4.6688$ \\\\ 9 & $768\\to1536$ & $0.0651034793638$",
   "paper_line": 2009,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0241",
   "section": "Feigenbaum ratios",
   "claim": "number 768 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 9 | 768 → 1536 | 0.0651034793638",
   "paper_text": "$5\\times10^{-15}$ & $4.6595$ \\\\ 768 & $0.066124974490236$ & $4.1\\times10^{-15}$",
   "paper_line": 1913,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0242",
   "section": "Feigenbaum ratios",
   "claim": "number 1536 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 9 | 768 → 1536 | 0.0651034793638 | \\(2.9\\times10^{-14}\\)",
   "paper_text": "period-768 orbit (the $768\\to1536$ flip), located with $|\\mu+1|=4.1\\times10^{-7}$.",
   "paper_line": 1940,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0243",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0651034793638 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 9 | 768 → 1536 | 0.0651034793638 | \\(2.9\\times10^{-14}\\)",
   "paper_text": "$4.6688$ \\\\ 9 & $768\\to1536$ & $0.0651034793638$ & $2.9\\times10^{-14}$ & \\\\",
   "paper_line": 2009,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0244",
   "section": "Feigenbaum ratios",
   "claim": "number 2.9\\times10^{-14} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "1536 | 0.0651034793638 | \\(2.9\\times10^{-14}\\) | |",
   "paper_text": "$96\\to192$ & $0.0651033196816$ & $2.9\\times10^{-14}$ & $4.6618$ \\\\ 7 & $192\\to384$",
   "paper_line": 2007,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0245",
   "section": "Feigenbaum ratios",
   "claim": "number -0.156 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "sequence along \\(\\log_{10}T = -0.156\\), in float64 (Qwen2.5-0.5B-Instruct,",
   "paper_text": "sequence along $\\log_{10}T=-0.156$, in float64. Flips 1--3 were",
   "paper_line": 2013,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0246",
   "section": "Feigenbaum ratios",
   "claim": "number 12 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "philosophy direction at layer 12). Flips 1 to 3 were computed",
   "paper_text": "(philosophy direction, layer 12), from flips and from superstable",
   "paper_line": 1873,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0247",
   "section": "Feigenbaum ratios",
   "claim": "number 4\\times10^{-16} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "computations of flip 3 agree to \\(4\\times10^{-16}\\), and an H100 computation",
   "paper_text": "computations of flip 3 agree to $4\\times10^{-16}$, and an H100 computation of",
   "paper_line": 2014,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0248",
   "section": "Feigenbaum ratios",
   "claim": "number 9\\times10^{-14} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "precision floor lies \\(9\\times10^{-14}\\) away. Every critical",
   "paper_text": "multiplier's precision floor lies $9\\times10^{-14}$ away. Flip 9 was computed",
   "paper_line": 2015,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0249",
   "section": "Feigenbaum ratios",
   "claim": "number 5\\times10^{-8} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "from \\(-1\\) by at most \\(5\\times10^{-8}\\), and for flip 9 by \\(4.1\\times10^{-7}\\).",
   "paper_text": "differs from $-1$ by at most $5\\times10^{-8}$, and for flip 9 by $4.1\\times10^{-7}$.",
   "paper_line": 2016,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0250",
   "section": "Feigenbaum ratios",
   "claim": "number 4.1\\times10^{-7} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(5\\times10^{-8}\\), and for flip 9 by \\(4.1\\times10^{-7}\\). Next moduli below about",
   "paper_text": "$5\\times10^{-8}$, and for flip 9 by $4.1\\times10^{-7}$. Next moduli below about $10^{-12}$",
   "paper_line": 2017,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0251",
   "section": "Feigenbaum ratios",
   "claim": "number 4.6692 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "constant is \\(\\delta = 4.6692\\ldots\\), and the first",
   "paper_text": "Feigenbaum's constant is $\\delta=4.6692\\ldots$ \\cite{feigenbaum1978quantitative};",
   "paper_line": 1989,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0252",
   "section": "Feigenbaum ratios",
   "claim": "number 4.751 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of the logistic map are 4.751, 4.656 and 4.668. Source:",
   "paper_text": "logistic map the first ratios are $4.751$, $4.656$, $4.668$. The first",
   "paper_line": 1990,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0253",
   "section": "Feigenbaum ratios",
   "claim": "number 4.656 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "logistic map are 4.751, 4.656 and 4.668. Source: the",
   "paper_text": "first ratios are $4.751$, $4.656$, $4.668$. The first four parameters",
   "paper_line": 1990,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0254",
   "section": "Feigenbaum ratios",
   "claim": "number 4.668 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "map are 4.751, 4.656 and 4.668. Source: the report's cascade",
   "paper_text": "ratios are $4.751$, $4.656$, $4.668$. The first four parameters",
   "paper_line": 1990,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0255",
   "section": "Feigenbaum ratios",
   "claim": "number 12 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "philosophy direction at layer 12, \\(\\log_{10}T = -0.156\\)):",
   "paper_text": "philosophy direction at layer 12, $\\log_{10}T=-0.156$): float64",
   "paper_line": 1890,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0256",
   "section": "Feigenbaum ratios",
   "claim": "number -0.156 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "layer 12, \\(\\log_{10}T = -0.156\\)): float64 line scans",
   "paper_text": "direction at layer 12, $\\log_{10}T=-0.156$): float64 line scans of 1600,",
   "paper_line": 1890,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0257",
   "section": "Feigenbaum ratios",
   "claim": "number 1600 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "-0.156\\)): float64 line scans of 1600, 1360 and 1000 cells, each",
   "paper_text": "$\\log_{10}T=-0.156$): float64 line scans of 1600, 1360 and 1000 cells, each",
   "paper_line": 1891,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0258",
   "section": "Feigenbaum ratios",
   "claim": "number 1360 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "float64 line scans of 1600, 1360 and 1000 cells, each with",
   "paper_text": "float64 line scans of 1600, 1360 and 1000 cells, each with 3000",
   "paper_line": 1891,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0259",
   "section": "Feigenbaum ratios",
   "claim": "number 1000 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "scans of 1600, 1360 and 1000 cells, each with 3000 transient",
   "paper_text": "line scans of 1600, 1360 and 1000 cells, each with 3000 transient",
   "paper_line": 1891,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0260",
   "section": "Feigenbaum ratios",
   "claim": "number 3000 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and 1000 cells, each with 3000 transient steps and 256",
   "paper_text": "1360 and 1000 cells, each with 3000 transient steps and 256 recorded",
   "paper_line": 1891,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0261",
   "section": "Feigenbaum ratios",
   "claim": "number 256 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "3000 transient steps and 256 recorded states projected",
   "paper_text": "with 3000 transient steps and 256 recorded states projected on",
   "paper_line": 1891,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0262",
   "section": "Feigenbaum ratios",
   "claim": "number 0.065278 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "which ends at \\(\\alpha = 0.065278\\), where the attractor",
   "paper_text": "chaos, which ends at $\\alpha=0.065278$, where the attractor jumps",
   "paper_line": 1892,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0263",
   "section": "Feigenbaum ratios",
   "claim": "number 12 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "showing the doublings 6 → 12 → 24 → 48 and 24 → 48 →",
   "paper_text": "showing the doublings $6\\to12\\to24\\to48$ and $24\\to48\\to96\\to192$.",
   "paper_line": 1894,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0264",
   "section": "Feigenbaum ratios",
   "claim": "number 24 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the doublings 6 → 12 → 24 → 48 and 24 → 48 → 96 →",
   "paper_text": "showing the doublings $6\\to12\\to24\\to48$ and $24\\to48\\to96\\to192$.",
   "paper_line": 1894,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0265",
   "section": "Feigenbaum ratios",
   "claim": "number 48 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "doublings 6 → 12 → 24 → 48 and 24 → 48 → 96 → 192.",
   "paper_text": "the doublings $6\\to12\\to24\\to48$ and $24\\to48\\to96\\to192$.",
   "paper_line": 1894,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0266",
   "section": "Feigenbaum ratios",
   "claim": "number 24 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "doublings 6 → 12 → 24 → 48 and 24 → 48 → 96 → 192. Dashed",
   "paper_text": "showing the doublings $6\\to12\\to24\\to48$ and $24\\to48\\to96\\to192$.",
   "paper_line": 1894,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0267",
   "section": "Feigenbaum ratios",
   "claim": "number 48 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "→ 12 → 24 → 48 and 24 → 48 → 96 → 192. Dashed lines:",
   "paper_text": "$6\\to12\\to24\\to48$ and $24\\to48\\to96\\to192$. Dashed lines:",
   "paper_line": 1894,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0268",
   "section": "Feigenbaum ratios",
   "claim": "number 96 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "→ 24 → 48 and 24 → 48 → 96 → 192. Dashed lines: flips",
   "paper_text": "$6\\to12\\to24\\to48$ and $24\\to48\\to96\\to192$. Dashed lines: flips",
   "paper_line": 1894,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0269",
   "section": "Feigenbaum ratios",
   "claim": "number 192 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "→ 48 and 24 → 48 → 96 → 192. Dashed lines: flips located",
   "paper_text": "$6\\to12\\to24\\to48$ and $24\\to48\\to96\\to192$. Dashed lines: flips located",
   "paper_line": 1894,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0270",
   "section": "Feigenbaum ratios",
   "claim": "number 3000 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "converges slowly, so with 3000 transient steps each fork",
   "paper_text": "orbit converges slowly, so with 3000 transient steps each fork opens",
   "paper_line": 1897,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0271",
   "section": "Feigenbaum ratios",
   "claim": "number 8.4\\times10^{-6} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "before its Newton flip, by \\(8.4\\times10^{-6}\\) in \\(\\alpha\\) at the",
   "paper_text": "before its Newton flip, by $8.4\\times10^{-6}$ in $\\alpha$ at the first and",
   "paper_line": 1898,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0272",
   "section": "Feigenbaum ratios",
   "claim": "number 1.1\\times10^{-6} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "first and by at most \\(1.1\\times10^{-6}\\) at the later ones. Source:",
   "paper_text": "at the first and by at most $1.1\\times10^{-6}$ at the later ones.} \\label{fig:feigtree}",
   "paper_line": 1898,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0273",
   "section": "Feigenbaum ratios",
   "claim": "number 4.665 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "same way: its last ratio, 4.665, is within 0.1% of",
   "paper_text": "same way: its last ratio, $4.665$, is within $0.1\\,\\%$ of $\\delta$",
   "paper_line": 2058,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0274",
   "section": "Feigenbaum ratios",
   "claim": "number 0.1 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "ratio, 4.665, is within 0.1% of",
   "paper_text": "ratio, $4.665$, is within $0.1\\,\\%$ of $\\delta$ (Figure~\\ref{fig:feigenbaum}).",
   "paper_line": 2058,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0275",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0319 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "region, along \\(\\log_{10}T = 0.0319\\), the",
   "paper_text": "Appendix~\\ref{sec:curves}), along $\\log_{10}T=0.0319$, the period-2 loop ``\\textbackslash",
   "paper_line": 2022,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0276",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0753534 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "`\"\\n\\nThe\"` flips at \\(\\alpha = 0.0753534\\) and its doubled loop",
   "paper_text": "n\\textbackslash nThe'' flips at $\\alpha=0.0753534$ and its doubled loop at $0.0736921$.",
   "paper_line": 2023,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0277",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0736921 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(0.0736921\\). These orbits are far",
   "paper_text": "$\\alpha=0.0753534$ and its doubled loop at $0.0736921$. These orbits are far from",
   "paper_line": 2023,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0278",
   "section": "Feigenbaum ratios",
   "claim": "number 0.38 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "one-dimensional (next moduli 0.38 and",
   "paper_text": "one-dimensional (next moduli $0.38$ and $0.28$). Toward smaller",
   "paper_line": 2024,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0279",
   "section": "Feigenbaum ratios",
   "claim": "number 0.28 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.28). Toward smaller \\(\\alpha\\)",
   "paper_text": "one-dimensional (next moduli $0.38$ and $0.28$). Toward smaller $\\alpha$",
   "paper_line": 2024,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0280",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0705 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\alpha \\approx 0.0705\\) it merges back into the",
   "paper_text": "double again: near $\\alpha\\approx0.0705$ it merges back into the period-4",
   "paper_line": 2025,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0281",
   "section": "Feigenbaum ratios",
   "claim": "number 1.005 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "ratios to the prediction are 1.005 and 1.003,",
   "paper_text": "offset the amplitude ratios are $1.005$ and $1.003$, and the multipliers",
   "paper_line": 2054,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0282",
   "section": "Feigenbaum ratios",
   "claim": "number 1.003 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "prediction are 1.005 and 1.003,",
   "paper_text": "amplitude ratios are $1.005$ and $1.003$, and the multipliers agree",
   "paper_line": 2054,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0283",
   "section": "Feigenbaum ratios",
   "claim": "number 1.5\\times10^{-4} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "multipliers agree within \\(1.5\\times10^{-4}\\) and \\(5\\times10^{-5}\\);",
   "paper_text": "the multipliers agree within $1.5\\times10^{-4}$ and $5\\times10^{-5}$; the",
   "paper_line": 2054,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0284",
   "section": "Feigenbaum ratios",
   "claim": "number 5\\times10^{-5} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(1.5\\times10^{-4}\\) and \\(5\\times10^{-5}\\); the",
   "paper_text": "within $1.5\\times10^{-4}$ and $5\\times10^{-5}$; the larger discrepancies",
   "paper_line": 2055,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0285",
   "section": "Feigenbaum ratios",
   "claim": "number 6.49\\times10^{3} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| period 2 → 4 (\\(c = 6.49\\times10^{3}\\)) | \\(2.5\\times10^{-5}\\)",
   "paper_text": "$0.96335$ & $0.96320$ \\\\ ($c=6.49\\times10^{3}$) & $1\\times10^{-4}$ & $0.0364$",
   "paper_line": 2034,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0286",
   "section": "Feigenbaum ratios",
   "claim": "number 2.5\\times10^{-5} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "6.49\\times10^{3}\\)) | \\(2.5\\times10^{-5}\\) | 0.0092 | 1.005 | 0.96335",
   "paper_text": "\\midrule period $2\\to4$ & $2.5\\times10^{-5}$ & $0.0092$ & $1.005$ & $0.96335$",
   "paper_line": 2033,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0287",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0092 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(2.5\\times10^{-5}\\) | 0.0092 | 1.005 | 0.96335 | 0.96320",
   "paper_text": "$2\\to4$ & $2.5\\times10^{-5}$ & $0.0092$ & $1.005$ & $0.96335$ & $0.96320$",
   "paper_line": 2034,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0288",
   "section": "Feigenbaum ratios",
   "claim": "number 1.005 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(2.5\\times10^{-5}\\) | 0.0092 | 1.005 | 0.96335 | 0.96320 |",
   "paper_text": "$2.5\\times10^{-5}$ & $0.0092$ & $1.005$ & $0.96335$ & $0.96320$ \\\\",
   "paper_line": 2034,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0289",
   "section": "Feigenbaum ratios",
   "claim": "number 0.96335 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(2.5\\times10^{-5}\\) | 0.0092 | 1.005 | 0.96335 | 0.96320 |",
   "paper_text": "$2.5\\times10^{-5}$ & $0.0092$ & $1.005$ & $0.96335$ & $0.96320$ \\\\ ($c=6.49\\times10^{3}$)",
   "paper_line": 2034,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0290",
   "section": "Feigenbaum ratios",
   "claim": "number 0.96320 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.0092 | 1.005 | 0.96335 | 0.96320 |",
   "paper_text": "$0.0092$ & $1.005$ & $0.96335$ & $0.96320$ \\\\ ($c=6.49\\times10^{3}$)",
   "paper_line": 2034,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0291",
   "section": "Feigenbaum ratios",
   "claim": "number 1\\times10^{-4} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| | \\(1\\times10^{-4}\\) | 0.0364 | 1.020 | 0.8572",
   "paper_text": "& $4/4$,\\ $2/2$,\\ $4/4$ \\\\ $1\\times10^{-4}$ & $10/10$,\\ $5/6$,\\ $10/10$",
   "paper_line": 1796,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0292",
   "section": "Feigenbaum ratios",
   "claim": "number 0.0364 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| \\(1\\times10^{-4}\\) | 0.0364 | 1.020 | 0.8572 | 0.8545",
   "paper_text": "($c=6.49\\times10^{3}$) & $1\\times10^{-4}$ & $0.0364$ & $1.020$ & $0.8572$ & $0.8545$",
   "paper_line": 2035,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0293",
   "section": "Feigenbaum ratios",
   "claim": "number 1.020 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(1\\times10^{-4}\\) | 0.0364 | 1.020 | 0.8572 | 0.8545 |",
   "paper_text": "$1\\times10^{-4}$ & $0.0364$ & $1.020$ & $0.8572$ & $0.8545$ \\\\ &",
   "paper_line": 2035,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0294",
   "section": "Feigenbaum ratios",
   "claim": "number 0.8572 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(1\\times10^{-4}\\) | 0.0364 | 1.020 | 0.8572 | 0.8545 |",
   "paper_text": "$1\\times10^{-4}$ & $0.0364$ & $1.020$ & $0.8572$ & $0.8545$ \\\\ & $4\\times10^{-4}$",
   "paper_line": 2035,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0295",
   "section": "Feigenbaum ratios",
   "claim": "number 0.8545 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.0364 | 1.020 | 0.8572 | 0.8545 |",
   "paper_text": "$0.0364$ & $1.020$ & $0.8572$ & $0.8545$ \\\\ & $4\\times10^{-4}$ & $0.1400$",
   "paper_line": 2035,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0296",
   "section": "Feigenbaum ratios",
   "claim": "number 4\\times10^{-4} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| | \\(4\\times10^{-4}\\) | 0.1400 | 1.078 | 0.513",
   "paper_text": "& $0.8572$ & $0.8545$ \\\\ & $4\\times10^{-4}$ & $0.1400$ & $1.078$ & $0.513$",
   "paper_line": 2035,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0297",
   "section": "Feigenbaum ratios",
   "claim": "number 0.1400 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| \\(4\\times10^{-4}\\) | 0.1400 | 1.078 | 0.513 | 0.440",
   "paper_text": "$0.8545$ \\\\ & $4\\times10^{-4}$ & $0.1400$ & $1.078$ & $0.513$ & $0.440$",
   "paper_line": 2035,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0298",
   "section": "Feigenbaum ratios",
   "claim": "number 1.078 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(4\\times10^{-4}\\) | 0.1400 | 1.078 | 0.513 | 0.440 |",
   "paper_text": "$4\\times10^{-4}$ & $0.1400$ & $1.078$ & $0.513$ & $0.440$ \\\\ \\midrule",
   "paper_line": 2036,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0299",
   "section": "Feigenbaum ratios",
   "claim": "number 0.513 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(4\\times10^{-4}\\) | 0.1400 | 1.078 | 0.513 | 0.440 |",
   "paper_text": "$4\\times10^{-4}$ & $0.1400$ & $1.078$ & $0.513$ & $0.440$ \\\\ \\midrule period",
   "paper_line": 2036,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0300",
   "section": "Feigenbaum ratios",
   "claim": "number 0.440 in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.1400 | 1.078 | 0.513 | 0.440 |",
   "paper_text": "$0.1400$ & $1.078$ & $0.513$ & $0.440$ \\\\ \\midrule period $4\\to8$",
   "paper_line": 2036,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0301",
   "section": "Feigenbaum ratios",
   "claim": "number 1.24\\times10^{4} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| period 4 → 8 (\\(c = 1.24\\times10^{4}\\)) | \\(2.5\\times10^{-5}\\)",
   "paper_text": "$0.92987$ & $0.92983$ \\\\ ($c=1.24\\times10^{4}$) & $1\\times10^{-4}$ & $0.0685$",
   "paper_line": 2038,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0302",
   "section": "Feigenbaum ratios",
   "claim": "number 2.5\\times10^{-5} in 'Feigenbaum ratios' (generated: post phrase matched to the paper's source text)",
   "appears_as": "1.24\\times10^{4}\\)) | \\(2.5\\times10^{-5}\\) | 0.0175 | 1.003 | 0.92987",
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   "section": "Feigenbaum ratios",
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   "appears_as": "\\(2.5\\times10^{-5}\\) | 0.0175 | 1.003 | 0.92987 | 0.92983 |",
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   "section": "Steering toward hostility",
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   "section": "Steering toward hostility",
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   "section": "Steering toward hostility",
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   "section": "Steering toward hostility",
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   "section": "Steering toward hostility",
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   "claim": "number 0.06 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((\\alpha, \\log_{10}T) = (0.06, 0.20)\\), shows branches",
   "paper_text": "near $(\\alpha,\\log_{10}T)=(0.06,0.20)$, shows arms of period-7",
   "paper_line": 2097,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0353",
   "section": "Steering toward hostility",
   "claim": "number 0.20 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((\\alpha, \\log_{10}T) = (0.06, 0.20)\\), shows branches of",
   "paper_text": "$(\\alpha,\\log_{10}T)=(0.06,0.20)$, shows arms of period-7 and",
   "paper_line": 2097,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0354",
   "section": "Steering toward hostility",
   "claim": "number 0.041 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "2-cycle at \\(\\alpha \\approx 0.041\\) and 0.079,",
   "paper_text": "a 2-cycle at $\\alpha\\approx0.041$ and $0.079$, and that 2-cycle",
   "paper_line": 2098,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0355",
   "section": "Steering toward hostility",
   "claim": "number 0.079 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\alpha \\approx 0.041\\) and 0.079,",
   "paper_text": "at $\\alpha\\approx0.041$ and $0.079$, and that 2-cycle has a Neimark--Sacker",
   "paper_line": 2098,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0356",
   "section": "Steering toward hostility",
   "claim": "number 0.062 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "spiral region: at \\(\\alpha = 0.062\\) a complex pair of its",
   "paper_text": "the spiral region: at $\\alpha=0.062$ its complex pair crosses the",
   "paper_line": 2099,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0357",
   "section": "Steering toward hostility",
   "claim": "number 0.1656 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "circle near \\(\\log_{10}T = 0.1656\\), turning 0.12 of a revolution",
   "paper_text": "unit circle near $\\log_{10}T=0.1656$, turning $0.12$ of a revolution",
   "paper_line": 2100,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0358",
   "section": "Steering toward hostility",
   "claim": "number 0.12 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = 0.1656\\), turning 0.12 of a revolution per step",
   "paper_text": "$\\log_{10}T=0.1656$, turning $0.12$ of a revolution per step of",
   "paper_line": 2100,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0359",
   "section": "Steering toward hostility",
   "claim": "number 16 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "have even periods, near 16 for this rotation, whereas",
   "paper_text": "them have even periods, near 16 for this rotation, whereas",
   "paper_line": 2102,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0360",
   "section": "Steering toward hostility",
   "claim": "number 0.087 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((\\alpha, \\log_{10}T) = (0.087, -0.069)\\) the period-12",
   "paper_text": "near $(\\alpha,\\log_{10}T)=(0.087,-0.069)$ the period-12 and",
   "paper_line": 2109,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0361",
   "section": "Steering toward hostility",
   "claim": "number -0.069 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((\\alpha, \\log_{10}T) = (0.087, -0.069)\\) the period-12 and period-14",
   "paper_text": "$(\\alpha,\\log_{10}T)=(0.087,-0.069)$ the period-12 and period-14",
   "paper_line": 2109,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0362",
   "section": "Steering toward hostility",
   "claim": "number 0.1925 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = 0.1925\\) the orbit exists between",
   "paper_text": "bounded by folds. At $\\log_{10}T=0.1925$ the orbit exists between $\\alpha=0.065966$",
   "paper_line": 2113,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0363",
   "section": "Steering toward hostility",
   "claim": "number 0.065966 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "exists between \\(\\alpha = 0.065966\\) and",
   "paper_text": "orbit exists between $\\alpha=0.065966$ and $0.071188$, and at $\\alpha=0.066$",
   "paper_line": 2113,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0364",
   "section": "Steering toward hostility",
   "claim": "number 0.071188 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.071188, and at \\(\\alpha = 0.066\\)",
   "paper_text": "between $\\alpha=0.065966$ and $0.071188$, and at $\\alpha=0.066$ it",
   "paper_line": 2113,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0365",
   "section": "Steering toward hostility",
   "claim": "number 0.066 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.071188, and at \\(\\alpha = 0.066\\) it ends in a fold at",
   "paper_text": "$0.071188$, and at $\\alpha=0.066$ it ends in a fold at $\\log_{10}T=0.19263$.",
   "paper_line": 2114,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0366",
   "section": "Steering toward hostility",
   "claim": "number 0.19263 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = 0.19263\\). Below that, the multiplier",
   "paper_text": "ends in a fold at $\\log_{10}T=0.19263$. Below that, the multiplier",
   "paper_line": 2114,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0367",
   "section": "Steering toward hostility",
   "claim": "number 0.19176 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(bracketed in [0.19176, 0.19196] and [0.18931,",
   "paper_text": "$-1$ twice (bracketed in $[0.19176,0.19196]$ and $[0.18931,0.19036]$),",
   "paper_line": 2115,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0368",
   "section": "Steering toward hostility",
   "claim": "number 0.19196 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(bracketed in [0.19176, 0.19196] and [0.18931, 0.19036]),",
   "paper_text": "twice (bracketed in $[0.19176,0.19196]$ and $[0.18931,0.19036]$),",
   "paper_line": 2115,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0369",
   "section": "Steering toward hostility",
   "claim": "number 0.18931 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "[0.19176, 0.19196] and [0.18931, 0.19036]), so the period-14",
   "paper_text": "in $[0.19176,0.19196]$ and $[0.18931,0.19036]$), so the period-14",
   "paper_line": 2115,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0370",
   "section": "Steering toward hostility",
   "claim": "number 0.19036 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.19196] and [0.18931, 0.19036]), so the period-14",
   "paper_text": "$[0.19176,0.19196]$ and $[0.18931,0.19036]$), so the period-14 crescent",
   "paper_line": 2115,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0371",
   "section": "Steering toward hostility",
   "claim": "number 0.18797 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the branch folds twice (0.18797 and 0.18922, the second",
   "paper_text": "down, the branch folds twice ($0.18797$ and $0.18922$, the second",
   "paper_line": 2116,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0372",
   "section": "Steering toward hostility",
   "claim": "number 0.18922 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "folds twice (0.18797 and 0.18922, the second located by",
   "paper_text": "folds twice ($0.18797$ and $0.18922$, the second located by continuing",
   "paper_line": 2117,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0373",
   "section": "Steering toward hostility",
   "claim": "number 1.5\\times10^{-3} in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "modulus stays below \\(1.5\\times10^{-3}\\), so only one multiplier",
   "paper_text": "simple (next modulus below $1.5\\times10^{-3}$). An S-shaped pair of folds",
   "paper_line": 2118,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0374",
   "section": "Steering toward hostility",
   "claim": "number -23.9 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-23.9\\) to \\(+244.6\\) on the",
   "paper_text": "Appendix~\\ref{sec:curves}) (upper fold: $-23.9$ to $+244.6$ between adjacent",
   "paper_line": 2122,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0375",
   "section": "Steering toward hostility",
   "claim": "number 244.6 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-23.9\\) to \\(+244.6\\) on the upper fold (with",
   "paper_text": "Appendix~\\ref{sec:curves}) (upper fold: $-23.9$ to $+244.6$ between adjacent points, with",
   "paper_line": 2122,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0376",
   "section": "Steering toward hostility",
   "claim": "number 2.0 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "fold (with \\(a \\approx 2.0\\)) and from",
   "paper_text": "adjacent points, with $a\\approx2.0$; lower fold: $+31.2$ to $-58.7$,",
   "paper_line": 2123,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0377",
   "section": "Steering toward hostility",
   "claim": "number 31.2 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(+31.2\\) to \\(-58.7\\) on the lower",
   "paper_text": "$a\\approx2.0$; lower fold: $+31.2$ to $-58.7$, with $a\\approx0.55$)",
   "paper_line": 2123,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0378",
   "section": "Steering toward hostility",
   "claim": "number -58.7 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(+31.2\\) to \\(-58.7\\) on the lower one (with",
   "paper_text": "$a\\approx2.0$; lower fold: $+31.2$ to $-58.7$, with $a\\approx0.55$) while",
   "paper_line": 2123,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0379",
   "section": "Steering toward hostility",
   "claim": "number 0.55 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "lower one (with \\(a \\approx 0.55\\)), while \\(a\\)",
   "paper_text": "$+31.2$ to $-58.7$, with $a\\approx0.55$) while $a$ stays away from",
   "paper_line": 2123,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0380",
   "section": "Steering toward hostility",
   "claim": "number 0.067213 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((\\alpha, \\log_{10}T) = (0.067213, 0.198983)\\) and \\((0.066611,",
   "paper_text": "lie at $(\\alpha,\\log_{10}T)=(0.067213,0.198983)$ and $(0.066611,0.189382)$.",
   "paper_line": 2124,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0381",
   "section": "Steering toward hostility",
   "claim": "number 0.198983 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\log_{10}T) = (0.067213, 0.198983)\\) and \\((0.066611, 0.189382)\\).",
   "paper_text": "$(\\alpha,\\log_{10}T)=(0.067213,0.198983)$ and $(0.066611,0.189382)$.",
   "paper_line": 2124,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0382",
   "section": "Steering toward hostility",
   "claim": "number 0.066611 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(0.067213, 0.198983)\\) and \\((0.066611, 0.189382)\\).",
   "paper_text": "$(\\alpha,\\log_{10}T)=(0.067213,0.198983)$ and $(0.066611,0.189382)$. There $b\\operatorname{sign}a$",
   "paper_line": 2124,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0383",
   "section": "Steering toward hostility",
   "claim": "number 0.189382 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.198983)\\) and \\((0.066611, 0.189382)\\).",
   "paper_text": "$(\\alpha,\\log_{10}T)=(0.067213,0.198983)$ and $(0.066611,0.189382)$. There $b\\operatorname{sign}a$",
   "paper_line": 2124,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0384",
   "section": "Steering toward hostility",
   "claim": "number 1.3\\times10^{-5} in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(b\\operatorname{sign}a\\) is below \\(1.3\\times10^{-5}\\) of its bracket",
   "paper_text": "$b\\operatorname{sign}a$ is below $1.3\\times10^{-5}$ of its bracket values, $c=-1.41\\times10^{6}$",
   "paper_line": 2125,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0385",
   "section": "Steering toward hostility",
   "claim": "number -1.41 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "values, \\(c = -1.41\\times10^{6}\\) and \\(-5.61\\times10^{5}\\),",
   "paper_text": "$1.3\\times10^{-5}$ of its bracket values, $c=-1.41\\times10^{6}$ and $-5.61\\times10^{5}$,",
   "paper_line": 2125,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0386",
   "section": "Steering toward hostility",
   "claim": "number -5.61 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "-1.41\\times10^{6}\\) and \\(-5.61\\times10^{5}\\), and",
   "paper_text": "$c=-1.41\\times10^{6}$ and $-5.61\\times10^{5}$, and $\\det K=58.2$",
   "paper_line": 2126,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0387",
   "section": "Steering toward hostility",
   "claim": "number 58.2 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\det K = 58.2\\) and 55.2. At the points",
   "paper_text": "$-5.61\\times10^{5}$, and $\\det K=58.2$ and $55.2$, all evaluated",
   "paper_line": 2126,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0388",
   "section": "Steering toward hostility",
   "claim": "number 55.2 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\det K = 58.2\\) and 55.2. At the points that bracket",
   "paper_text": "$-5.61\\times10^{5}$, and $\\det K=58.2$ and $55.2$, all evaluated at the located",
   "paper_line": 2126,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0389",
   "section": "Steering toward hostility",
   "claim": "number -1.4 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "coefficient is \\(c \\approx -1.4\\times10^{6}\\) to \\(-2.0\\times10^{6}\\)",
   "paper_text": "both sign changes: $c\\approx-1.4\\times10^{6}$ to $-2.0\\times10^{6}$",
   "paper_line": 2128,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0390",
   "section": "Steering toward hostility",
   "claim": "number -2.0 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "-1.4\\times10^{6}\\) to \\(-2.0\\times10^{6}\\) (step",
   "paper_text": "$c\\approx-1.4\\times10^{6}$ to $-2.0\\times10^{6}$ (step agreement",
   "paper_line": 2128,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0391",
   "section": "Steering toward hostility",
   "claim": "number -5.8 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "leaves the sign) and \\(-5.8\\times10^{5}\\) to \\(-5.3\\times10^{5}\\).",
   "paper_text": "extrapolation leaves the sign) and $-5.8\\times10^{5}$ to $-5.3\\times10^{5}$.",
   "paper_line": 2129,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0392",
   "section": "Steering toward hostility",
   "claim": "number -5.3 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-5.8\\times10^{5}\\) to \\(-5.3\\times10^{5}\\).",
   "paper_text": "and $-5.8\\times10^{5}$ to $-5.3\\times10^{5}$. This supports",
   "paper_line": 2129,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0393",
   "section": "Steering toward hostility",
   "claim": "number 31.4 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "lower cusp (where \\(b = 31.4\\)) the estimated unfolding",
   "paper_text": "near the lower cusp (where $b=31.4$) the estimated unfolding is",
   "paper_line": 2131,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0394",
   "section": "Steering toward hostility",
   "claim": "number 53.5 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "nonsingular too (\\(\\det K = 53.5\\), singular values 262",
   "paper_text": "is nonsingular too ($\\det K=53.5$ in the same coordinates, singular",
   "paper_line": 2132,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0395",
   "section": "Steering toward hostility",
   "claim": "number 262 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "53.5\\), singular values 262 and 0.20). Its local",
   "paper_text": "coordinates, singular values $262$ and $0.20$). Its local predictions",
   "paper_line": 2132,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0396",
   "section": "Steering toward hostility",
   "claim": "number 0.20 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "singular values 262 and 0.20). Its local",
   "paper_text": "singular values $262$ and $0.20$). Its local predictions at",
   "paper_line": 2132,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0397",
   "section": "Steering toward hostility",
   "claim": "number 12 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "hostility direction at layer 12): attractor periods of",
   "paper_text": "hostility direction at layer 12): attractor periods of a float64",
   "paper_line": 2219,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0398",
   "section": "Steering toward hostility",
   "claim": "number 0.062 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "zoom (white at \\(\\alpha < 0.062\\): outside the zoom), the",
   "paper_text": "float64 zoom (white at $\\alpha<0.062$: outside the zoom), the float64",
   "paper_line": 2220,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0399",
   "section": "Steering toward hostility",
   "claim": "number 14 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "flip curves into period 14 (red, dashed), with the",
   "paper_text": "the flip curves into period 14 (red, dashed), with the two",
   "paper_line": 2221,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0400",
   "section": "Steering toward hostility",
   "claim": "number 0.1830 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "too. At \\(\\log_{10}T = 0.1830\\), float64",
   "paper_text": "shrimp-like too. At $\\log_{10}T=0.1830$, float64 bifurcation diagrams",
   "paper_line": 2138,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0401",
   "section": "Steering toward hostility",
   "claim": "number 1400 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "; 1400 cells",
   "paper_text": "(Figure~\\ref{fig:hubcascade}; 1400 cells per line) show the period-7",
   "paper_line": 2139,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0402",
   "section": "Steering toward hostility",
   "claim": "number 14 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "orbit doubling to periods 14 and 28 and entering chaos",
   "paper_text": "period-7 orbit doubling to periods 14 and 28 and entering chaos (largest",
   "paper_line": 2139,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0403",
   "section": "Steering toward hostility",
   "claim": "number 28 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "doubling to periods 14 and 28 and entering chaos",
   "paper_text": "doubling to periods 14 and 28 and entering chaos (largest",
   "paper_line": 2139,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0404",
   "section": "Steering toward hostility",
   "claim": "number 0.1 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(largest exponent up to \\(+0.1\\)) for \\(\\alpha \\approx",
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   "paper_line": 2140,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0405",
   "section": "Steering toward hostility",
   "claim": "number 0.0659 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(+0.1\\)) for \\(\\alpha \\approx 0.0659\\) to 0.0673.",
   "paper_text": "to $+0.1$) for $\\alpha\\approx0.0659$--$0.0673$. Windows of periods",
   "paper_line": 2140,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0406",
   "section": "Steering toward hostility",
   "claim": "number 0.0673 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "paper_line": 2140,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0407",
   "section": "Steering toward hostility",
   "claim": "number 28 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "paper_line": 2140,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0408",
   "section": "Steering toward hostility",
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   "paper_line": 2140,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0409",
   "section": "Steering toward hostility",
   "claim": "number 42 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "Windows of periods 28, 35 and 42 sit inside the chaotic band,",
   "paper_line": 2140,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0410",
   "section": "Steering toward hostility",
   "claim": "number 28 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Steering toward hostility",
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   "paper_line": 2141,
   "paper_file": "paper/llm/main.tex"
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   "section": "Steering toward hostility",
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   "paper_line": 2142,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0413",
   "section": "Steering toward hostility",
   "claim": "number 28 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "paper_line": 2142,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0414",
   "section": "Steering toward hostility",
   "claim": "number 21 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "paper_line": 2142,
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  {
   "id": "shrimp-0415",
   "section": "Steering toward hostility",
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   "paper_line": 2142,
   "paper_file": "paper/llm/main.tex"
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   "id": "shrimp-0416",
   "section": "Steering toward hostility",
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   "paper_file": "paper/llm/main.tex"
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   "id": "shrimp-0417",
   "section": "Steering toward hostility",
   "claim": "number 5\\times10^{-13} in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "$3\\times10^{-15}$, $2\\times10^{-14}$ and $5\\times10^{-13}$; spectral radii $0.08$, $4\\times10^{-4}$",
   "paper_line": 2143,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0418",
   "section": "Steering toward hostility",
   "claim": "number 0.08 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "$5\\times10^{-13}$; spectral radii $0.08$, $4\\times10^{-4}$ and $0.006$).",
   "paper_line": 2143,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0419",
   "section": "Steering toward hostility",
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   "paper_text": "$5\\times10^{-13}$; spectral radii $0.08$, $4\\times10^{-4}$ and $0.006$). Periods 21,",
   "paper_line": 2143,
   "paper_file": "paper/llm/main.tex"
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   "section": "Steering toward hostility",
   "claim": "number 0.006 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "$0.08$, $4\\times10^{-4}$ and $0.006$). Periods 21, 35 and 42 are",
   "paper_line": 2143,
   "paper_file": "paper/llm/main.tex"
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   "id": "shrimp-0421",
   "section": "Steering toward hostility",
   "claim": "number 21 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "$4\\times10^{-4}$ and $0.006$). Periods 21, 35 and 42 are three, five",
   "paper_line": 2143,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0422",
   "section": "Steering toward hostility",
   "claim": "number 35 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "$4\\times10^{-4}$ and $0.006$). Periods 21, 35 and 42 are three, five and",
   "paper_line": 2143,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0423",
   "section": "Steering toward hostility",
   "claim": "number 42 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "$0.006$). Periods 21, 35 and 42 are three, five and six times",
   "paper_line": 2143,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0424",
   "section": "Steering toward hostility",
   "claim": "number 28 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "orbit flips into period 28 near",
   "paper_text": "period-14 orbit flips into period 28 near $\\log_{10}T=0.1841$ and",
   "paper_line": 2144,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0425",
   "section": "Steering toward hostility",
   "claim": "number 0.1841 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = 0.1841\\) and back near 0.1857,",
   "paper_text": "period 28 near $\\log_{10}T=0.1841$ and back near $0.1857$, the",
   "paper_line": 2144,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0426",
   "section": "Steering toward hostility",
   "claim": "number 0.1857 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "$\\log_{10}T=0.1841$ and back near $0.1857$, the two ends of a doubling",
   "paper_line": 2145,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0427",
   "section": "Steering toward hostility",
   "claim": "number 28 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "doubling bubble that holds period 28 and chaos. Lower down, its",
   "paper_line": 2145,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0428",
   "section": "Steering toward hostility",
   "claim": "number 0.1824 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.1824 and 0.18244, with three",
   "paper_text": "branch is S-shaped (folds near $0.1824$ and $0.18244$, with three",
   "paper_line": 2146,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0429",
   "section": "Steering toward hostility",
   "claim": "number 0.18244 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.1824 and 0.18244, with three coexisting",
   "paper_text": "S-shaped (folds near $0.1824$ and $0.18244$, with three coexisting period-14",
   "paper_line": 2146,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0430",
   "section": "Steering toward hostility",
   "claim": "number 0.1819 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "another flip near 0.1819. All these crossings are",
   "paper_text": "them) before another flip near $0.1819$. All these crossings are simple",
   "paper_line": 2146,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0431",
   "section": "Steering toward hostility",
   "claim": "number 4\\times10^{-5} in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "simple (next modulus below $4\\times10^{-5}$). A $160^2$ float64 zoom of",
   "paper_line": 2147,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0432",
   "section": "Steering toward hostility",
   "claim": "number 160 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(4\\times10^{-5}\\)). A \\(160^2\\) float64 zoom of the",
   "paper_text": "below $4\\times10^{-5}$). A $160^2$ float64 zoom of the lower",
   "paper_line": 2147,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0433",
   "section": "Steering toward hostility",
   "claim": "number 18 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "low-dimensional maps. In this zoom 18% of cells are",
   "paper_text": "low-dimensional maps. In this zoom 18\\,\\% of cells are chaotic. \\begin{figure}[H]",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0434",
   "section": "Steering toward hostility",
   "claim": "number 12 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "hostility direction at layer 12): float64 bifurcation diagrams",
   "paper_line": 2167,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0435",
   "section": "Steering toward hostility",
   "claim": "number 0.0655 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "temperature at \\(\\alpha = 0.0655\\) (left) and along the",
   "paper_text": "along temperature at $\\alpha=0.0655$ (left) and along the steering",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0436",
   "section": "Steering toward hostility",
   "claim": "number 0.1830 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "strength at \\(\\log_{10}T = 0.1830\\) (right). Top: the last",
   "paper_text": "steering strength at $\\log_{10}T=0.1830$ (right). Top: the last 160",
   "paper_line": 2168,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0437",
   "section": "Steering toward hostility",
   "claim": "number 160 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "$\\log_{10}T=0.1830$ (right). Top: the last 160 states of the attractor reached",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0438",
   "section": "Steering toward hostility",
   "claim": "number 14 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the cells of periods 7, 14, 21, 28, 35 and 42 marked",
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  {
   "id": "shrimp-0439",
   "section": "Steering toward hostility",
   "claim": "number 21 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "cells of periods 7, 14, 21, 28, 35 and 42 marked (cells",
   "paper_text": "the cells of periods 7, 14, 21, 28, 35 and 42 marked (cells",
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  {
   "id": "shrimp-0440",
   "section": "Steering toward hostility",
   "claim": "number 28 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "cells of periods 7, 14, 21, 28, 35 and 42 marked (cells",
   "paper_text": "cells of periods 7, 14, 21, 28, 35 and 42 marked (cells of",
   "paper_line": 2171,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0441",
   "section": "Steering toward hostility",
   "claim": "number 35 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "periods 7, 14, 21, 28, 35 and 42 marked (cells of",
   "paper_text": "cells of periods 7, 14, 21, 28, 35 and 42 marked (cells of other",
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   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0442",
   "section": "Steering toward hostility",
   "claim": "number 42 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "periods 7, 14, 21, 28, 35 and 42 marked (cells of other",
   "paper_text": "periods 7, 14, 21, 28, 35 and 42 marked (cells of other periods",
   "paper_line": 2171,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0443",
   "section": "Steering toward hostility",
   "claim": "number 14 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "right, period 7 doubles to 14 and 28, enters chaos with",
   "paper_text": "right, period 7 doubles to 14 and 28, enters chaos with windows",
   "paper_line": 2172,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0444",
   "section": "Steering toward hostility",
   "claim": "number 28 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "period 7 doubles to 14 and 28, enters chaos with windows",
   "paper_text": "period 7 doubles to 14 and 28, enters chaos with windows",
   "paper_line": 2172,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0445",
   "section": "Steering toward hostility",
   "claim": "number 28 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "with windows of periods 28, 35 and 42, and undoubles",
   "paper_text": "chaos with windows of periods 28, 35 and 42, and undoubles back",
   "paper_line": 2172,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0446",
   "section": "Steering toward hostility",
   "claim": "number 35 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "windows of periods 28, 35 and 42, and undoubles back",
   "paper_text": "with windows of periods 28, 35 and 42, and undoubles back",
   "paper_line": 2172,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0447",
   "section": "Steering toward hostility",
   "claim": "number 42 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "windows of periods 28, 35 and 42, and undoubles back to",
   "paper_text": "windows of periods 28, 35 and 42, and undoubles back to 7. Labels",
   "paper_line": 2173,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0448",
   "section": "Steering toward hostility",
   "claim": "number 400 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "to 7. Labels come from 400 measured steps after 1000",
   "paper_text": "back to 7. Labels come from 400 measured steps after 1000 transient",
   "paper_line": 2173,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0449",
   "section": "Steering toward hostility",
   "claim": "number 1000 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "400 measured steps after 1000 transient steps; with 2000",
   "paper_text": "from 400 measured steps after 1000 transient steps; with 2000",
   "paper_line": 2173,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0450",
   "section": "Steering toward hostility",
   "claim": "number 2000 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "1000 transient steps; with 2000 measured steps at two twin",
   "paper_text": "1000 transient steps; with 2000 measured steps at two twin",
   "paper_line": 2173,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0451",
   "section": "Steering toward hostility",
   "claim": "number 135 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "steps at two twin offsets, 135 of the 235 red cells on",
   "paper_text": "steps at two twin offsets, 135 of the 235 red cells on the",
   "paper_line": 2174,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0452",
   "section": "Steering toward hostility",
   "claim": "number 235 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "twin offsets, 135 of the 235 red cells on the left stay",
   "paper_text": "two twin offsets, 135 of the 235 red cells on the left stay",
   "paper_line": 2174,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0453",
   "section": "Steering toward hostility",
   "claim": "number 91 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the left stay chaotic and 91 are periodic. Source: byte-identical",
   "paper_text": "on the left stay chaotic and 91 are periodic (Appendix~\\ref{sec:limits}).}",
   "paper_line": 2174,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0454",
   "section": "Steering toward hostility",
   "claim": "number 12 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Qwen2.5-0.5B-Instruct map (layer 12) at higher resolution (\\(160^2\\)",
   "paper_text": "Qwen2.5-0.5B-Instruct map (layer 12) at higher resolution ($160^2$",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0455",
   "section": "Steering toward hostility",
   "claim": "number 160 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at higher resolution (\\(160^2\\) float64 cells). Left:",
   "paper_text": "12) at higher resolution ($160^2$ float64 cells). Left: period",
   "paper_line": 5153,
   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Steering toward hostility",
   "claim": "number 48 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "white: no period up to 48). Right: largest Lyapunov",
   "paper_text": "exponent; white: no period up to 48). Right: largest Lyapunov exponent",
   "paper_line": 5154,
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   "section": "Steering toward hostility",
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   "section": "Steering toward hostility",
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   "section": "Steering toward hostility",
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   "section": "Steering toward hostility",
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   "section": "Steering toward hostility",
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   "section": "Steering toward hostility",
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   "section": "Steering toward hostility",
   "claim": "number 0.0700 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "paper_line": 2209,
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  {
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   "section": "Steering toward hostility",
   "claim": "number 0.206 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "section": "Steering toward hostility",
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   "section": "Steering toward hostility",
   "claim": "number 0.07142 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "section": "Steering toward hostility",
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   "section": "Steering toward hostility",
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   "section": "Steering toward hostility",
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   "appears_as": "(bottom row: \\(\\alpha = 0.0655\\), \\(\\log_{10}T = 0.1848\\));",
   "paper_text": "Figure~\\ref{fig:hubcascade} (bottom row: $\\alpha=0.0655$, $\\log_{10}T=0.1848$); $s$",
   "paper_line": 5119,
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  {
   "id": "shrimp-0478",
   "section": "Steering toward hostility",
   "claim": "number 0.1848 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "section": "Steering toward hostility",
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   "section": "Steering toward hostility",
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   "paper_line": 5120,
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  {
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   "section": "Steering toward hostility",
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  {
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   "section": "Steering toward hostility",
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  {
   "id": "shrimp-0483",
   "section": "Steering toward hostility",
   "claim": "number 0.0655 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "section": "Steering toward hostility",
   "claim": "number 0.19082 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "section": "Steering toward hostility",
   "claim": "number 0.19029 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "section": "Steering toward hostility",
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   "paper_line": 5132,
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   "id": "shrimp-0487",
   "section": "Steering toward hostility",
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   "paper_line": 5132,
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   "id": "shrimp-0488",
   "section": "Steering toward hostility",
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   "paper_line": 5132,
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   "section": "Steering toward hostility",
   "claim": "number 0.0655 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "paper_line": 5119,
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   "id": "shrimp-0490",
   "section": "Steering toward hostility",
   "claim": "number 2000 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "section": "Steering toward hostility",
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   "section": "Steering toward hostility",
   "claim": "number 10^{-6} in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "section": "Steering toward hostility",
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   "section": "Steering toward hostility",
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   "section": "Steering toward hostility",
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   "section": "Steering toward hostility",
   "claim": "number 0.176 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "paper_line": 2229,
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   "section": "Steering toward hostility",
   "claim": "number 0.191 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "paper_line": 2229,
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   "section": "Steering toward hostility",
   "claim": "number 65 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "section": "Steering toward hostility",
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   "section": "Steering toward hostility",
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   "section": "Steering toward hostility",
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   "section": "Steering toward hostility",
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   "section": "Steering toward hostility",
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   "section": "Steering toward hostility",
   "claim": "number 0.098 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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  {
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   "section": "Steering toward hostility",
   "claim": "number 2000 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "repeats at every one of the 2000 steps. Within each group",
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   "section": "Steering toward hostility",
   "claim": "number 4\\times10^{-4} in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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  {
   "id": "shrimp-0508",
   "section": "Steering toward hostility",
   "claim": "number 0.647 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
   "appears_as": "map's Lyapunov exponent, 0.647 per repetition, is within",
   "paper_text": "fitted map's Lyapunov exponent, 0.647 per repetition, is within 2\\,\\%",
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  {
   "id": "shrimp-0509",
   "section": "Steering toward hostility",
   "claim": "number 0.636 in 'Steering toward hostility' (generated: post phrase matched to the paper's source text)",
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   "id": "shrimp-0565",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.12 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "next modulus falls from 0.12 at the first flip to",
   "paper_text": "the next modulus falls from $0.12$ at the first flip to $0.045$,",
   "paper_line": 4468,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0566",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.045 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.045, \\(7\\times10^{-5}\\), \\(4\\times10^{-7}\\)",
   "paper_text": "$0.12$ at the first flip to $0.045$, $7\\times10^{-5}$, $4\\times10^{-7}$",
   "paper_line": 4469,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0567",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 7\\times10^{-5} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.045, \\(7\\times10^{-5}\\), \\(4\\times10^{-7}\\) and",
   "paper_text": "the first flip to $0.045$, $7\\times10^{-5}$, $4\\times10^{-7}$ and $2\\times10^{-13}$",
   "paper_line": 4469,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0568",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 4\\times10^{-7} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.045, \\(7\\times10^{-5}\\), \\(4\\times10^{-7}\\) and \\(2\\times10^{-13}\\)",
   "paper_text": "$0.045$, $7\\times10^{-5}$, $4\\times10^{-7}$ and $2\\times10^{-13}$ at the",
   "paper_line": 4469,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0569",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 2\\times10^{-13} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(4\\times10^{-7}\\) and \\(2\\times10^{-13}\\) at the next",
   "paper_text": "$7\\times10^{-5}$, $4\\times10^{-7}$ and $2\\times10^{-13}$ at the next four. Temperature,",
   "paper_line": 4469,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0570",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.28 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "bubble (next moduli 0.28 and 0.38) and along the",
   "paper_text": "Section~\\ref{sec:cascade} (next moduli $0.28$ and $0.38$) and along the",
   "paper_line": 4477,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0571",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.38 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "bubble (next moduli 0.28 and 0.38) and along the period-5",
   "paper_text": "Section~\\ref{sec:cascade} (next moduli $0.28$ and $0.38$) and along the period-5 curves",
   "paper_line": 4477,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0572",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.39 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.39), the global reduction",
   "paper_text": "Section~\\ref{sec:organization} (up to $0.39$), the global reduction is",
   "paper_line": 4478,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0573",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -1.1 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the text). Left, \\(a = -1.1\\): a crossroad area; passing",
   "paper_text": "$c$ in the text). Left, $a=-1.1$: a crossroad area; passing",
   "paper_line": 2353,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0574",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -2.05 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(red dot). Middle, \\(a = -2.05\\): a spring area; a flip",
   "paper_text": "branches (red dot). Middle, $a=-2.05$: a spring area; a flip curve",
   "paper_line": 2355,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0575",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 1.1 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "= -2\\)). Right, \\(a = +1.1\\): the saddle kind; passing",
   "paper_text": "Carcass\\`es et al.). Right, $a=+1.1$: the saddle kind; passing",
   "paper_line": 2357,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0576",
   "section": "Cusps and shrimp-like windows",
   "claim": "smallest |det K| at the thirteen located cusps (paper 17353aec)",
   "appears_as": "K\\rvert\\) lies between 14",
   "paper_text": "$|\\det K|$ lies between $14$ and $2416$",
   "paper_line": 4871,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0577",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 2416 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and 2416. These are float64 computations",
   "paper_text": "K|$ lies between $14$ and $2416$. These are float64 computations",
   "paper_line": 4871,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0578",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 1.2 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "within 1.2% and \\(c\\) to two figures,",
   "paper_text": "change of $b$: $|b|$ within $1.2\\,\\%$ and $c$ to two figures,",
   "paper_line": 4875,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0579",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 10^{-15} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "residuals \\(10^{-15}\\) to \\(10^{-13}\\)) show",
   "paper_text": "Float64 orbits (Newton residuals $10^{-15}$--$10^{-13}$) show that its",
   "paper_line": 4731,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0580",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 10^{-13} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "residuals \\(10^{-15}\\) to \\(10^{-13}\\)) show that its curved",
   "paper_text": "(Newton residuals $10^{-15}$--$10^{-13}$) show that its curved body",
   "paper_line": 4731,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0581",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.061 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "window: the multipliers are \\(-0.061\\) and \\(+0.048\\) at the",
   "paper_text": "window: the multipliers are $-0.061$ and $+0.048$ at the body,",
   "paper_line": 4732,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0582",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.048 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "multipliers are \\(-0.061\\) and \\(+0.048\\) at the body,",
   "paper_text": "multipliers are $-0.061$ and $+0.048$ at the body, $-0.564$ lower",
   "paper_line": 4732,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0583",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.564 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-0.564\\) lower down and \\(-0.645\\)",
   "paper_text": "and $+0.048$ at the body, $-0.564$ lower down and $-0.645$ on",
   "paper_line": 4732,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0584",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.645 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-0.564\\) lower down and \\(-0.645\\) on the leg. The foot",
   "paper_text": "body, $-0.564$ lower down and $-0.645$ on the leg. The foot is its",
   "paper_line": 4733,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0585",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 12 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "loop (period 12, leading multiplier \\(-0.156\\)).",
   "paper_text": "period-doubled loop (period 12, leading multiplier $-0.156$).",
   "paper_line": 4733,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0586",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.156 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "12, leading multiplier \\(-0.156\\)). Inside the body lies",
   "paper_text": "(period 12, leading multiplier $-0.156$). Inside the body lies a different",
   "paper_line": 4733,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0587",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.031 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-0.031 \\pm 0.152i\\). One-parameter",
   "paper_text": "multipliers are a complex pair, $-0.031\\pm0.152i$. One-parameter branches",
   "paper_line": 4735,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0588",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.0558 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "direction: at \\(\\log_{10}T = -0.0558\\) and \\(-0.0721\\) in temperature,",
   "paper_text": "every direction: at $\\log_{10}T=-0.0558$ and $-0.0721$ in temperature,",
   "paper_line": 4736,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0589",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.0721 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = -0.0558\\) and \\(-0.0721\\) in temperature, at",
   "paper_text": "at $\\log_{10}T=-0.0558$ and $-0.0721$ in temperature, at $\\alpha=0.08074$",
   "paper_line": 4736,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0590",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.08074 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\alpha = 0.08074\\) in steering, and, toward",
   "paper_text": "in temperature, at $\\alpha=0.08074$ in steering, and, toward smaller",
   "paper_line": 4736,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0591",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 10^{-5} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(10^{-5}\\) apart. Such a close pair",
   "paper_text": "$\\alpha$, in two folds only $10^{-5}$ apart. Such a close pair is",
   "paper_line": 4737,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0592",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.0797 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\alpha \\approx 0.0797\\) then opens the period-12",
   "paper_text": "cusp. A flip at $\\alpha\\approx0.0797$ then opens the period-12 foot.",
   "paper_line": 4737,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0593",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.020 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "complex pair, \\(-0.020 \\pm 0.264i\\), or has a",
   "paper_text": "multiplier is a complex pair, $-0.020\\pm0.264i$, or has a second",
   "paper_line": 4739,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0594",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.261 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(\\(-0.261\\) against 0.099). The hook's",
   "paper_text": "multiplier of comparable size ($-0.261$ against $0.099$). Below the",
   "paper_line": 4739,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0595",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.099 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(\\(-0.261\\) against 0.099). The hook's orbit never",
   "paper_text": "comparable size ($-0.261$ against $0.099$). Below the body, where the",
   "paper_line": 4739,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0596",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.028 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "multiplier stays above 0.028 in modulus. Below the body,",
   "paper_text": "leading multiplier stays above $0.028$ in modulus. And the X-shaped",
   "paper_line": 4886,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0597",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.0773 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((\\alpha, \\log_{10}T) = (0.0773, -0.0774)\\), both orbits",
   "paper_text": "near $(\\alpha,\\log_{10}T)=(0.0773,-0.0774)$, both orbits continued",
   "paper_line": 4740,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0598",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.0774 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\log_{10}T) = (0.0773, -0.0774)\\), both orbits continued",
   "paper_text": "$(\\alpha,\\log_{10}T)=(0.0773,-0.0774)$, both orbits continued from",
   "paper_line": 4741,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0599",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -1.88 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(leading multipliers \\(-1.88\\) and",
   "paper_text": "crossing (leading multipliers $-1.88$ and $-6.59$). The crossing",
   "paper_line": 4741,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0600",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -6.59 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-6.59\\)). That X-shaped crossing",
   "paper_text": "(leading multipliers $-1.88$ and $-6.59$). The crossing is therefore",
   "paper_line": 4742,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0601",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 256 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": ": zooms of \\(256^2\\) float64 cells of the",
   "paper_text": "\\includegraphics[width=0.49\\linewidth]{fig-zoom-z3-families.png} \\caption{Zooms of $256^2$ float64 cells of the Qwen2.5-0.5B-Instruct",
   "paper_line": 927,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0602",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 12 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(philosophy direction, layer 12), shown as four images:",
   "paper_text": "(philosophy direction, layer 12), with the largest Lyapunov",
   "paper_line": 928,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0603",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.068 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "period-8 window (\\(\\alpha \\in [0.068, 0.076]\\), \\(\\log_{10}T",
   "paper_text": "period-8 window ($\\alpha\\in[0.068,0.076]$, $\\log_{10}T\\in[-0.135,-0.085]$).",
   "paper_line": 930,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0604",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.076 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "window (\\(\\alpha \\in [0.068, 0.076]\\), \\(\\log_{10}T \\in [-0.135,",
   "paper_text": "period-8 window ($\\alpha\\in[0.068,0.076]$, $\\log_{10}T\\in[-0.135,-0.085]$).",
   "paper_line": 930,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0605",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.135 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.076]\\), \\(\\log_{10}T \\in [-0.135, -0.085]\\)). Second pair:",
   "paper_text": "($\\alpha\\in[0.068,0.076]$, $\\log_{10}T\\in[-0.135,-0.085]$). Bottom: the period-6",
   "paper_line": 930,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0606",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.085 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T \\in [-0.135, -0.085]\\)). Second pair: the period-6",
   "paper_text": "($\\alpha\\in[0.068,0.076]$, $\\log_{10}T\\in[-0.135,-0.085]$). Bottom: the period-6 hooks",
   "paper_line": 930,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0607",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.072 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "period-6 hooks (\\(\\alpha \\in [0.072, 0.082]\\), \\(\\log_{10}T",
   "paper_text": "period-6 hooks ($\\alpha\\in[0.072,0.082]$, $\\log_{10}T\\in[-0.085,-0.04]$),",
   "paper_line": 930,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0608",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.082 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "hooks (\\(\\alpha \\in [0.072, 0.082]\\), \\(\\log_{10}T \\in [-0.085,",
   "paper_text": "period-6 hooks ($\\alpha\\in[0.072,0.082]$, $\\log_{10}T\\in[-0.085,-0.04]$),",
   "paper_line": 930,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0609",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.085 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.082]\\), \\(\\log_{10}T \\in [-0.085, -0.04]\\)), whose curved",
   "paper_text": "($\\alpha\\in[0.072,0.082]$, $\\log_{10}T\\in[-0.085,-0.04]$), whose curved period-6",
   "paper_line": 931,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0610",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.04 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T \\in [-0.085, -0.04]\\)), whose curved period-6",
   "paper_text": "($\\alpha\\in[0.072,0.082]$, $\\log_{10}T\\in[-0.085,-0.04]$), whose curved period-6 body,",
   "paper_line": 931,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0611",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.069106 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((\\alpha, \\log_{10}T) = (0.069106, -0.039750)\\). The fold",
   "paper_text": "cusp at $(\\alpha,\\log_{10}T)=(0.069106,-0.039750)$. The fold curve",
   "paper_line": 4749,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0612",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.039750 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\log_{10}T) = (0.069106, -0.039750)\\). The fold curve through",
   "paper_text": "$(\\alpha,\\log_{10}T)=(0.069106,-0.039750)$. The fold curve through the",
   "paper_line": 4749,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0613",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.080097 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "inside the body, at \\((0.080097, -0.058344)\\),",
   "paper_text": "cusp inside the body, at $(0.080097,-0.058344)$, from which two",
   "paper_line": 4750,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0614",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.058344 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the body, at \\((0.080097, -0.058344)\\),",
   "paper_text": "inside the body, at $(0.080097,-0.058344)$, from which two fold branches",
   "paper_line": 4750,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0615",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 5\\times10^{-6} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(5\\times10^{-6}\\) of its bracket values;",
   "paper_text": "$b\\operatorname{sign}a$ falls to below $5\\times10^{-6}$ of its bracket values at $(\\alpha,\\log_{10}T)=(0.069106,-0.039750)$",
   "paper_line": 4764,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0616",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -1.51 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "values; at these points \\(c = -1.51\\times10^{4}\\)",
   "paper_text": "body. At these same points $c=-1.51\\times10^{4}$ and $-2.38\\times10^{5}$,",
   "paper_line": 4765,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0617",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -2.38 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and \\(-2.38\\times10^{5}\\), and \\(\\det",
   "paper_text": "$c=-1.51\\times10^{4}$ and $-2.38\\times10^{5}$, and the unfolding",
   "paper_line": 4765,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0618",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 2416 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-2.38\\times10^{5}\\), and \\(\\det K = 2416\\) and 14.0. The negative",
   "paper_text": "defined below is regular ($\\det K=2416$ and $14.0$): two numerically",
   "paper_line": 4766,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0619",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 14.0 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and \\(\\det K = 2416\\) and 14.0. The negative sign of",
   "paper_text": "regular ($\\det K=2416$ and $14.0$): two numerically located",
   "paper_line": 4766,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0620",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 14.7 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\operatorname{sign} a = 14.7\\)) the estimated unfolding",
   "paper_text": "(where $b\\operatorname{sign}a=14.7$): $\\det K=2737$ (singular",
   "paper_line": 4776,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0621",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 2737 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(\\(\\det K = 2737\\), singular values 1630",
   "paper_text": "$b\\operatorname{sign}a=14.7$): $\\det K=2737$ (singular values $1630$ and",
   "paper_line": 4776,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0622",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 1630 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "2737\\), singular values 1630 and 1.7). With these derivatives",
   "paper_text": "$\\det K=2737$ (singular values $1630$ and $1.7$), so the estimated",
   "paper_line": 4777,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0623",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 1.7 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "singular values 1630 and 1.7). With these derivatives",
   "paper_text": "(singular values $1630$ and $1.7$), so the estimated unfolding",
   "paper_line": 4777,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0624",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 92.9 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "consecutive curve points | +92.9, +42.9, +14.7, **−16.9**,",
   "paper_text": "consecutive curve points & $+92.9$, $+42.9$, $+14.7$, $\\mathbf{-16.9}$,",
   "paper_line": 4788,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0625",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 42.9 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "curve points | +92.9, +42.9, +14.7, **−16.9**, −52.8",
   "paper_text": "consecutive curve points & $+92.9$, $+42.9$, $+14.7$, $\\mathbf{-16.9}$,",
   "paper_line": 4788,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0626",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 14.7 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "points | +92.9, +42.9, +14.7, **−16.9**, −52.8 | −24.7,",
   "paper_text": "points & $+92.9$, $+42.9$, $+14.7$, $\\mathbf{-16.9}$, $-52.8$",
   "paper_line": 4788,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0627",
   "section": "Cusps and shrimp-like windows",
   "claim": "number −16.9 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "+92.9, +42.9, +14.7, **−16.9**, −52.8 | −24.7, −14.3,",
   "paper_text": "$+42.9$, $+14.7$, $\\mathbf{-16.9}$, $-52.8$ & $-24.7$, $-14.3$,",
   "paper_line": 4788,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0628",
   "section": "Cusps and shrimp-like windows",
   "claim": "number −52.8 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "+42.9, +14.7, **−16.9**, −52.8 | −24.7, −14.3, −2.0, **+12.8**,",
   "paper_text": "$+14.7$, $\\mathbf{-16.9}$, $-52.8$ & $-24.7$, $-14.3$, $-2.0$,",
   "paper_line": 4788,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0629",
   "section": "Cusps and shrimp-like windows",
   "claim": "number −24.7 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "+14.7, **−16.9**, −52.8 | −24.7, −14.3, −2.0, **+12.8**,",
   "paper_text": "$\\mathbf{-16.9}$, $-52.8$ & $-24.7$, $-14.3$, $-2.0$, $\\mathbf{+12.8}$,",
   "paper_line": 4788,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0630",
   "section": "Cusps and shrimp-like windows",
   "claim": "number −14.3 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "**−16.9**, −52.8 | −24.7, −14.3, −2.0, **+12.8**, +28.0,",
   "paper_text": "$\\mathbf{-16.9}$, $-52.8$ & $-24.7$, $-14.3$, $-2.0$, $\\mathbf{+12.8}$,",
   "paper_line": 4788,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0631",
   "section": "Cusps and shrimp-like windows",
   "claim": "number −2.0 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "**−16.9**, −52.8 | −24.7, −14.3, −2.0, **+12.8**, +28.0, +45.9,",
   "paper_text": "$c\\approx-1.4\\times10^{6}$ to $-2.0\\times10^{6}$ (step agreement",
   "paper_line": 2128,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0632",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 12.8 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "−24.7, −14.3, −2.0, **+12.8**, +28.0, +45.9, +58.9",
   "paper_text": "$-14.3$, $-2.0$, $\\mathbf{+12.8}$, $+28.0$, $+45.9$, $+58.9$",
   "paper_line": 4789,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0633",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 28.0 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "−14.3, −2.0, **+12.8**, +28.0, +45.9, +58.9 |",
   "paper_text": "$-2.0$, $\\mathbf{+12.8}$, $+28.0$, $+45.9$, $+58.9$ \\\\ $|a|$",
   "paper_line": 4789,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0634",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 45.9 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "−2.0, **+12.8**, +28.0, +45.9, +58.9 |",
   "paper_text": "$\\mathbf{+12.8}$, $+28.0$, $+45.9$, $+58.9$ \\\\ $|a|$ & $1.2$--$6.9$",
   "paper_line": 4789,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0635",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 58.9 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "**+12.8**, +28.0, +45.9, +58.9 |",
   "paper_text": "$\\mathbf{+12.8}$, $+28.0$, $+45.9$, $+58.9$ \\\\ $|a|$ & $1.2$--$6.9$ &",
   "paper_line": 4789,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0636",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 1.2 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| \\(\\lvert a\\rvert\\) | 1.2 to 6.9 | 3.13 to 3.35 |",
   "paper_text": "at $+1$ or $-1$ to within $1.2\\times10^{-7}$, and no other",
   "paper_line": 2374,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0637",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 6.9 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lvert a\\rvert\\) | 1.2 to 6.9 | 3.13 to 3.35 |",
   "paper_text": "of $1.24\\times10^{-5}$ and $6.9\\times10^{-7}$, and the ratios",
   "paper_line": 1867,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0638",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 3.13 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "a\\rvert\\) | 1.2 to 6.9 | 3.13 to 3.35 |",
   "paper_text": "\\\\ $|a|$ & $1.2$--$6.9$ & $3.13$--$3.35$ \\\\ $c$ at the two",
   "paper_line": 4789,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0639",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 3.35 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| 1.2 to 6.9 | 3.13 to 3.35 |",
   "paper_text": "$|a|$ & $1.2$--$6.9$ & $3.13$--$3.35$ \\\\ $c$ at the two points around",
   "paper_line": 4790,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0640",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -1.37 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "points around \\(b = 0\\) | \\(-1.37\\times10^{4}\\), \\(-1.65\\times10^{4}\\)",
   "paper_text": "two points around $b=0$ & $-1.37\\times10^{4}$, $-1.65\\times10^{4}$",
   "paper_line": 4791,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0641",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -1.65 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-1.37\\times10^{4}\\), \\(-1.65\\times10^{4}\\) | \\(-2.38\\times10^{5}\\),",
   "paper_text": "$b=0$ & $-1.37\\times10^{4}$, $-1.65\\times10^{4}$ & $-2.38\\times10^{5}$,",
   "paper_line": 4791,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0642",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -2.38 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-1.65\\times10^{4}\\) | \\(-2.38\\times10^{5}\\), \\(-2.34\\times10^{5}\\)",
   "paper_text": "$-1.37\\times10^{4}$, $-1.65\\times10^{4}$ & $-2.38\\times10^{5}$, $-2.34\\times10^{5}$",
   "paper_line": 4791,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0643",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -2.34 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-2.38\\times10^{5}\\), \\(-2.34\\times10^{5}\\) |",
   "paper_text": "$-1.65\\times10^{4}$ & $-2.38\\times10^{5}$, $-2.34\\times10^{5}$ \\\\ \\bottomrule",
   "paper_line": 4791,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0644",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 10^{-7} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "critical multiplier 1 to \\(10^{-7}\\)). \\(c\\): cubic coefficient",
   "paper_text": "critical multiplier $1$ to $10^{-7}$). $c$: cubic coefficient at",
   "paper_line": 4795,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0645",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.1 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(finite-difference steps agree to 0.1 and 0.7%). Bisection along",
   "paper_text": "(finite-difference steps agree to $0.1$ and $0.7\\,\\%$). Bisection",
   "paper_line": 4796,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0646",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.7 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "steps agree to 0.1 and 0.7%). Bisection along the",
   "paper_text": "(finite-difference steps agree to $0.1$ and $0.7\\,\\%$). Bisection along the",
   "paper_line": 4796,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0647",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 12 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(philosophy direction, layer 12) with its float64 fold",
   "paper_text": "(philosophy direction, layer 12) with its float64 fold curves",
   "paper_line": 4802,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0648",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 480 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "a float32 phase map of 480 × 400 cells (largest exponent",
   "paper_text": "is a float32 phase map of $480\\times400$ cells (largest exponent",
   "paper_line": 4804,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0649",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 400 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "float32 phase map of 480 × 400 cells (largest exponent",
   "paper_text": "float32 phase map of $480\\times400$ cells (largest exponent from",
   "paper_line": 4804,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0650",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 300 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(largest exponent from 300 steps after 300 transient",
   "paper_text": "cells (largest exponent from 300 steps after 300 transient steps;",
   "paper_line": 4804,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0651",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 300 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "exponent from 300 steps after 300 transient steps; chaotic",
   "paper_text": "exponent from 300 steps after 300 transient steps; chaotic cells",
   "paper_line": 4804,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0652",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 95 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "float64 map of the stripes, 95% of cells carry the same",
   "paper_text": "of Figure~\\ref{fig:stripes}, 95\\,\\% of cells carry the same",
   "paper_line": 4805,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0653",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 60 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "branches stopped after 60 points near \\((0.0753,",
   "paper_text": "lower branches stopped after 60 points near $(0.0753,-0.089)$,",
   "paper_line": 4806,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0654",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.0753 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "after 60 points near \\((0.0753, -0.089)\\), where they",
   "paper_text": "stopped after 60 points near $(0.0753,-0.089)$, where they approach",
   "paper_line": 4806,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0655",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.089 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "points near \\((0.0753, -0.089)\\), where they approach",
   "paper_text": "after 60 points near $(0.0753,-0.089)$, where they approach each",
   "paper_line": 4806,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0656",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.1 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T \\approx 0\\) to 0.1, periodic orbits are no",
   "paper_text": "temperature, $\\log_{10}T\\approx0$--$0.1$, periodic orbits are no longer",
   "paper_line": 4811,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0657",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.06 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "one-dimensional (second multipliers 0.06 to 0.09). At",
   "paper_text": "one-dimensional (second multipliers $0.06$--$0.09$). At $\\alpha=0.06484$",
   "paper_line": 4812,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0658",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.09 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(second multipliers 0.06 to 0.09). At",
   "paper_text": "(second multipliers $0.06$--$0.09$). At $\\alpha=0.06484$ the",
   "paper_line": 4812,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0659",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.06484 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\alpha = 0.06484\\) the temperature branch",
   "paper_text": "$0.06$--$0.09$). At $\\alpha=0.06484$ the temperature branch of",
   "paper_line": 4812,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0660",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.0640 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "folds at \\(\\log_{10}T = 0.0640\\) and 0.0664.",
   "paper_text": "S-shaped, with folds at $\\log_{10}T=0.0640$ and $0.0664$. When that fold",
   "paper_line": 4813,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0661",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.0664 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = 0.0640\\) and 0.0664.",
   "paper_text": "at $\\log_{10}T=0.0640$ and $0.0664$. When that fold is continued",
   "paper_line": 4814,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0662",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.062959 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((\\alpha, \\log_{10}T) = (0.062959, 0.059958)\\) and \\((0.065574,",
   "paper_text": "lie at $(\\alpha,\\log_{10}T)=(0.062959,0.059958)$ and $(0.065574,0.074447)$.",
   "paper_line": 4816,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0663",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.059958 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\log_{10}T) = (0.062959, 0.059958)\\) and \\((0.065574, 0.074447)\\).",
   "paper_text": "$(\\alpha,\\log_{10}T)=(0.062959,0.059958)$ and $(0.065574,0.074447)$.",
   "paper_line": 4817,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0664",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.065574 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(0.062959, 0.059958)\\) and \\((0.065574, 0.074447)\\). There",
   "paper_text": "$(\\alpha,\\log_{10}T)=(0.062959,0.059958)$ and $(0.065574,0.074447)$. There $b\\operatorname{sign}a$",
   "paper_line": 4817,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0665",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.074447 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.059958)\\) and \\((0.065574, 0.074447)\\). There",
   "paper_text": "$(\\alpha,\\log_{10}T)=(0.062959,0.059958)$ and $(0.065574,0.074447)$. There $b\\operatorname{sign}a$",
   "paper_line": 4817,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0666",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 1.1\\times10^{-5} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\operatorname{sign} a\\) is below \\(1.1\\times10^{-5}\\) of its bracket values,",
   "paper_text": "$b\\operatorname{sign}a$ is below $1.1\\times10^{-5}$ of its bracket values, $c=-1.02\\times10^{4}$",
   "paper_line": 4817,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0667",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -1.02 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(c = -1.02\\times10^{4}\\) and \\(+1.37\\times10^{5}\\),",
   "paper_text": "$1.1\\times10^{-5}$ of its bracket values, $c=-1.02\\times10^{4}$ and $+1.37\\times10^{5}$,",
   "paper_line": 4818,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0668",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 1.37\\times10^{5} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "-1.02\\times10^{4}\\) and \\(+1.37\\times10^{5}\\), and \\(\\det K = -42.0\\)",
   "paper_text": "$c=-1.02\\times10^{4}$ and $+1.37\\times10^{5}$, and $\\det K=-42.0$ and $35.5$.",
   "paper_line": 4818,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0669",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -42.0 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(+1.37\\times10^{5}\\), and \\(\\det K = -42.0\\) and",
   "paper_text": "$+1.37\\times10^{5}$, and $\\det K=-42.0$ and $35.5$. Further traces",
   "paper_line": 4818,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0670",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 35.5 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "35.5. Further traces of the",
   "paper_text": "$+1.37\\times10^{5}$, and $\\det K=-42.0$ and $35.5$. Further traces of the same",
   "paper_line": 4818,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0671",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 3\\times10^{-7} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "retrace it to within \\(3\\times10^{-7}\\), and one of them finds",
   "paper_text": "branches, retrace it to within $3\\times10^{-7}$, and one of them finds two",
   "paper_line": 4819,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0672",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.012 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "near \\(\\log_{10}T \\approx 0.012\\). All five reversals are",
   "paper_text": "reversals near $\\log_{10}T\\approx0.012$. All five reversals are located",
   "paper_line": 4820,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0673",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.083082 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "The other three lie at \\((0.083082, 0.108633)\\),",
   "paper_text": "lie at $(\\alpha,\\log_{10}T)=(0.083082,0.108633)$, $(0.074072,0.011831)$",
   "paper_line": 4820,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0674",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.108633 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "three lie at \\((0.083082, 0.108633)\\),",
   "paper_text": "$(\\alpha,\\log_{10}T)=(0.083082,0.108633)$, $(0.074072,0.011831)$ and",
   "paper_line": 4821,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0675",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.074072 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((0.074072, 0.011831)\\) and \\((0.073220,",
   "paper_text": "$(\\alpha,\\log_{10}T)=(0.083082,0.108633)$, $(0.074072,0.011831)$ and $(0.073220,0.012759)$.",
   "paper_line": 4821,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0676",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.011831 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((0.074072, 0.011831)\\) and \\((0.073220, 0.012759)\\);",
   "paper_text": "$(\\alpha,\\log_{10}T)=(0.083082,0.108633)$, $(0.074072,0.011831)$ and $(0.073220,0.012759)$.",
   "paper_line": 4821,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0677",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.073220 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((0.074072, 0.011831)\\) and \\((0.073220, 0.012759)\\); there \\(c\\)",
   "paper_text": "$(0.074072,0.011831)$ and $(0.073220,0.012759)$. There $c$ is $-9.7\\times10^{4}$,",
   "paper_line": 4821,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0678",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.012759 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.011831)\\) and \\((0.073220, 0.012759)\\); there \\(c\\) is",
   "paper_text": "$(0.074072,0.011831)$ and $(0.073220,0.012759)$. There $c$ is $-9.7\\times10^{4}$,",
   "paper_line": 4821,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0679",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -9.7 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-9.7\\times10^{4}\\), \\(-5.7\\times10^{3}\\)",
   "paper_text": "$(0.073220,0.012759)$. There $c$ is $-9.7\\times10^{4}$, $-5.7\\times10^{3}$",
   "paper_line": 4821,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0680",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -5.7 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-9.7\\times10^{4}\\), \\(-5.7\\times10^{3}\\) and \\(+1.7\\times10^{3}\\),",
   "paper_text": "$c$ is $-9.7\\times10^{4}$, $-5.7\\times10^{3}$ and $+1.7\\times10^{3}$,",
   "paper_line": 4821,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0681",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 1.7\\times10^{3} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-5.7\\times10^{3}\\) and \\(+1.7\\times10^{3}\\), and",
   "paper_text": "$-9.7\\times10^{4}$, $-5.7\\times10^{3}$ and $+1.7\\times10^{3}$, and $\\det K$ is $25.3$, $-188.5$",
   "paper_line": 4822,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0682",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 25.3 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\det K\\) is 25.3, \\(-188.5\\) and 68.5. The",
   "paper_text": "$+1.7\\times10^{3}$, and $\\det K$ is $25.3$, $-188.5$ and $68.5$. The",
   "paper_line": 4822,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0683",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -188.5 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\det K\\) is 25.3, \\(-188.5\\) and 68.5. The last two",
   "paper_text": "$+1.7\\times10^{3}$, and $\\det K$ is $25.3$, $-188.5$ and $68.5$. The last two cusps,",
   "paper_line": 4822,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0684",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 68.5 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "is 25.3, \\(-188.5\\) and 68.5. The last two cusps, close",
   "paper_text": "K$ is $25.3$, $-188.5$ and $68.5$. The last two cusps, close",
   "paper_line": 4822,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0685",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.062483 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((\\alpha, \\log_{10}T) = (0.062483, 0.004955)\\) and",
   "paper_text": "reaches $+1$ twice, at $\\alpha=0.062483$, $\\log_{10}T=0.004955$ and",
   "paper_line": 4862,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0686",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.004955 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\log_{10}T) = (0.062483, 0.004955)\\) and",
   "paper_text": "$\\alpha=0.062483$, $\\log_{10}T=0.004955$ and at $\\alpha=0.062499$,",
   "paper_line": 4862,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0687",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.062499 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((0.062499, -0.001780)\\). Both points",
   "paper_text": "$\\log_{10}T=0.004955$ and at $\\alpha=0.062499$, $\\log_{10}T=-0.001780$. Both",
   "paper_line": 4862,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0688",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.001780 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((0.062499, -0.001780)\\). Both points are 1:1",
   "paper_text": "$\\alpha=0.062499$, $\\log_{10}T=-0.001780$. Both points are 1:1 resonances,",
   "paper_line": 4863,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0689",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 3\\times10^{-4} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "multiplier parallel to \\(3\\times10^{-4}\\) degrees. Close by, at",
   "paper_text": "double multiplier parallel to $3\\times10^{-4}$ degrees. Close by, at $\\alpha=0.062522$,",
   "paper_line": 4863,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0690",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.062522 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((0.062522, -0.002667)\\), a multiplier",
   "paper_text": "degrees. Close by, at $\\alpha=0.062522$, $\\log_{10}T=-0.002667$, a",
   "paper_line": 4864,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0691",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.002667 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((0.062522, -0.002667)\\), a multiplier reaches",
   "paper_text": "$\\alpha=0.062522$, $\\log_{10}T=-0.002667$, a multiplier reaches $-1$:",
   "paper_line": 4864,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0692",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 28.1 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at five curve points | +28.1, +18.7, +8.4, **−1.1**,",
   "paper_text": "$b$ at five curve points & $+28.1,\\ +18.7,\\ +8.4,\\ \\mathbf{-1.1},\\",
   "paper_line": 4832,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0693",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 18.7 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "curve points | +28.1, +18.7, +8.4, **−1.1**, −12.8",
   "paper_text": "five curve points & $+28.1,\\ +18.7,\\ +8.4,\\ \\mathbf{-1.1},\\ -12.8$",
   "paper_line": 4832,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0694",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 8.4 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "points | +28.1, +18.7, +8.4, **−1.1**, −12.8 | +51.8,",
   "paper_text": "points & $+28.1,\\ +18.7,\\ +8.4,\\ \\mathbf{-1.1},\\ -12.8$ &",
   "paper_line": 4832,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0695",
   "section": "Cusps and shrimp-like windows",
   "claim": "number −1.1 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| +28.1, +18.7, +8.4, **−1.1**, −12.8 | +51.8, +29.7,",
   "paper_text": "$+28.1,\\ +18.7,\\ +8.4,\\ \\mathbf{-1.1},\\ -12.8$ & $+51.8,\\ +29.7,\\",
   "paper_line": 4832,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0696",
   "section": "Cusps and shrimp-like windows",
   "claim": "number −12.8 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "+18.7, +8.4, **−1.1**, −12.8 | +51.8, +29.7, +9.3, **−9.0**,",
   "paper_text": "+18.7,\\ +8.4,\\ \\mathbf{-1.1},\\ -12.8$ & $+51.8,\\ +29.7,\\ +9.3,\\",
   "paper_line": 4832,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0697",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 51.8 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "+8.4, **−1.1**, −12.8 | +51.8, +29.7, +9.3, **−9.0**,",
   "paper_text": "\\mathbf{-1.1},\\ -12.8$ & $+51.8,\\ +29.7,\\ +9.3,\\ \\mathbf{-9.0},\\",
   "paper_line": 4832,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0698",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 29.7 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "**−1.1**, −12.8 | +51.8, +29.7, +9.3, **−9.0**, −23.4",
   "paper_text": "requests by 23.4 points ($[17.1,29.7]$). An excursion of the same",
   "paper_line": 4685,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0699",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 9.3 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "−12.8 | +51.8, +29.7, +9.3, **−9.0**, −23.4 |",
   "paper_text": "points (95\\,\\% interval $[4.8,9.3]$; 10 samples per prompt).",
   "paper_line": 4566,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0700",
   "section": "Cusps and shrimp-like windows",
   "claim": "number −9.0 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| +51.8, +29.7, +9.3, **−9.0**, −23.4 |",
   "paper_text": "$+51.8,\\ +29.7,\\ +9.3,\\ \\mathbf{-9.0},\\ -23.4$ \\\\ $a$ & $3.02$--$3.08$",
   "paper_line": 4833,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0701",
   "section": "Cusps and shrimp-like windows",
   "claim": "number −23.4 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "+29.7, +9.3, **−9.0**, −23.4 |",
   "paper_text": "+29.7,\\ +9.3,\\ \\mathbf{-9.0},\\ -23.4$ \\\\ $a$ & $3.02$--$3.08$ &",
   "paper_line": 4833,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0702",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 3.02 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| \\(a\\) | 3.02 to 3.08 | −2.58 to −2.57",
   "paper_text": "\\mathbf{-9.0},\\ -23.4$ \\\\ $a$ & $3.02$--$3.08$ & $-2.58$ to $-2.57$",
   "paper_line": 4833,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0703",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 3.08 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| \\(a\\) | 3.02 to 3.08 | −2.58 to −2.57 |",
   "paper_text": "\\mathbf{-9.0},\\ -23.4$ \\\\ $a$ & $3.02$--$3.08$ & $-2.58$ to $-2.57$ \\\\ critical",
   "paper_line": 4833,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0704",
   "section": "Cusps and shrimp-like windows",
   "claim": "number −2.58 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(a\\) | 3.02 to 3.08 | −2.58 to −2.57 |",
   "paper_text": "\\\\ $a$ & $3.02$--$3.08$ & $-2.58$ to $-2.57$ \\\\ critical multiplier",
   "paper_line": 4833,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0705",
   "section": "Cusps and shrimp-like windows",
   "claim": "number −2.57 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "3.02 to 3.08 | −2.58 to −2.57 |",
   "paper_text": "$3.02$--$3.08$ & $-2.58$ to $-2.57$ \\\\ critical multiplier & $1\\pm10^{-9}$",
   "paper_line": 4834,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0706",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -1.06 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(c\\) around \\(b = 0\\) | \\(-1.06\\), \\(-1.01\\) (\\(\\times10^{4}\\))",
   "paper_text": "$1\\pm10^{-8}$ \\\\ $c$ around $b=0$ & $-1.06$, $-1.01\\ (\\times10^{4})$ &",
   "paper_line": 4835,
   "paper_file": "paper/llm/main.tex"
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   "id": "shrimp-0707",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -1.01 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(b = 0\\) | \\(-1.06\\), \\(-1.01\\) (\\(\\times10^{4}\\)) |",
   "paper_text": "$c$ around $b=0$ & $-1.06$, $-1.01\\ (\\times10^{4})$ & $+1.39$,",
   "paper_line": 4836,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0708",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 1.39 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(\\(\\times10^{4}\\)) | \\(+1.39\\), \\(+1.36\\) (\\(\\times10^{5}\\))",
   "paper_text": "$-1.01\\ (\\times10^{4})$ & $+1.39$, $+1.36\\ (\\times10^{5})$ \\\\",
   "paper_line": 4836,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0709",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 1.36 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(\\(\\times10^{4}\\)) | \\(+1.39\\), \\(+1.36\\) (\\(\\times10^{5}\\)) |",
   "paper_text": "(\\times10^{4})$ & $+1.39$, $+1.36\\ (\\times10^{5})$ \\\\ \\bottomrule",
   "paper_line": 4836,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0710",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 10^{-4} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "reversals (steps agree to \\(10^{-4}\\)), which supports a nondegenerate",
   "paper_text": "reversals (steps agree to $10^{-4}$), which supports a nondegenerate",
   "paper_line": 4840,
   "paper_file": "paper/llm/main.tex"
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   "id": "shrimp-0711",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 12 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(philosophy direction, layer 12; \\(192^2\\) float64 cells)",
   "paper_text": "(philosophy direction, layer 12; $192^2$ float64 cells) with",
   "paper_line": 4847,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0712",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 192 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "direction, layer 12; \\(192^2\\) float64 cells) with",
   "paper_text": "(philosophy direction, layer 12; $192^2$ float64 cells) with float64",
   "paper_line": 4847,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0713",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 2\\times10^{-3} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "curve, nowhere within \\(2\\times10^{-3}\\) of it in the traced ranges;",
   "paper_text": "fold curve, nowhere within $2\\times10^{-3}$ of it in the traced ranges;",
   "paper_line": 4857,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0714",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 16 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "hostility at layer 16, Figure",
   "paper_text": "block~4 and hostility at block~16, $\\log_{10}T=-0.1$, float64).",
   "paper_line": 3035,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0715",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 1584 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "turning point. We drew 1584 chaotic cells from the",
   "paper_text": "second turning point. We drew 1584 chaotic cells (200 from each",
   "paper_line": 4892,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0716",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.1 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = -0.1\\), have smooth, single-valued",
   "paper_text": "two-block planes at $\\log_{10}T=-0.1$, have smooth, single-valued",
   "paper_line": 4897,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0717",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 16 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "layer 4, gratitude at layer 16), every one-dimensional",
   "paper_text": "block~4, gratitude at block~16), every one-dimensional phase",
   "paper_line": 4899,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0718",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 20 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "20-band attractor is N-shaped:",
   "paper_text": "one-dimensional phase of a 20-band attractor is N-shaped:",
   "paper_line": 4899,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0719",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.1 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(float64, \\(\\log_{10}T = -0.1\\)). Each panel shows one",
   "paper_text": "Qwen2.5-0.5B-Instruct (float64, $\\log_{10}T=-0.1$). Each panel shows one phase",
   "paper_line": 5092,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0720",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 16 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and gratitude at layer 16, \\((\\alpha_1, \\alpha_2)",
   "paper_text": "block~4 and gratitude at block~16, $(\\alpha_1,\\alpha_2)=(0.0568,-0.0189)$:",
   "paper_line": 5096,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0721",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.0568 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((\\alpha_1, \\alpha_2) = (0.0568, -0.0189)\\): phase 0 of",
   "paper_text": "block~16, $(\\alpha_1,\\alpha_2)=(0.0568,-0.0189)$: phase 0 of a 20-band",
   "paper_line": 5096,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0722",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.0189 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((\\alpha_1, \\alpha_2) = (0.0568, -0.0189)\\): phase 0 of a 20-band",
   "paper_text": "$(\\alpha_1,\\alpha_2)=(0.0568,-0.0189)$: phase 0 of a 20-band attractor,",
   "paper_line": 5096,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0723",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 20 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "-0.0189)\\): phase 0 of a 20-band attractor, N-shaped.",
   "paper_text": "$(\\alpha_1,\\alpha_2)=(0.0568,-0.0189)$: phase 0 of a 20-band attractor, N-shaped",
   "paper_line": 5096,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0724",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.0366 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "c) The same plane at \\((-0.0366, -0.0467)\\): two phases",
   "paper_text": "(b, c) The same plane at $(-0.0366,-0.0467)$: two phases of a",
   "paper_line": 5097,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0725",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.0467 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "same plane at \\((-0.0366, -0.0467)\\): two phases of a 12-band",
   "paper_text": "The same plane at $(-0.0366,-0.0467)$: two phases of a 12-band",
   "paper_line": 5097,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0726",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 12 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "-0.0467)\\): two phases of a 12-band attractor, N-shaped",
   "paper_text": "$(-0.0366,-0.0467)$: two phases of a 12-band attractor, N-shaped maps",
   "paper_line": 5097,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0727",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 16 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and hostility at layer 16, \\((-0.1099, 0.0998)\\):",
   "paper_text": "block~4 and hostility at block~16, $(-0.1099,0.0998)$: phase",
   "paper_line": 5098,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0728",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.1099 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "hostility at layer 16, \\((-0.1099, 0.0998)\\): phase 4 of",
   "paper_text": "and hostility at block~16, $(-0.1099,0.0998)$: phase 4 of a 9-band",
   "paper_line": 5098,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0729",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.0998 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at layer 16, \\((-0.1099, 0.0998)\\): phase 4 of a 9-band",
   "paper_text": "hostility at block~16, $(-0.1099,0.0998)$: phase 4 of a 9-band attractor,",
   "paper_line": 5098,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0730",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 128 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "**The window.** A 128 × 128 zoom around the cell",
   "paper_text": "a bimodal map. A $128\\times128$ zoom around another, whose",
   "paper_line": 4900,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0731",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 128 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "**The window.** A 128 × 128 zoom around the cell with",
   "paper_text": "a bimodal map. A $128\\times128$ zoom around another, whose",
   "paper_line": 4900,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0732",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 31 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "window's period-5 orbit over a 31 × 31 grid of its body:",
   "paper_text": "window's period-5 orbit over a $31\\times31$ grid of its body:",
   "paper_line": 4902,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0733",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 31 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "period-5 orbit over a 31 × 31 grid of its body: 608 cells",
   "paper_text": "window's period-5 orbit over a $31\\times31$ grid of its body:",
   "paper_line": 4902,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0734",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 608 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "× 31 grid of its body: 608 cells solved,",
   "paper_text": "$31\\times31$ grid of its body: 608 cells solved, all with the",
   "paper_line": 4902,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0735",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 447 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "with the same token loop, 447 of them attracting. In",
   "paper_text": "all with the same token loop, 447 of them attracting. In 61 of",
   "paper_line": 4903,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0736",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 61 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of them attracting. In 61 of these 447 cells,",
   "paper_text": "447 of them attracting. In 61 of these 447 cells, the nearest",
   "paper_line": 4903,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0737",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 447 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "attracting. In 61 of these 447 cells,",
   "paper_text": "all with the same token loop, 447 of them attracting. In 61 of",
   "paper_line": 4903,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0738",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 2.0\\times10^{-5} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of the zoom (at most \\(2.0\\times10^{-5}\\) away in \\(\\alpha_1\\)",
   "paper_text": "cell of the zoom (at most $2.0\\times10^{-5}$ away in $\\alpha_1$ and $3.2\\times10^{-5}$",
   "paper_line": 4903,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0739",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 3.2\\times10^{-5} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and \\(3.2\\times10^{-5}\\) in \\(\\alpha_2\\)) settles",
   "paper_text": "$2.0\\times10^{-5}$ away in $\\alpha_1$ and $3.2\\times10^{-5}$ in $\\alpha_2$) settles on",
   "paper_line": 4904,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0740",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.0139 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "its modulus is at least 0.0139 in all 608",
   "paper_text": "zero: its modulus is at least $0.0139$ in all 608 cells. Where a",
   "paper_line": 4908,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0741",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 608 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at least 0.0139 in all 608",
   "paper_text": "is at least $0.0139$ in all 608 cells. Where a one-dimensional",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0742",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 91 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "two form a complex pair (91 cells, in narrow strips)",
   "paper_text": "the two form a complex pair (91 cells, in narrow strips) or,",
   "paper_line": 4910,
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  {
   "id": "shrimp-0743",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 41 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "their product is negative (41 other cells), pass each",
   "paper_text": "their product is negative (41 other cells), pass each other",
   "paper_line": 4910,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0744",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.44 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "contracts by a median factor of 0.44 and the first by 0.76 over",
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   "paper_line": 4912,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0745",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.76 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of 0.44 and the first by 0.76 over the attracting",
   "paper_text": "of $0.44$ and the first by $0.76$ over the attracting cells,",
   "paper_line": 4912,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0746",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 1.65 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(\\(\\mu_1 = 1.65\\)), and near the top of",
   "paper_text": "the same token loop ($\\mu_1=1.65$), and near the top of the",
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  {
   "id": "shrimp-0747",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.88 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "leading multiplier rises to 0.88; both are explained by",
   "paper_text": "leading multiplier rises to $0.88$; both are explained by the",
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  {
   "id": "shrimp-0748",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 16 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and hostility at layer 16 (Qwen2.5-0.5B-Instruct,",
   "paper_text": "block~4 and hostility at block~16 (Qwen2.5-0.5B-Instruct, float64,",
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  {
   "id": "shrimp-0749",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.1 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "float64, \\(\\log_{10}T = -0.1\\)). (a) Attractor reached",
   "paper_text": "(Qwen2.5-0.5B-Instruct, float64, $\\log_{10}T=-0.1$). (a) Attractor reached from",
   "paper_line": 5105,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0750",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 128 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "from the fixed start on a 128 × 128 grid (black: chaotic),",
   "paper_text": "from the fixed start on a $128\\times128$ grid (black: chaotic),",
   "paper_line": 5106,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0751",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 128 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "fixed start on a 128 × 128 grid (black: chaotic),",
   "paper_text": "from the fixed start on a $128\\times128$ grid (black: chaotic),",
   "paper_line": 5106,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0752",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 31 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "continued over the box (31 × 31, 608 cells solved,",
   "paper_text": "orbit continued over the box ($31\\times31$, 608 cells solved,",
   "paper_line": 5107,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0753",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 31 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "continued over the box (31 × 31, 608 cells solved, one",
   "paper_text": "orbit continued over the box ($31\\times31$, 608 cells solved,",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0754",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 608 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "over the box (31 × 31, 608 cells solved, one token",
   "paper_text": "over the box ($31\\times31$, 608 cells solved, one token loop):",
   "paper_line": 5107,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0755",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.0139 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "modulus never falls below 0.0139; the dark strips, where",
   "paper_text": "modulus never falls below $0.0139$; the dark strips, where a",
   "paper_line": 5110,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0756",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.118730 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((\\alpha_1, \\alpha_2) = (-0.118730, 0.100693)\\), and then",
   "paper_text": "cell, $(\\alpha_1,\\alpha_2)=(-0.118730,0.100693)$, and then the boundaries",
   "paper_line": 4963,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0757",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.100693 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\alpha_2) = (-0.118730, 0.100693)\\), and then the boundaries",
   "paper_text": "$(\\alpha_1,\\alpha_2)=(-0.118730,0.100693)$, and then the boundaries",
   "paper_line": 4963,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0758",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 18 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "both directions (float64; 18 to 73 points per line,",
   "paper_text": "in both directions (float64; 18 to 73 points per line, 30 to",
   "paper_line": 4964,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0759",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 73 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "directions (float64; 18 to 73 points per line, 30 to",
   "paper_text": "directions (float64; 18 to 73 points per line, 30 to 120",
   "paper_line": 4964,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0760",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 30 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "to 73 points per line, 30 to 120",
   "paper_text": "(float64; 18 to 73 points per line, 30 to 120 per curve; one of the",
   "paper_line": 4964,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0761",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 120 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "points per line, 30 to 120",
   "paper_text": "to 73 points per line, 30 to 120 per curve; one of the eight",
   "paper_line": 4964,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0762",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 10^{-10} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the residual is below \\(10^{-10}\\) and the test",
   "paper_text": "point the residual is below $10^{-10}$ and the test function below",
   "paper_line": 4966,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0763",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 10^{-9} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "function below \\(10^{-9}\\). The critical multiplier",
   "paper_text": "and the test function below $10^{-9}$. The critical multiplier stays",
   "paper_line": 4966,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0764",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 6\\times10^{-8} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(6\\times10^{-8}\\) of \\(+1\\) on the fold",
   "paper_text": "multiplier stays real and within $6\\times10^{-8}$ of $+1$ on the fold curve",
   "paper_line": 4967,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0765",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.040 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "other multiplier modulus is 0.040 on that fold curve and",
   "paper_text": "other multiplier modulus is $0.040$ on that fold curve and $0.122$",
   "paper_line": 4968,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0766",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.122 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "on that fold curve and 0.122 on the",
   "paper_text": "$0.040$ on that fold curve and $0.122$ on the flip curves. A rerun",
   "paper_line": 4968,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0767",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.118166 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\alpha_1 = -0.118166\\) and \\(\\alpha_2 = 0.102715\\)",
   "paper_text": "dies in folds at $\\alpha_1=-0.118166$ and $\\alpha_2=0.102715$ (next",
   "paper_line": 4971,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0768",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.102715 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "-0.118166\\) and \\(\\alpha_2 = 0.102715\\) (next moduli 0.0012 and",
   "paper_text": "$\\alpha_1=-0.118166$ and $\\alpha_2=0.102715$ (next moduli $0.0012$ and",
   "paper_line": 4972,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0769",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.0012 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.102715\\) (next moduli 0.0012 and",
   "paper_text": "$\\alpha_2=0.102715$ (next moduli $0.0012$ and $0.0008$). Going left",
   "paper_line": 4972,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0770",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.0008 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.0008). Going left and down,",
   "paper_text": "(next moduli $0.0012$ and $0.0008$). Going left and down, it",
   "paper_line": 4972,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0771",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.12147 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\alpha_1 = -0.12147\\) and \\(\\alpha_2 = 0.09954\\)),",
   "paper_text": "stability in flips (at $\\alpha_1=-0.12147$ and $\\alpha_2=0.09954$), regains",
   "paper_line": 4973,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0772",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.09954 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "-0.12147\\) and \\(\\alpha_2 = 0.09954\\)), regains it where the",
   "paper_text": "$\\alpha_1=-0.12147$ and $\\alpha_2=0.09954$), regains it where the same",
   "paper_line": 4973,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0773",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.12305 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "crosses \\(-1\\) again (at \\(-0.12305\\) and 0.09586; a doubling",
   "paper_text": "multiplier crosses $-1$ again (at $-0.12305$ and $0.09586$; a doubling",
   "paper_line": 4973,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0774",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.09586 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "again (at \\(-0.12305\\) and 0.09586; a doubling bubble),",
   "paper_text": "$-1$ again (at $-0.12305$ and $0.09586$; a doubling bubble), and dies",
   "paper_line": 4974,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0775",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.123323 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and dies in a fold (at \\(-0.123323\\) and 0.095720). Three",
   "paper_text": "bubble), and dies in a fold (at $-0.123323$ and $0.095720$). Three of",
   "paper_line": 4974,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0776",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.095720 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "fold (at \\(-0.123323\\) and 0.095720). Three of these four folds",
   "paper_text": "a fold (at $-0.123323$ and $0.095720$). Three of these four folds",
   "paper_line": 4974,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0777",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 3.1\\times10^{-7} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "continued fold curve (within \\(3.1\\times10^{-7}\\)); the left one lies on",
   "paper_text": "continued fold curve (within $3.1\\times10^{-7}$); the left one lies on a second.",
   "paper_line": 4975,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0778",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 10 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "flips lie shells of periods 10",
   "paper_text": "flips lie shells of periods 10 and 20. Where the upper leg",
   "paper_line": 2368,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0779",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 20 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and 20. Near \\(\\alpha_1 = -0.1192\\)",
   "paper_text": "lie shells of periods 10 and 20. Where the upper leg leaves",
   "paper_line": 2368,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0780",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.1192 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and 20. Near \\(\\alpha_1 = -0.1192\\) the first fold curve",
   "paper_text": "the upper leg. Near $\\alpha_1=-0.1192$ its parameter tangent reverses",
   "paper_line": 4977,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0781",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.1192221 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((\\alpha_1, \\alpha_2) = (-0.1192221, 0.1040536)\\),",
   "paper_text": "trace): at $(\\alpha_1,\\alpha_2)=(-0.1192221,0.1040536)$, with $c=+2.60\\times10^{4}$",
   "paper_line": 4979,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0782",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.1040536 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\alpha_2) = (-0.1192221, 0.1040536)\\),",
   "paper_text": "$(\\alpha_1,\\alpha_2)=(-0.1192221,0.1040536)$, with $c=+2.60\\times10^{4}$",
   "paper_line": 4979,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0783",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 2.60\\times10^{4} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "with \\(c = +2.60\\times10^{4}\\) and \\(\\det K = 176.6\\),",
   "paper_text": "$(\\alpha_1,\\alpha_2)=(-0.1192221,0.1040536)$, with $c=+2.60\\times10^{4}$ and $\\det K=176.6$, and at",
   "paper_line": 4979,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0784",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 176.6 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "+2.60\\times10^{4}\\) and \\(\\det K = 176.6\\), and at",
   "paper_text": "$c=+2.60\\times10^{4}$ and $\\det K=176.6$, and at $(-0.1191670,0.1028019)$,",
   "paper_line": 4980,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0785",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.1191670 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((-0.1191670, 0.1028019)\\), with \\(c",
   "paper_text": "and $\\det K=176.6$, and at $(-0.1191670,0.1028019)$, with $c=-2.05\\times10^{4}$",
   "paper_line": 4980,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0786",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.1028019 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((-0.1191670, 0.1028019)\\), with \\(c = -2.05\\times10^{4}\\)",
   "paper_text": "K=176.6$, and at $(-0.1191670,0.1028019)$, with $c=-2.05\\times10^{4}$",
   "paper_line": 4980,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0787",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -2.05 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.1028019)\\), with \\(c = -2.05\\times10^{4}\\) and",
   "paper_text": "$(-0.1191670,0.1028019)$, with $c=-2.05\\times10^{4}$ and $\\det K=88.6$.",
   "paper_line": 4980,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0788",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 88.6 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\det K = 88.6\\). The two traces agree",
   "paper_text": "$c=-2.05\\times10^{4}$ and $\\det K=88.6$. The two traces agree to $2\\times10^{-12}$",
   "paper_line": 4980,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0789",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 2\\times10^{-12} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "The two traces agree to \\(2\\times10^{-12}\\) in these positions",
   "paper_text": "K=88.6$. The two traces agree to $2\\times10^{-12}$ in these positions and to",
   "paper_line": 4981,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0790",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.11901 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((-0.11901, 0.10346)\\). There they",
   "paper_text": "K$. Its outer arms cross at $(-0.11901,0.10346)$ (Figure~\\ref{fig:period5folds}d).",
   "paper_line": 4981,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0791",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.10346 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((-0.11901, 0.10346)\\). There they are folds",
   "paper_text": "outer arms cross at $(-0.11901,0.10346)$ (Figure~\\ref{fig:period5folds}d).",
   "paper_line": 4982,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0792",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 3.65 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "two branches differ by 3.65 to 3.78% of the state",
   "paper_text": "on the two arms differ by $3.65$ to $3.78\\,\\%$ of the state",
   "paper_line": 4983,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0793",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 3.78 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "branches differ by 3.65 to 3.78% of the state",
   "paper_text": "two arms differ by $3.65$ to $3.78\\,\\%$ of the state norm (root-mean-square",
   "paper_line": 4983,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0794",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 15.8 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "norm, 15.8 to 44.5 times the state",
   "paper_text": "phase alignment; both traces), 15.8 to 44.5 times the state change",
   "paper_line": 4984,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0795",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 44.5 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "norm, 15.8 to 44.5 times the state change",
   "paper_text": "alignment; both traces), 15.8 to 44.5 times the state change between",
   "paper_line": 4984,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0796",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 1.2\\times10^{-7} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(critical multiplier within \\(1.2\\times10^{-7}\\) of",
   "paper_text": "(critical multiplier within $1.2\\times10^{-7}$ of $+1$ and other multipliers",
   "paper_line": 4986,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0797",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.4 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and other multipliers below 0.4; in the rerun, \\(1.9\\times10^{-7}\\) and 0.61).",
   "paper_text": "$+1$ and other multipliers below $0.4$; in the rerun, $1.9\\times10^{-7}$ and $0.61$)",
   "paper_line": 4987,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0798",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.1238662 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "cusps: \\((-0.1238662, 0.0961512)\\), with \\(c",
   "paper_text": "reversals, both located cusps: $(-0.1238662,0.0961512)$, with $c=-9.65\\times10^{3}$",
   "paper_line": 4988,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0799",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.0961512 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "cusps: \\((-0.1238662, 0.0961512)\\), with \\(c = -9.65\\times10^{3}\\)",
   "paper_text": "located cusps: $(-0.1238662,0.0961512)$, with $c=-9.65\\times10^{3}$",
   "paper_line": 4988,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0800",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -9.65 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.0961512)\\), with \\(c = -9.65\\times10^{3}\\) and",
   "paper_text": "$(-0.1238662,0.0961512)$, with $c=-9.65\\times10^{3}$ and $\\det K=405.9$,",
   "paper_line": 4989,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0801",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 405.9 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\det K = 405.9\\), and \\((-0.1214073, 0.1028234)\\),",
   "paper_text": "$c=-9.65\\times10^{3}$ and $\\det K=405.9$, and $(-0.1214073,0.1028234)$,",
   "paper_line": 4989,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0802",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.1214073 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\det K = 405.9\\), and \\((-0.1214073, 0.1028234)\\), with",
   "paper_text": "$c=-9.65\\times10^{3}$ and $\\det K=405.9$, and $(-0.1214073,0.1028234)$, with $c=+4.75\\times10^{4}$",
   "paper_line": 4989,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0803",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.1028234 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "405.9\\), and \\((-0.1214073, 0.1028234)\\), with",
   "paper_text": "K=405.9$, and $(-0.1214073,0.1028234)$, with $c=+4.75\\times10^{4}$",
   "paper_line": 4989,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0804",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 4.75\\times10^{4} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(c = +4.75\\times10^{4}\\) and \\(\\det K = -535.4\\).",
   "paper_text": "$(-0.1214073,0.1028234)$, with $c=+4.75\\times10^{4}$ and $\\det K=-535.4$ (condition",
   "paper_line": 4989,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0805",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -535.4 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "+4.75\\times10^{4}\\) and \\(\\det K = -535.4\\). The rerun finds a third reversal,",
   "paper_text": "$c=+4.75\\times10^{4}$ and $\\det K=-535.4$ (condition $1.2\\times10^{4}$).",
   "paper_line": 4990,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0806",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.12341 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "itself, at \\((-0.12341, 0.09904)\\), so that its",
   "paper_text": "curve also crosses itself, at $(-0.12341,0.09904)$, between its points",
   "paper_line": 4991,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0807",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.09904 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "itself, at \\((-0.12341, 0.09904)\\), so that its two cusps",
   "paper_text": "crosses itself, at $(-0.12341,0.09904)$, between its points 6 and",
   "paper_line": 4991,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0808",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 8.83 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "token loop, which differ by 8.83 to 9.06%",
   "paper_text": "token loop, which differ by $8.83$ to $9.06\\,\\%$ of the state",
   "paper_line": 4994,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0809",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 9.06 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "which differ by 8.83 to 9.06%",
   "paper_text": "which differ by $8.83$ to $9.06\\,\\%$ of the state norm (measured",
   "paper_line": 4994,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0810",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 1.3\\times10^{-9} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(1.3\\times10^{-9}\\) of 1 and the second modulus",
   "paper_text": "critical multiplier is within $1.3\\times10^{-9}$ of $1$ and the second modulus",
   "paper_line": 4996,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0811",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.008 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the second modulus below 0.008. Along the curves",
   "paper_text": "and the second modulus below $0.008$. The flip curves bound the",
   "paper_line": 4997,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0812",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.4 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "continued on 15 October no other multiplier exceeds 0.4 in modulus; with the curves of",
   "paper_text": "and no other multiplier exceeds $0.4$ in modulus; with the curves of 18",
   "paper_line": 2375,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0813",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 1.65 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "repelling cell (\\(\\mu_1 = +1.65\\)) lies",
   "paper_text": "isolated repelling cell ($\\mu_1=+1.65$) lies $1.2\\times10^{-5}$ from",
   "paper_line": 4998,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0814",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 1.2\\times10^{-5} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(1.2\\times10^{-5}\\) from it, on the saddle",
   "paper_text": "cell ($\\mu_1=+1.65$) lies $1.2\\times10^{-5}$ from it, on the saddle branch,",
   "paper_line": 4998,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0815",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.119167 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "solves at \\(\\alpha_1 = -0.119167\\) runs into the lower reversal,",
   "paper_text": "Newton solves at $\\alpha_1=-0.119167$ runs into the lower reversal,",
   "paper_line": 4999,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0816",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.119166 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\alpha_1 = -0.119166\\), where the followed orbit",
   "paper_text": "lower reversal, at $\\alpha_1=-0.119166$, where the followed orbit",
   "paper_line": 5000,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0817",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 16 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and hostility at layer 16, \\(\\log_{10}T = -0.1\\),",
   "paper_text": "block~4 and hostility at block~16, $\\log_{10}T=-0.1$, float64).",
   "paper_line": 3035,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0818",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.1 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "layer 16, \\(\\log_{10}T = -0.1\\), float64). (a) The two",
   "paper_text": "hostility at block~16, $\\log_{10}T=-0.1$, float64). (a) The two fold",
   "paper_line": 2972,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0819",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 13 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "coincide. Circles: the 13 points of the orbit census,",
   "paper_text": "dashed), coincide. Circles: the 13 points of the orbit census,",
   "paper_line": 2979,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0820",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 13 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Before any solve we fixed 13 points around the junction",
   "paper_text": "junction.} Before any solve we fixed 13 points around the junction",
   "paper_line": 5043,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0821",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 27 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(27 starts per point). Orbits",
   "paper_text": "$s\\in\\{0,\\pm10^{-3},\\pm3\\times10^{-3},\\pm10^{-2},\\pm3\\times10^{-2}\\}$ (27 starts per point). Orbits are",
   "paper_line": 5048,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0822",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 10^{-7} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(10^{-7}\\) of the state norm at",
   "paper_text": "when they differ by more than $10^{-7}$ of the state norm at every",
   "paper_line": 5048,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0823",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 13 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "gives the results: 9 of the 13 counts match. Four orbits",
   "paper_text": "gives the results: 9 of the 13 counts match. The three undercounts",
   "paper_line": 5051,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0824",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 1.44 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "a saddle (multiplier \\(+1.44\\)) and the node, which",
   "paper_text": "loop: a saddle (multiplier $+1.44$) and the node, which lies",
   "paper_line": 5053,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0825",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -1.35 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the cusp (multiplier \\(-1.35\\)), so that no period-5",
   "paper_text": "passes the cusp (multiplier $-1.35$), so that no period-5 orbit",
   "paper_line": 5054,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0826",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -130 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "loop and the multiplier \\(-130\\), and",
   "paper_text": "token loop and the multiplier $-130$, and only one start reached",
   "paper_line": 5056,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0827",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 27 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "period-5 orbits found from 27 starts per point, and how",
   "paper_text": "period-5 orbits found from 27 starts per point, and how many",
   "paper_line": 5072,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0828",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.1 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "layer 16, \\(\\log_{10}T = -0.1\\), float64). The continued",
   "paper_text": "hostility at block~16, $\\log_{10}T=-0.1$, float64). The continued fold",
   "paper_line": 3035,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0829",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 86 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "coordinate of these states (86% of their variance), with",
   "paper_text": "coordinate of these states (86\\,\\% of their variance), with",
   "paper_line": 3036,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0830",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.0032 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the leading pair are below 0.0032 (on later curves",
   "paper_text": "the leading pair are below $0.0032$ (on the curves of 18 October",
   "paper_line": 2419,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0831",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.0139 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "modulus stays at least 0.0139): where a",
   "paper_text": "(its modulus stays at least $0.0139$): where a one-dimensional",
   "paper_line": 2422,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0832",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.1184836 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\((\\alpha_1, \\alpha_2) = (-0.1184836, 0.1017217)\\). There the",
   "paper_text": "converges at $(\\alpha_1,\\alpha_2)=(-0.1184836,0.1017217)$ (\\path{docs/review/p5-nilpotent.jsonl}).",
   "paper_line": 2425,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0833",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.1017217 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\alpha_2) = (-0.1184836, 0.1017217)\\). There the three leading",
   "paper_text": "$(\\alpha_1,\\alpha_2)=(-0.1184836,0.1017217)$ (\\path{docs/review/p5-nilpotent.jsonl}).",
   "paper_line": 2425,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0834",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 3.4 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "multipliers have moduli \\(3.4\\) to \\(3.6\\times10^{-3}\\).",
   "paper_text": "the three leading multipliers have nearly equal moduli, $3.4$ to $3.6\\times10^{-3}$, as the two conditions would make",
   "paper_line": 2426,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0835",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 3.6\\times10^{-3} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "moduli \\(3.4\\) to \\(3.6\\times10^{-3}\\). In the long run",
   "paper_text": "nearly equal moduli, $3.4$ to $3.6\\times10^{-3}$, as the two conditions",
   "paper_line": 2426,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0836",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 280 in 'Cusps and shrimp-like windows' (asymptotic linear contraction per period at the head)",
   "appears_as": "by a factor of about 280 per",
   "paper_text": "The leading modulus sets the asymptotic linear contraction, a factor of about 280 per period",
   "paper_line": 2428,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0837",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 41 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "window (\\(D < 0\\) at 41 of its 447 attracting cells),",
   "paper_text": "sign in the window ($D<0$ at 41 of its 447 attracting cells),",
   "paper_line": 2449,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0838",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 447 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(\\(D < 0\\) at 41 of its 447 attracting cells), so the",
   "paper_text": "window ($D<0$ at 41 of its 447 attracting cells), so the linearization restricted",
   "paper_line": 2450,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0839",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.105 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "tongues near \\(\\alpha_1 = -0.105\\),",
   "paper_text": "V-shaped tongues near $\\alpha_1=-0.105$, $\\alpha_2=0.105$. Continued",
   "paper_line": 2464,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0840",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.105 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\alpha_2 = 0.105\\). Continued in float64",
   "paper_text": "$\\alpha_1=-0.105$, $\\alpha_2=0.105$. Continued in float64 on grids",
   "paper_line": 2464,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0841",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.222 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "leading moduli are 0.222, 0.041 and 0.034), and",
   "paper_text": "smallest leading moduli are 0.222, 0.041 and 0.034), and complex",
   "paper_line": 2465,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0842",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.041 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "leading moduli are 0.222, 0.041 and 0.034), and complex",
   "paper_text": "smallest leading moduli are 0.222, 0.041 and 0.034), and complex leading",
   "paper_line": 2465,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0843",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.034 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "moduli are 0.222, 0.041 and 0.034), and complex leading pairs",
   "paper_text": "moduli are 0.222, 0.041 and 0.034), and complex leading pairs",
   "paper_line": 2465,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0844",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.59 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the leading multiplier is 0.59, 0.125 and 0.027. Per step,",
   "paper_text": "to the leading multiplier is 0.59, 0.125 and 0.027. Per step,",
   "paper_line": 2467,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0845",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.125 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "leading multiplier is 0.59, 0.125 and 0.027. Per step, the",
   "paper_text": "leading multiplier is 0.59, 0.125 and 0.027. Per step, the second",
   "paper_line": 2468,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0846",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.027 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "multiplier is 0.59, 0.125 and 0.027. Per step, the",
   "paper_text": "multiplier is 0.59, 0.125 and 0.027. Per step, the second multiplier",
   "paper_line": 2468,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0847",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.50 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "constant factor (medians 0.50 to 0.57), so",
   "paper_text": "nearly constant factor (medians 0.50 to 0.57), so its share shrinks",
   "paper_line": 2468,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0848",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.57 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "factor (medians 0.50 to 0.57), so",
   "paper_text": "constant factor (medians 0.50 to 0.57), so its share shrinks like",
   "paper_line": 2468,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0849",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.52 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "per-step medians predict 0.52,",
   "paper_text": "the per-step medians predict 0.52, 0.146 and 0.029, within 17\\,\\%",
   "paper_line": 2469,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0850",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.146 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.146 and 0.029, within 17% of",
   "paper_text": "per-step medians predict 0.52, 0.146 and 0.029, within 17\\,\\% of",
   "paper_line": 2469,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0851",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.029 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.146 and 0.029, within 17% of the measured",
   "paper_text": "medians predict 0.52, 0.146 and 0.029, within 17\\,\\% of the measured",
   "paper_line": 2469,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0852",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 17 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.146 and 0.029, within 17% of the measured ratios.",
   "paper_text": "0.52, 0.146 and 0.029, within 17\\,\\% of the measured ratios.",
   "paper_line": 2469,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0853",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.41 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "b\\rvert\\); its medians are 0.41, 0.41 and 0.50.",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0854",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.50 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
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   "paper_line": 2472,
   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Cusps and shrimp-like windows",
   "claim": "number 6\\times10^{-5} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at most \\(6\\times10^{-5}\\) of the second, so the",
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   "paper_line": 2475,
   "paper_file": "paper/llm/main.tex"
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   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.0325 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "have nearly equal modulus, 0.0325, and lie",
   "paper_text": "have nearly equal modulus, 0.0325, and lie $120^{\\circ}$ apart,",
   "paper_line": 2480,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0857",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 120 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(120^{\\circ}\\) apart, ten times",
   "paper_text": "equal modulus, 0.0325, and lie $120^{\\circ}$ apart, ten times the",
   "paper_line": 2480,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0858",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 3.5\\times10^{-3} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the period-5 point's \\(3.5\\times10^{-3}\\). Under a",
   "paper_text": "times the period-5 point's $3.5\\times10^{-3}$",
   "paper_line": 2480,
   "paper_file": "paper/llm/main.tex"
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   "id": "shrimp-0859",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 10^{-3} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Perturbations of relative size \\(10^{-3}\\) and \\(10^{-2}\\) (64 per",
   "paper_text": "Perturbations of relative size $10^{-3}$ and $10^{-2}$ (64 per size,",
   "paper_line": 5078,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0860",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 10^{-2} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "size \\(10^{-3}\\) and \\(10^{-2}\\) (64 per size, half to",
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   "paper_line": 5078,
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  {
   "id": "shrimp-0861",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 64 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(10^{-3}\\) and \\(10^{-2}\\) (64 per size, half to",
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   "paper_line": 5078,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0862",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 2\\times10^{122} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "with median errors up to \\(2\\times10^{122}\\), against at",
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   "paper_line": 5082,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0863",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.71 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "$2\\times10^{122}$, against at most $0.71$ for the linearized map in",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Cusps and shrimp-like windows",
   "claim": "number 12 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of these 12 rows even the one-coordinate",
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   "section": "Cusps and shrimp-like windows",
   "claim": "number 12 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
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   "id": "shrimp-0866",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 18 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "1 as degenerate; 12 of the 18 location-and-size rows are.",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0867",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.026 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0868",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.031 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.026 and 0.031 and two coordinates below",
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   "paper_line": 5086,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0869",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 6\\times10^{-5} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
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   "paper_file": "paper/llm/main.tex"
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   "id": "shrimp-0870",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 13 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "the predicted counts at 9 of 13 points and found two coexisting",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Cusps and shrimp-like windows",
   "claim": "number 896 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Cusps and shrimp-like windows",
   "claim": "number 896 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.0630 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "between 0.06301 and 0.07773",
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   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.0777 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "between 0.06301 and 0.07773",
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   "id": "shrimp-0875",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.0661 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "between 0.06609 and 0.07006",
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   "paper_file": "paper/llm/main.tex"
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   "id": "shrimp-0876",
   "section": "Cusps and shrimp-like windows",
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   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.070 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "these. At \\(\\alpha = 0.070\\), in a column of 96 temperatures",
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   "paper_line": 3057,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0878",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 96 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
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   "paper_line": 3057,
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  {
   "id": "shrimp-0879",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 59 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = -2\\) upward, 59 end on `\"\\n\\nThe question\"`",
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   "paper_line": 3058,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0880",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 16 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0881",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.12 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "between 0 and 0.12 (in steps of 0.0005)",
   "paper_text": "between 0 and 0.12 (in steps of 0.0005)",
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   "id": "shrimp-0882",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.070 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\alpha = 0.070\\) the 2-cycle loses stability",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0883",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.5147881 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "stability at \\(\\log_{10}T = -0.5147881\\),",
   "paper_text": "stable between $\\log_{10}T=-0.5147881$, where a multiplier reaches",
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  {
   "id": "shrimp-0884",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.070 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "weakens. At \\(\\alpha = 0.070\\) the",
   "paper_text": "At $\\alpha=0.070$ the 2-cycle is stable between",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0885",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.1741065 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
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   "id": "shrimp-0886",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.065 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "extrapolated to \\(\\log_{10}T = -0.14536\\)",
   "paper_text": "extrapolated to $\\log_{10}T=-0.14536$",
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   "id": "shrimp-0887",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.14536 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "extrapolated to \\(\\log_{10}T = -0.14536\\)",
   "paper_text": "extrapolated to $\\log_{10}T=-0.14536$",
   "paper_line": 3072,
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   "id": "shrimp-0888",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.148 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the cut \\(\\log_{10}T = -0.148\\) it is born at a fold",
   "paper_text": "$0.0715$. On the cut $\\log_{10}T=-0.148$, the crescent's period-3 orbit",
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  {
   "id": "shrimp-0889",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.06444 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\alpha = 0.06444\\) and flips at \\(\\alpha",
   "paper_text": "is born at a fold ($\\alpha=0.06444$) and flips at $\\alpha=0.06548$.",
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   "id": "shrimp-0890",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.06548 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and flips at \\(\\alpha = 0.06548\\) (Figure",
   "paper_text": "($\\alpha=0.06444$) and flips at $\\alpha=0.06548$. White circles: the census",
   "paper_line": 3221,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0891",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 12 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "period 3 becomes 6, then 12, then 24, and the sequence",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0892",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 24 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "becomes 6, then 12, then 24, and the sequence",
   "paper_text": "showing the doublings $6\\to12\\to24\\to48$",
   "paper_line": 1894,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0893",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.14 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = -0.14\\) is the first doubling",
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  {
   "id": "shrimp-0894",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.070 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\alpha\\). At \\(\\alpha = 0.070\\) it is bounded by two",
   "paper_text": "larger $\\alpha$. At $\\alpha=0.070$ it is bounded by two flips,",
   "paper_line": 3082,
   "paper_file": "paper/llm/main.tex"
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   "id": "shrimp-0895",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.1392937 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at \\(\\log_{10}T = -0.1392937\\) above and \\(-0.1414292\\)",
   "paper_text": "by two flips, at $\\log_{10}T=-0.1392937$ above and $-0.1414292$ below.",
   "paper_line": 3082,
   "paper_file": "paper/llm/main.tex"
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   "id": "shrimp-0896",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.1414292 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "-0.1392937\\) above and \\(-0.1414292\\) below. The two families",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0897",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 896 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "896 dimensions. Whether such simple laws can describe it",
   "paper_text": "a network with 896-dimensional states shows the signatures of one-dimensional maps.",
   "paper_line": 3047,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0898",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.23 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "covariance \\(\\Sigma_p\\) is 0.23 to 0.87 of the first,",
   "paper_text": "readout covariance $\\Sigma_p$ is 0.23 to 0.87 of the first, and the",
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   "id": "shrimp-0899",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.87 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\Sigma_p\\) is 0.23 to 0.87 of the first,",
   "paper_text": "covariance $\\Sigma_p$ is 0.23 to 0.87 of the first, and the second",
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   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0900",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.12 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "step derivative is 0.11 to 0.90 of the",
   "paper_text": "step derivative is 0.11 to 0.90 of the first",
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  },
  {
   "id": "shrimp-0901",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.80 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "step derivative is 0.11 to 0.90 of the",
   "paper_text": "step derivative is 0.11 to 0.90 of the first",
   "paper_line": 3185,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0902",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.081 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of the composed map is 0.081 for the 2-cycle, 0.092",
   "paper_text": "leading singular values is 0.081 for the 2-cycle, 0.092 for",
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  {
   "id": "shrimp-0903",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.092 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "values of the composed map is 0.081 for the 2-cycle, 0.092",
   "paper_text": "values is 0.081 for the 2-cycle, 0.092 for the period-3 loop and 0.26",
   "paper_line": 3186,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0904",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.26 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "period-3 loop and 0.26 for the period-6 band.",
   "paper_text": "0.092 for the period-3 loop and 0.26 for the period-6 band; it falls",
   "paper_line": 3186,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0905",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 3\\times10^{-4} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "period-6 band. It falls to \\(3\\times10^{-4}\\) over",
   "paper_text": "period-6 band; it falls to $3\\times10^{-4}$ over twelve steps of the chaotic",
   "paper_line": 3187,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0906",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 4\\times10^{-9} in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "chaotic crescent and to \\(4\\times10^{-9}\\) in the chaotic stripes",
   "paper_text": "the chaotic crescent and to $4\\times10^{-9}$ in the chaotic stripes. These ratios",
   "paper_line": 3187,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0907",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.109 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "600 steps their largest exponents are 0.109, 0.424 and 0.239 per step",
   "paper_text": "Over 600 steps their largest exponents are $0.109$, $0.424$ and $0.239$ per step",
   "paper_line": 3194,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0908",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.424 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "largest exponents are 0.109, 0.424 and 0.239 per step, and the next",
   "paper_text": "largest exponents are $0.109$, $0.424$ and $0.239$ per step, and the next three",
   "paper_line": 3194,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0909",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.239 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "exponents are 0.109, 0.424 and 0.239 per step, and the next",
   "paper_text": "exponents are $0.109$, $0.424$ and $0.239$ per step, and the next three are strongly negative",
   "paper_line": 3194,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0910",
   "section": "Cusps and shrimp-like windows",
   "claim": "number −0.82 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "strongly negative, between −0.82 and −2.01",
   "paper_text": "strongly negative, between $-0.82$ and $-2.01$",
   "paper_line": 3195,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0911",
   "section": "Cusps and shrimp-like windows",
   "claim": "number −2.0 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "three are strongly negative, between −0.82 and −2.01",
   "paper_text": "are strongly negative, between $-0.82$ and $-2.01$",
   "paper_line": 3195,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0912",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 1.13 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "The finite-time estimates are 1.13, 1.43 and 1.21 at the three",
   "paper_text": "the magnitude of the next, are 1.13, 1.43 and 1.21",
   "paper_line": 3196,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0913",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 1.43 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "shape. The finite-time estimates are 1.13, 1.43 and 1.21 at the three cells",
   "paper_text": "divided by the magnitude of the next, are 1.13, 1.43 and 1.21.",
   "paper_line": 3196,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0914",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 1.21 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "estimates are 1.13, 1.43 and 1.21 at the three cells",
   "paper_text": "are 1.13, 1.43 and 1.21. These estimates suggest",
   "paper_line": 3197,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0915",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 600 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "600 steps their largest exponents are 0.109",
   "paper_text": "Over 600 steps their largest exponents are",
   "paper_line": 3194,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0916",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 3000 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "3000 steps the largest exponents are",
   "paper_text": "(Over 3000 steps the largest exponents are",
   "paper_line": 3198,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0917",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.098 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "largest exponents are \\(0.098\\pm0.010\\), \\(0.437\\pm0.016\\)",
   "paper_text": "the largest exponents are $0.098\\pm0.010$, $0.437\\pm0.016$ and",
   "paper_line": 3198,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0918",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.437 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "are \\(0.098\\pm0.010\\), \\(0.437\\pm0.016\\) and",
   "paper_text": "exponents are $0.098\\pm0.010$, $0.437\\pm0.016$ and $0.196\\pm0.014$;",
   "paper_line": 3198,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0919",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.196 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "\\(0.196\\pm0.014\\), the values used",
   "paper_text": "$0.437\\pm0.016$ and $0.196\\pm0.014$; Section~\\ref{sec:dialogue}.)",
   "paper_line": 3199,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0920",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.156 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = -0.156\\), places its first flip",
   "paper_text": "at $\\log_{10}T=-0.156$, places its first flip between",
   "paper_line": 3204,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0921",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.06476 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "between \\(\\alpha = 0.0646\\) and 0.0648",
   "paper_text": "between $\\alpha=0.0646$ and 0.0648",
   "paper_line": 3205,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0922",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.0644767 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.0644767 in the full map.",
   "paper_text": "against 0.0644767 in the full map",
   "paper_line": 3205,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0923",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 12 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "philosophy direction, layer 12). <strong>(a) A compromise",
   "paper_text": "philosophy direction at layer 12, $256^2$ float64 cells. Left:",
   "paper_line": 875,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0924",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.070 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "temperature at \\(\\alpha = 0.070\\). The orbit is stable",
   "paper_text": "along temperature at $\\alpha=0.070$. It is stable (blue, inside",
   "paper_line": 3212,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0925",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.5148 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the flip (\\(\\log_{10}T = -0.5148\\)), where the multiplier",
   "paper_text": "between the flip ($\\log_{10}T=-0.5148$) and the fold ($-0.1741$).",
   "paper_line": 3212,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0926",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.1741 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "passes −1, and the fold (\\(-0.1741\\)), where it reaches +1;",
   "paper_text": "($\\log_{10}T=-0.5148$) and the fold ($-0.1741$). The boxes give the two blended",
   "paper_line": 3213,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0927",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.115 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the row \\(\\log_{10}T = -0.115\\) of the \\(256\\times256\\)",
   "paper_text": "exponent along the row $\\log_{10}T=-0.115$ of the $256\\times256$ map.",
   "paper_line": 3214,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0928",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 256 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = -0.115\\) of the \\(256\\times256\\) map. Past the",
   "paper_text": "$\\log_{10}T=-0.115$ of the $256\\times256$ map. Beyond the fold",
   "paper_line": 3214,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0929",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 16 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "longer windows (periods 16 to 20) it grows linearly",
   "paper_text": "the longer windows (periods 16 to 20) it grows linearly with",
   "paper_line": 3217,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0930",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 20 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "windows (periods 16 to 20) it grows linearly with",
   "paper_text": "longer windows (periods 16 to 20) it grows linearly with the",
   "paper_line": 3217,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0931",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.069 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "located on cuts at \\(\\alpha = 0.069\\), 0.070 and 0.0715. On",
   "paper_text": "located on cuts at $\\alpha=0.069$, $0.070$ and $0.0715$. On",
   "paper_line": 3220,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0932",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.070 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at \\(\\alpha = 0.069\\), 0.070 and 0.0715. On the cut",
   "paper_text": "on cuts at $\\alpha=0.069$, $0.070$ and $0.0715$. On the cut $\\log_{10}T=-0.148$,",
   "paper_line": 3220,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0933",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.0715 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\alpha = 0.069\\), 0.070 and 0.0715. On the cut \\(\\log_{10}T",
   "paper_text": "$\\alpha=0.069$, $0.070$ and $0.0715$. On the cut $\\log_{10}T=-0.148$,",
   "paper_line": 3220,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0934",
   "section": "Cusps and shrimp-like windows",
   "claim": "number -0.148 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the cut \\(\\log_{10}T = -0.148\\), the crescent's period-3",
   "paper_text": "$0.0715$. On the cut $\\log_{10}T=-0.148$, the crescent's period-3 orbit",
   "paper_line": 3220,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0935",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.06444 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "born at a fold (\\(\\alpha = 0.06444\\), green square) and flips",
   "paper_text": "is born at a fold ($\\alpha=0.06444$) and flips at $\\alpha=0.06548$.",
   "paper_line": 3221,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0936",
   "section": "Cusps and shrimp-like windows",
   "claim": "number 0.06548 in 'Cusps and shrimp-like windows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and flips at \\(\\alpha = 0.06548\\). White circles mark the",
   "paper_text": "($\\alpha=0.06444$) and flips at $\\alpha=0.06548$. White circles: the census",
   "paper_line": 3221,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0937",
   "section": "Neuron steering diagram",
   "claim": "number 4864 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Inside the MLP, each of the 4864 neurons writes its activation",
   "paper_text": "with residual vector $x$), the 4864 neurons write $\\sum_i h_i w_i$",
   "paper_line": 5664,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-0938",
   "section": "Neuron steering diagram",
   "claim": "number 12 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "neuron, in decoder layer 12 of Qwen2.5-0.5B-Instruct.",
   "paper_text": "MLP neuron, in decoder layer 12 of Qwen2.5-0.5B-Instruct. Each",
   "paper_line": 5662,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0939",
   "section": "Neuron steering diagram",
   "claim": "number 896 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "own residual stream, one 896-dimensional vector per",
   "paper_text": "a network with 896-dimensional states shows the signatures of one-dimensional maps.",
   "paper_line": 3047,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0940",
   "section": "Neuron steering diagram",
   "claim": "number 4864 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "residual vector \\(x\\)), the 4864 neurons write \\(\\sum_i",
   "paper_text": "with residual vector $x$), the 4864 neurons write $\\sum_i h_i w_i$",
   "paper_line": 5664,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0941",
   "section": "Neuron steering diagram",
   "claim": "number 312 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the activation), and \\(312 = \\lVert v_{\\mathrm{phil}}\\rVert/\\lVert",
   "paper_text": "lower the activation), and $312=\\lVert v_{\\mathrm{phil}}\\rVert/\\lVert",
   "paper_line": 5666,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0942",
   "section": "Neuron steering diagram",
   "claim": "number 188.99 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "v_{\\mathrm{phil}}\\rVert/\\lVert w_{832}\\rVert = 188.99/0.606\\) is a fixed scale",
   "paper_text": "v_{\\mathrm{phil}}\\rVert/\\lVert w_{832}\\rVert=188.99/0.606$ is a fixed scale for",
   "paper_line": 5667,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0943",
   "section": "Neuron steering diagram",
   "claim": "number 832 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "fixed scale for neuron 832. Raising \\(h_{832}\\) by",
   "paper_text": "is a fixed scale for neuron 832. Raising $h_{832}$ by $312\\alpha$",
   "paper_line": 5667,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0944",
   "section": "Neuron steering diagram",
   "claim": "number 312 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Raising \\(h_{832}\\) by \\(312\\alpha\\) for every token",
   "paper_text": "832. Raising $h_{832}$ by $312\\alpha$ for every token is the",
   "paper_line": 5667,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0945",
   "section": "Neuron steering diagram",
   "claim": "number 312 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\alpha v\\), with \\(v = 312\\,w_{832}\\), to the layer's",
   "paper_text": "adding $\\alpha v$, with $v=312\\,w_{832}$, to the layer's output,",
   "paper_line": 5668,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0946",
   "section": "Neuron steering diagram",
   "claim": "number 312 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "it: \\(\\sum_i h_i w_i + 312\\alpha\\,w_{832} = \\sum_{i\\neq832}",
   "paper_text": "implement it: $\\sum_i h_i w_i+312\\alpha\\,w_{832}=\\sum_{i\\neq832}h_i",
   "paper_line": 5669,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0947",
   "section": "Neuron steering diagram",
   "claim": "number 312 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\sum_{i\\neq832} h_i w_i + (h_{832} + 312\\alpha)\\,w_{832}\\). At \\(\\lvert\\alpha\\rvert",
   "paper_text": "w_i+312\\alpha\\,w_{832}=\\sum_{i\\neq832}h_i w_i+(h_{832}+312\\alpha)\\,w_{832}$. At $|\\alpha|=0.12$",
   "paper_line": 5669,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0948",
   "section": "Neuron steering diagram",
   "claim": "number 0.12 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lvert\\alpha\\rvert = 0.12\\) the increase is 37.4,",
   "paper_text": "w_i+(h_{832}+312\\alpha)\\,w_{832}$. At $|\\alpha|=0.12$ the increase is 37.4, against",
   "paper_line": 5669,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0949",
   "section": "Neuron steering diagram",
   "claim": "number 37.4 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.12\\) the increase is 37.4, against a mean activation",
   "paper_text": "$|\\alpha|=0.12$ the increase is 37.4, against a mean activation",
   "paper_line": 5670,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0950",
   "section": "Neuron steering diagram",
   "claim": "number 0.27 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "against a mean activation of 0.27 on the philosophy texts;",
   "paper_text": "against a mean activation of 0.27 on the philosophy texts; for",
   "paper_line": 5670,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0951",
   "section": "Neuron steering diagram",
   "claim": "number 833 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "philosophy texts; for neurons 833 and 4137 the scale is 329",
   "paper_text": "philosophy texts; for neurons 833 and 4137 the scale is 329 and",
   "paper_line": 5670,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0952",
   "section": "Neuron steering diagram",
   "claim": "number 4137 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "texts; for neurons 833 and 4137 the scale is 329 and 346.",
   "paper_text": "texts; for neurons 833 and 4137 the scale is 329 and 346. The",
   "paper_line": 5670,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0953",
   "section": "Neuron steering diagram",
   "claim": "number 329 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "833 and 4137 the scale is 329 and 346. The tokens shown",
   "paper_text": "neurons 833 and 4137 the scale is 329 and 346. The tokens shown are",
   "paper_line": 5670,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0954",
   "section": "Neuron steering diagram",
   "claim": "number 346 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "4137 the scale is 329 and 346. The tokens shown are only",
   "paper_text": "and 4137 the scale is 329 and 346. The tokens shown are only",
   "paper_line": 5670,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0955",
   "section": "Neuron steering diagram",
   "claim": "number 26 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "exponents in Llama-3.1-8B (26 of 64 temperatures),",
   "paper_text": "exponents in Llama-3.1 8B (26 of 64 temperatures), Qwen2.5-7B",
   "paper_line": 5597,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0956",
   "section": "Neuron steering diagram",
   "claim": "number 64 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "in Llama-3.1-8B (26 of 64 temperatures),",
   "paper_text": "exponents in Llama-3.1 8B (26 of 64 temperatures), Qwen2.5-7B (15",
   "paper_line": 5597,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0957",
   "section": "Neuron steering diagram",
   "claim": "number 15 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Qwen2.5-7B (15 of 64) and OLMo-2-7B (11",
   "paper_text": "temperatures), Qwen2.5-7B (15 of 64) and OLMo-2 7B (11 of",
   "paper_line": 5597,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0958",
   "section": "Neuron steering diagram",
   "claim": "number 64 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Qwen2.5-7B (15 of 64) and OLMo-2-7B (11 of 64),",
   "paper_text": "temperatures), Qwen2.5-7B (15 of 64) and OLMo-2 7B (11 of 64),",
   "paper_line": 5597,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0959",
   "section": "Neuron steering diagram",
   "claim": "number 11 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(15 of 64) and OLMo-2-7B (11 of 64), while the near-zero",
   "paper_text": "Qwen2.5-7B (15 of 64) and OLMo-2 7B (11 of 64), while the near-zero",
   "paper_line": 5597,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0960",
   "section": "Neuron steering diagram",
   "claim": "number 64 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "64) and OLMo-2-7B (11 of 64), while the near-zero columns",
   "paper_text": "temperatures), Qwen2.5-7B (15 of 64) and OLMo-2 7B (11 of 64),",
   "paper_line": 5597,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0961",
   "section": "Neuron steering diagram",
   "claim": "number 128 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "one such cell each (of 128 and 64). A longer float64",
   "paper_text": "contain one such cell each (of 128 and 64). A longer float64 sweep",
   "paper_line": 5598,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0962",
   "section": "Neuron steering diagram",
   "claim": "number 64 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "such cell each (of 128 and 64). A longer float64",
   "paper_text": "such cell each (of 128 and 64). A longer float64 sweep of",
   "paper_line": 5598,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0963",
   "section": "Neuron steering diagram",
   "claim": "number 512 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the unsteered 0.5B map (512 temperatures over",
   "paper_text": "of the unsteered 0.5B map (512 temperatures over $\\log_{10}T\\in[-1,0.3]$,",
   "paper_line": 5599,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0964",
   "section": "Neuron steering diagram",
   "claim": "number 0.3 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T \\in [-1, 0.3]\\), 1000 transient and",
   "paper_text": "temperatures over $\\log_{10}T\\in[-1,0.3]$, 1000 transient and 2000",
   "paper_line": 5599,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0965",
   "section": "Neuron steering diagram",
   "claim": "number 1000 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T \\in [-1, 0.3]\\), 1000 transient and 2000 measured",
   "paper_text": "over $\\log_{10}T\\in[-1,0.3]$, 1000 transient and 2000 measured",
   "paper_line": 5599,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0966",
   "section": "Neuron steering diagram",
   "claim": "number 2000 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.3]\\), 1000 transient and 2000 measured steps) finds a",
   "paper_text": "$\\log_{10}T\\in[-1,0.3]$, 1000 transient and 2000 measured steps) finds a narrow",
   "paper_line": 5599,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0967",
   "section": "Neuron steering diagram",
   "claim": "number 0.15 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at \\(\\log_{10}T \\approx 0.15\\) to 0.21 (7 temperatures,",
   "paper_text": "chaotic band at $\\log_{10}T\\approx0.15$--$0.21$ (7 temperatures, exponents",
   "paper_line": 5600,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0968",
   "section": "Neuron steering diagram",
   "claim": "number 0.21 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T \\approx 0.15\\) to 0.21 (7 temperatures, exponents",
   "paper_text": "at $\\log_{10}T\\approx0.15$--$0.21$ (7 temperatures, exponents",
   "paper_line": 5600,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0969",
   "section": "Neuron steering diagram",
   "claim": "number 0.28 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.28), with a period-5 loop",
   "paper_text": "temperatures, exponents up to $0.28$), with a period-5 loop at",
   "paper_line": 5600,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0970",
   "section": "Neuron steering diagram",
   "claim": "number 437 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "with a period-5 loop at 437 of the 512 temperatures.",
   "paper_text": "$0.28$), with a period-5 loop at 437 of the 512 temperatures. The",
   "paper_line": 5601,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0971",
   "section": "Neuron steering diagram",
   "claim": "number 512 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "period-5 loop at 437 of the 512 temperatures. The same",
   "paper_text": "period-5 loop at 437 of the 512 temperatures. The same long",
   "paper_line": 5601,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0972",
   "section": "Neuron steering diagram",
   "claim": "number 96 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "96 chaotic temperatures in",
   "paper_text": "temperatures. The same long sweep finds 96 chaotic temperatures in Llama-3.1",
   "paper_line": 5601,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0973",
   "section": "Neuron steering diagram",
   "claim": "number -0.20 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "between \\(\\log_{10}T = -0.20\\) and 0.24",
   "paper_text": "Llama-3.1 8B, between $\\log_{10}T=-0.20$ and $0.24$ (exponents up to",
   "paper_line": 5602,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0974",
   "section": "Neuron steering diagram",
   "claim": "number 0.24 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = -0.20\\) and 0.24",
   "paper_text": "between $\\log_{10}T=-0.20$ and $0.24$ (exponents up to $0.66$),",
   "paper_line": 5602,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0975",
   "section": "Neuron steering diagram",
   "claim": "number 0.66 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(exponents up to 0.66), interleaved with periodic",
   "paper_text": "and $0.24$ (exponents up to $0.66$), interleaved with periodic",
   "paper_line": 5602,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0976",
   "section": "Neuron steering diagram",
   "claim": "number 52 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "windows of periods 2 to 52; within",
   "paper_text": "periodic windows of periods 2 to 52; within $\\log_{10}T\\in[-0.3,0.3]$",
   "paper_line": 5602,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0977",
   "section": "Neuron steering diagram",
   "claim": "number -0.3 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T \\in [-0.3, 0.3]\\) its chaotic share,",
   "paper_text": "to 52; within $\\log_{10}T\\in[-0.3,0.3]$ its chaotic share, 41\\,\\%,",
   "paper_line": 5603,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0978",
   "section": "Neuron steering diagram",
   "claim": "number 0.3 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T \\in [-0.3, 0.3]\\) its chaotic share, 41%,",
   "paper_text": "52; within $\\log_{10}T\\in[-0.3,0.3]$ its chaotic share, 41\\,\\%,",
   "paper_line": 5603,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0979",
   "section": "Neuron steering diagram",
   "claim": "number 41 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.3]\\) its chaotic share, 41%, equals that of the coarse",
   "paper_text": "$\\log_{10}T\\in[-0.3,0.3]$ its chaotic share, 41\\,\\%, equals that of the coarse",
   "paper_line": 5603,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0980",
   "section": "Neuron steering diagram",
   "claim": "number 65 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "column. Qwen2.5-7B has 65 chaotic temperatures between",
   "paper_text": "coarse column. Qwen2.5-7B has 65 chaotic temperatures between",
   "paper_line": 5603,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0981",
   "section": "Neuron steering diagram",
   "claim": "number -0.07 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "between \\(\\log_{10}T = -0.07\\) and",
   "paper_text": "temperatures between $\\log_{10}T=-0.07$ and $0.28$ (exponents up to",
   "paper_line": 5604,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0982",
   "section": "Neuron steering diagram",
   "claim": "number 0.28 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.28 (exponents up to 0.74),",
   "paper_text": "between $\\log_{10}T=-0.07$ and $0.28$ (exponents up to $0.74$),",
   "paper_line": 5604,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0983",
   "section": "Neuron steering diagram",
   "claim": "number 0.74 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.28 (exponents up to 0.74), and OLMo-2-7B has 32",
   "paper_text": "and $0.28$ (exponents up to $0.74$), and OLMo-2 7B has 32 between",
   "paper_line": 5604,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0984",
   "section": "Neuron steering diagram",
   "claim": "number 32 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.74), and OLMo-2-7B has 32 between 0.04 and 0.14 (up",
   "paper_text": "$0.74$), and OLMo-2 7B has 32 between $0.04$ and $0.14$ (up",
   "paper_line": 5604,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0985",
   "section": "Neuron steering diagram",
   "claim": "number 0.04 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "OLMo-2-7B has 32 between 0.04 and 0.14 (up to",
   "paper_text": "and OLMo-2 7B has 32 between $0.04$ and $0.14$ (up to $0.30$).",
   "paper_line": 5604,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0986",
   "section": "Neuron steering diagram",
   "claim": "number 0.14 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "has 32 between 0.04 and 0.14 (up to",
   "paper_text": "has 32 between $0.04$ and $0.14$ (up to $0.30$). Steering is",
   "paper_line": 5605,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0987",
   "section": "Neuron steering diagram",
   "claim": "number 0.30 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.30). Steering is therefore",
   "paper_text": "between $0.04$ and $0.14$ (up to $0.30$). Steering is therefore not",
   "paper_line": 5605,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0988",
   "section": "Neuron steering diagram",
   "claim": "number -1.5 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "exponent (clipped at \\(-1.5\\)) from float64 sweeps",
   "paper_text": "Lyapunov exponent (clipped at $-1.5$) from float64 sweeps of 512",
   "paper_line": 5643,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0989",
   "section": "Neuron steering diagram",
   "claim": "number 512 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "from float64 sweeps of 512 temperatures (128 for the",
   "paper_text": "$-1.5$) from float64 sweeps of 512 temperatures (128 for the 70B-class",
   "paper_line": 5643,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0990",
   "section": "Neuron steering diagram",
   "claim": "number 128 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "sweeps of 512 temperatures (128 for the 70B-class and mixture-of-experts",
   "paper_text": "sweeps of 512 temperatures (128 for the 70B-class and mixture-of-experts",
   "paper_line": 5643,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0991",
   "section": "Neuron steering diagram",
   "claim": "number 1000 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "mixture-of-experts models; 1000 transient and 2000 measured",
   "paper_text": "mixture-of-experts models; 1000 transient and 2000 measured",
   "paper_line": 5644,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0992",
   "section": "Neuron steering diagram",
   "claim": "number 2000 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "models; 1000 transient and 2000 measured steps). Red: no",
   "paper_text": "models; 1000 transient and 2000 measured steps). Red: no period",
   "paper_line": 5644,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0993",
   "section": "Neuron steering diagram",
   "claim": "number 64 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "steps). Red: no period up to 64 and an exponent above \\(10^{-3}\\);",
   "paper_text": "steps). Red: no period up to 64 and an exponent above $10^{-3}$;",
   "paper_line": 5644,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0994",
   "section": "Neuron steering diagram",
   "claim": "number 10^{-3} in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and an exponent above \\(10^{-3}\\); black crosses: neither",
   "paper_text": "to 64 and an exponent above $10^{-3}$; black crosses: neither a",
   "paper_line": 5645,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0995",
   "section": "Neuron steering diagram",
   "claim": "number 128 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "). On the same \\(128^2\\) grid, 7.6, 8.3",
   "paper_text": "(Figure~\\ref{fig:controls}). On the same $128^2$ grid, 7.6, 8.3 and 12.5\\,\\%",
   "paper_line": 5615,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0996",
   "section": "Neuron steering diagram",
   "claim": "number 7.6 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the same \\(128^2\\) grid, 7.6, 8.3",
   "paper_text": "(Figure~\\ref{fig:controls}). On the same $128^2$ grid, 7.6, 8.3 and 12.5\\,\\% of cells",
   "paper_line": 5615,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0997",
   "section": "Neuron steering diagram",
   "claim": "number 8.3 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "same \\(128^2\\) grid, 7.6, 8.3",
   "paper_text": "the same $128^2$ grid, 7.6, 8.3 and 12.5\\,\\% of cells are chaotic",
   "paper_line": 5615,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0998",
   "section": "Neuron steering diagram",
   "claim": "number 12.5 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and 12.5% of cells are chaotic for",
   "paper_text": "$128^2$ grid, 7.6, 8.3 and 12.5\\,\\% of cells are chaotic for",
   "paper_line": 5615,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-0999",
   "section": "Neuron steering diagram",
   "claim": "number 6.8 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "vector's norm, against 6.8% for philosophy and 7.5%",
   "paper_text": "philosophy vector's norm, against 6.8\\,\\% for philosophy and 7.5\\,\\%",
   "paper_line": 5616,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1000",
   "section": "Neuron steering diagram",
   "claim": "number 7.5 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "6.8% for philosophy and 7.5% for gratitude. In all",
   "paper_text": "6.8\\,\\% for philosophy and 7.5\\,\\% for gratitude. In all five",
   "paper_line": 5617,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1001",
   "section": "Neuron steering diagram",
   "claim": "number 0.01 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lvert\\alpha\\rvert < 0.01\\) to between 5",
   "paper_text": "from about 1\\,\\% at $|\\alpha|<0.01$ to between 5 and 22\\,\\% at",
   "paper_line": 5617,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1002",
   "section": "Neuron steering diagram",
   "claim": "number 22 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and 22% at larger \\(\\lvert\\alpha\\rvert\\),",
   "paper_text": "$|\\alpha|<0.01$ to between 5 and 22\\,\\% at larger $|\\alpha|$, and",
   "paper_line": 5618,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1003",
   "section": "Neuron steering diagram",
   "claim": "number 13 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "chaotic share stays between 13 and 24% at every one",
   "paper_text": "chaotic share stays between 13 and 24\\,\\% at every one of",
   "paper_line": 5622,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1004",
   "section": "Neuron steering diagram",
   "claim": "number 24 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "share stays between 13 and 24% at every one",
   "paper_text": "share stays between 13 and 24\\,\\% at every one of 103 angles",
   "paper_line": 5622,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1005",
   "section": "Neuron steering diagram",
   "claim": "number 103 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of 103 angles.",
   "paper_text": "and 24\\,\\% at every one of 103 angles (Figure~\\ref{fig:morph});",
   "paper_line": 766,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1006",
   "section": "Neuron steering diagram",
   "claim": "number 9.9 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": ") gives 9.9% chaotic cells for the",
   "paper_text": "philosophy texts is 0.27) gives 9.9\\,\\% chaotic cells for the neuron",
   "paper_line": 5624,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1007",
   "section": "Neuron steering diagram",
   "claim": "number 5.1 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "fixed before any map, 5.1% for its index neighbor",
   "paper_text": "rule fixed before any map, 5.1\\,\\% for its index neighbor",
   "paper_line": 5626,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1008",
   "section": "Neuron steering diagram",
   "claim": "number 12.9 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "its index neighbor and 12.9% for a random neuron",
   "paper_text": "for its index neighbor and 12.9\\,\\% for a random neuron (Figure~\\ref{fig:neurons});",
   "paper_line": 5626,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1009",
   "section": "Neuron steering diagram",
   "claim": "number 0.4 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\alpha = 0\\) the share is 0.4 to",
   "paper_text": "near $\\alpha=0$ the share is 0.4 to 1.2\\,\\%. The direction does",
   "paper_line": 5627,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1010",
   "section": "Neuron steering diagram",
   "claim": "number 1.2 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "1.2%. The direction does select",
   "paper_text": "$\\alpha=0$ the share is 0.4 to 1.2\\,\\%. The direction does select",
   "paper_line": 5627,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1011",
   "section": "Neuron steering diagram",
   "claim": "number 26 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "loop, but beyond it only 26 to 56% of one map's cells",
   "paper_text": "period-5 loop, but beyond it only 26 to 56\\,\\% of one map's cells",
   "paper_line": 5628,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1012",
   "section": "Neuron steering diagram",
   "claim": "number 56 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "but beyond it only 26 to 56% of one map's cells",
   "paper_text": "loop, but beyond it only 26 to 56\\,\\% of one map's cells carry",
   "paper_line": 5628,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1013",
   "section": "Neuron steering diagram",
   "claim": "number 26 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the same layer give 26 and 17% chaotic cells against",
   "paper_text": "directions at the same layer give 26 and 17\\,\\% chaotic cells against",
   "paper_line": 5629,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1014",
   "section": "Neuron steering diagram",
   "claim": "number 17 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "same layer give 26 and 17% chaotic cells against",
   "paper_text": "the same layer give 26 and 17\\,\\% chaotic cells against 28\\,\\%",
   "paper_line": 5629,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1015",
   "section": "Neuron steering diagram",
   "claim": "number 28 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "17% chaotic cells against 28% along the concept direction;",
   "paper_text": "17\\,\\% chaotic cells against 28\\,\\% along the concept direction;",
   "paper_line": 5630,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1016",
   "section": "Neuron steering diagram",
   "claim": "number 34 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "all three carry 34 to 44% near \\(\\alpha =",
   "paper_text": "direction; all three carry 34 to 44\\,\\% near $\\alpha=0$,",
   "paper_line": 5630,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1017",
   "section": "Neuron steering diagram",
   "claim": "number 44 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "all three carry 34 to 44% near \\(\\alpha = 0\\), and",
   "paper_text": "direction; all three carry 34 to 44\\,\\% near $\\alpha=0$, and the",
   "paper_line": 5630,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1018",
   "section": "Neuron steering diagram",
   "claim": "number 19 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lvert\\alpha\\rvert\\). At layer 19, where a sparse autoencoder",
   "paper_text": "large $|\\alpha|$. At layer 19, where a sparse autoencoder",
   "paper_line": 5631,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1019",
   "section": "Neuron steering diagram",
   "claim": "number 28 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "vector rebuilt there gives 28%. The decoder direction",
   "paper_text": "vector rebuilt there gives 28\\,\\%. The decoder direction",
   "paper_line": 5632,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1020",
   "section": "Neuron steering diagram",
   "claim": "number 0.10 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "before any map; cosine 0.10 with the",
   "paper_text": "fixed before any map; cosine $0.10$ with the concept vector) gives",
   "paper_line": 5633,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1021",
   "section": "Neuron steering diagram",
   "claim": "number 29 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "concept vector) gives 29%, a random live feature",
   "paper_text": "with the concept vector) gives 29\\,\\%, a random live feature",
   "paper_line": 5634,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1022",
   "section": "Neuron steering diagram",
   "claim": "number 27 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "29%, a random live feature 27% and a Gaussian direction",
   "paper_text": "29\\,\\%, a random live feature 27\\,\\% and a Gaussian direction",
   "paper_line": 5634,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1023",
   "section": "Neuron steering diagram",
   "claim": "number 39 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and a Gaussian direction 39%,",
   "paper_text": "27\\,\\% and a Gaussian direction 39\\,\\%, all at the same norm.",
   "paper_line": 5634,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1024",
   "section": "Neuron steering diagram",
   "claim": "number 128 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Qwen2.5-0.5B-Instruct (\\(128^2\\) float64 cells, steering",
   "paper_text": "in Qwen2.5-0.5B-Instruct ($128^2$ float64 cells, steering",
   "paper_line": 5653,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1025",
   "section": "Neuron steering diagram",
   "claim": "number 12 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "cells, steering at layer 12, one grid and one set of",
   "paper_text": "float64 cells, steering at layer 12, one grid and one set of settings):",
   "paper_line": 5653,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1026",
   "section": "Neuron steering diagram",
   "claim": "number 10^{-3} in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(finite-horizon exponent above \\(10^{-3}\\), no period up to 48);",
   "paper_text": "(finite-horizon exponent above $10^{-3}$, no period up to 48); color",
   "paper_line": 5655,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1027",
   "section": "Neuron steering diagram",
   "claim": "number 48 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(10^{-3}\\), no period up to 48); color gives the exponent,",
   "paper_text": "$10^{-3}$, no period up to 48); color gives the exponent,",
   "paper_line": 5655,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1028",
   "section": "Neuron steering diagram",
   "claim": "number 832 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "specific to philosophy (832), of its index neighbor",
   "paper_text": "philosophy on held-out texts (832), of its index neighbor (833)",
   "paper_line": 5679,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1029",
   "section": "Neuron steering diagram",
   "claim": "number 833 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of its index neighbor (833) and of a random neuron",
   "paper_text": "(832), of its index neighbor (833) and of a random neuron (4137),",
   "paper_line": 5680,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1030",
   "section": "Neuron steering diagram",
   "claim": "number 4137 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and of a random neuron (4137), each rescaled to the",
   "paper_text": "(833) and of a random neuron (4137), each rescaled to the philosophy",
   "paper_line": 5680,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1031",
   "section": "Neuron steering diagram",
   "claim": "number 0.013 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "vector's norm (cosines with it 0.013, \\(-0.028\\) and 0.022).",
   "paper_text": "vector's norm (cosines with it 0.013, $-0.028$ and 0.022). Titles",
   "paper_line": 5680,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1032",
   "section": "Neuron steering diagram",
   "claim": "number -0.028 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(cosines with it 0.013, \\(-0.028\\) and 0.022). Titles give",
   "paper_text": "norm (cosines with it 0.013, $-0.028$ and 0.022). Titles give the",
   "paper_line": 5680,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1033",
   "section": "Neuron steering diagram",
   "claim": "number 0.022 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "it 0.013, \\(-0.028\\) and 0.022). Titles give the chaotic",
   "paper_text": "with it 0.013, $-0.028$ and 0.022). Titles give the chaotic share.}",
   "paper_line": 5681,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1034",
   "section": "Neuron steering diagram",
   "claim": "number 0.03 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "uniform fixed point within 0.03",
   "paper_text": "uniform fixed point within 0.03 decades of temperature, and",
   "paper_line": 4504,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1035",
   "section": "Neuron steering diagram",
   "claim": "number 1000 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "exponents by QR iteration (1000 transient and 2000 measured",
   "paper_text": "(Appendix~\\ref{sec:methods}; 1000 transient and 2000 measured",
   "paper_line": 4529,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1036",
   "section": "Neuron steering diagram",
   "claim": "number 2000 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "iteration (1000 transient and 2000 measured steps, float64)",
   "paper_text": "(Appendix~\\ref{sec:methods}; 1000 transient and 2000 measured steps, float64) at",
   "paper_line": 4529,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1037",
   "section": "Neuron steering diagram",
   "claim": "number 35 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at 35 completed cells: 28 chosen",
   "paper_text": "measured steps, float64) at 35 completed cells: 28 chosen",
   "paper_line": 4529,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1038",
   "section": "Neuron steering diagram",
   "claim": "number 28 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at 35 completed cells: 28 chosen by percentile of",
   "paper_text": "float64) at 35 completed cells: 28 chosen by percentile of their",
   "paper_line": 4529,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1039",
   "section": "Neuron steering diagram",
   "claim": "number 30 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "their spectra were seen (of 30 requested), and seven from",
   "paper_text": "their spectra were seen (of 30 requested), and seven from",
   "paper_line": 4530,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1040",
   "section": "Neuron steering diagram",
   "claim": "number 31 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "control. At this horizon 31 have a positive",
   "paper_text": "periodic control. At this horizon 31 have a positive leading estimate",
   "paper_line": 4531,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1041",
   "section": "Neuron steering diagram",
   "claim": "number 1.008 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "have \\(D_{\\mathrm{KY}} = 1.008\\) to 1.16, consistent with",
   "paper_text": "cells have $D_{\\mathrm{KY}}=1.008$ to $1.16$, consistent with",
   "paper_line": 4533,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1042",
   "section": "Neuron steering diagram",
   "claim": "number 1.16 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(D_{\\mathrm{KY}} = 1.008\\) to 1.16, consistent with nearly",
   "paper_text": "$D_{\\mathrm{KY}}=1.008$ to $1.16$, consistent with nearly one-dimensional",
   "paper_line": 4533,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1043",
   "section": "Neuron steering diagram",
   "claim": "number -0.17 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(\\(\\log_{10}T\\) from \\(-0.17\\) to",
   "paper_text": "headline maps ($\\log_{10}T$ from $-0.17$ to $-0.04$) it is $1.03$ to",
   "paper_line": 4535,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1044",
   "section": "Neuron steering diagram",
   "claim": "number -0.04 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-0.04\\)) it is 1.03 to 1.65,",
   "paper_text": "($\\log_{10}T$ from $-0.17$ to $-0.04$) it is $1.03$ to $1.65$, rising",
   "paper_line": 4535,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1045",
   "section": "Neuron steering diagram",
   "claim": "number 1.03 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-0.04\\)) it is 1.03 to 1.65, rising with \\(\\lambda_1\\).",
   "paper_text": "$-0.17$ to $-0.04$) it is $1.03$ to $1.65$, rising with $\\lambda_1$.",
   "paper_line": 4535,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1046",
   "section": "Neuron steering diagram",
   "claim": "number 1.65 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-0.04\\)) it is 1.03 to 1.65, rising with \\(\\lambda_1\\).",
   "paper_text": "to $-0.04$) it is $1.03$ to $1.65$, rising with $\\lambda_1$.",
   "paper_line": 4535,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1047",
   "section": "Neuron steering diagram",
   "claim": "number -0.02 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(\\(\\log_{10}T\\) from \\(-0.02\\) to 0.13), nine",
   "paper_text": "region ($\\log_{10}T$ from $-0.02$ to $0.13$), nine chaotic cells",
   "paper_line": 4536,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1048",
   "section": "Neuron steering diagram",
   "claim": "number 0.13 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(\\(\\log_{10}T\\) from \\(-0.02\\) to 0.13), nine",
   "paper_text": "($\\log_{10}T$ from $-0.02$ to $0.13$), nine chaotic cells have",
   "paper_line": 4536,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1049",
   "section": "Neuron steering diagram",
   "claim": "number 1.37 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "have \\(D_{\\mathrm{KY}} = 1.37\\) to 2.02; at two of them",
   "paper_text": "cells have $D_{\\mathrm{KY}}=1.37$ to $2.02$; at two of them",
   "paper_line": 4536,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1050",
   "section": "Neuron steering diagram",
   "claim": "number 2.02 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(D_{\\mathrm{KY}} = 1.37\\) to 2.02; at two of them the sum",
   "paper_text": "$D_{\\mathrm{KY}}=1.37$ to $2.02$; at two of them the sum of",
   "paper_line": 4536,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1051",
   "section": "Neuron steering diagram",
   "claim": "number 0.72 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "group of cells (Spearman 0.72 over 17",
   "paper_text": "each group of cells (Spearman $0.72$ over 17 philosophy cells and",
   "paper_line": 4544,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1052",
   "section": "Neuron steering diagram",
   "claim": "number 17 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "cells (Spearman 0.72 over 17",
   "paper_text": "cells (Spearman $0.72$ over 17 philosophy cells and $0.69$",
   "paper_line": 4544,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1053",
   "section": "Neuron steering diagram",
   "claim": "number 0.69 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "philosophy cells and 0.69 over 8 hostile cells, computed",
   "paper_text": "over 17 philosophy cells and $0.69$ over 8 hostile cells, computed",
   "paper_line": 4544,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1054",
   "section": "Neuron steering diagram",
   "claim": "number 16 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "cells have ratios of about 16 to 19 and",
   "paper_text": "cells have ratios of about 16 to 19 and next-token entropies",
   "paper_line": 4546,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1055",
   "section": "Neuron steering diagram",
   "claim": "number 19 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "have ratios of about 16 to 19 and",
   "paper_text": "have ratios of about 16 to 19 and next-token entropies of",
   "paper_line": 4546,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1056",
   "section": "Neuron steering diagram",
   "claim": "number 1.16 in 'Neuron steering diagram' (generated: post phrase matched to the paper's source text)",
   "appears_as": "yet \\(D_{\\mathrm{KY}} \\le 1.16\\)",
   "paper_text": "nats, yet $D_{\\mathrm{KY}}\\le1.16$. The readout supplies many",
   "paper_line": 4547,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1057",
   "section": "Two steering vectors",
   "claim": "number 8.3 in 'Two steering vectors' (generated: post phrase matched to the paper's source text)",
   "appears_as": "share is 8.3 to 16.9% of the plane,",
   "paper_text": "$\\log_{10}T=\\pm0.1$) this share is 8.3 to 16.9\\,\\% of the plane, and",
   "paper_line": 1505,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1058",
   "section": "Two steering vectors",
   "claim": "number 16.9 in 'Two steering vectors' (generated: post phrase matched to the paper's source text)",
   "appears_as": "share is 8.3 to 16.9% of the plane, and 7.8",
   "paper_text": "$\\log_{10}T=\\pm0.1$) this share is 8.3 to 16.9\\,\\% of the plane, and 7.8 to",
   "paper_line": 1505,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1059",
   "section": "Two steering vectors",
   "claim": "number 7.8 in 'Two steering vectors' (generated: post phrase matched to the paper's source text)",
   "appears_as": "16.9% of the plane, and 7.8 to 16.5% with both single",
   "paper_text": "16.9\\,\\% of the plane, and 7.8 to 16.5\\,\\% with both single",
   "paper_line": 1506,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1060",
   "section": "Two steering vectors",
   "claim": "number 16.5 in 'Two steering vectors' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of the plane, and 7.8 to 16.5% with both single pushes",
   "paper_text": "16.9\\,\\% of the plane, and 7.8 to 16.5\\,\\% with both single pushes",
   "paper_line": 1506,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1061",
   "section": "Two steering vectors",
   "claim": "number 16 in 'Two steering vectors' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(hostility at 4, gratitude at 16) the plane is",
   "paper_text": "(hostility at 4, gratitude at 16) the plane is 23.4\\,\\% chaotic,",
   "paper_line": 1506,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1062",
   "section": "Two steering vectors",
   "claim": "number 23.4 in 'Two steering vectors' (generated: post phrase matched to the paper's source text)",
   "appears_as": "23.4% chaotic, and at \\(\\log_{10}T",
   "paper_text": "gratitude at 16) the plane is 23.4\\,\\% chaotic, and at $\\log_{10}T=0.1$",
   "paper_line": 1507,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1063",
   "section": "Two steering vectors",
   "claim": "number 0.1 in 'Two steering vectors' (generated: post phrase matched to the paper's source text)",
   "appears_as": "chaotic, and at \\(\\log_{10}T = 0.1\\) both pairs give 33 and",
   "paper_text": "chaotic, and at $\\log_{10}T=0.1$ both pairs give 33 and 42\\,\\%.",
   "paper_line": 1507,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1064",
   "section": "Two steering vectors",
   "claim": "number 33 in 'Two steering vectors' (generated: post phrase matched to the paper's source text)",
   "appears_as": "= 0.1\\) both pairs give 33 and 42% (Figure",
   "paper_text": "$\\log_{10}T=0.1$ both pairs give 33 and 42\\,\\%. Each plane keeps",
   "paper_line": 1507,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1065",
   "section": "Two steering vectors",
   "claim": "number 42 in 'Two steering vectors' (generated: post phrase matched to the paper's source text)",
   "appears_as": "both pairs give 33 and 42% (Figure",
   "paper_text": "$\\log_{10}T=0.1$ both pairs give 33 and 42\\,\\%. Each plane keeps a periodic",
   "paper_line": 1507,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1066",
   "section": "Two steering vectors",
   "claim": "number 96 in 'Two steering vectors' (generated: post phrase matched to the paper's source text)",
   "appears_as": "largest Lyapunov exponent on 96 × 96 float64 cells over",
   "paper_text": "largest Lyapunov exponent on $96\\times96$ float64 cells over",
   "paper_line": 1513,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1067",
   "section": "Two steering vectors",
   "claim": "number 96 in 'Two steering vectors' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Lyapunov exponent on 96 × 96 float64 cells over the",
   "paper_text": "Lyapunov exponent on $96\\times96$ float64 cells over the two",
   "paper_line": 1513,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1068",
   "section": "Two steering vectors",
   "claim": "number -0.1 in 'Two steering vectors' (generated: post phrase matched to the paper's source text)",
   "appears_as": "strengths, at \\(\\log_{10}T = -0.1\\) (left) and 0.1 (right).",
   "paper_text": "two strengths, at $\\log_{10}T=-0.1$ (left) and $0.1$ (right).",
   "paper_line": 1514,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1069",
   "section": "Two steering vectors",
   "claim": "number 0.1 in 'Two steering vectors' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = -0.1\\) (left) and 0.1 (right). Top: gratitude",
   "paper_text": "$\\log_{10}T=-0.1$ (left) and $0.1$ (right). Top: gratitude at",
   "paper_line": 1514,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1070",
   "section": "Two steering vectors",
   "claim": "number 16 in 'Two steering vectors' (generated: post phrase matched to the paper's source text)",
   "appears_as": "layer 4, hostility at layer 16; bottom: the layers exchanged.",
   "paper_text": "block 4, hostility at block 16; bottom: the blocks exchanged.",
   "paper_line": 1514,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1071",
   "section": "Soft Thinking as published",
   "claim": "number 15 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "embeddings) restricted to the 15 most probable tokens, \\(T",
   "paper_text": "concept tokens restricted to the 15 most probable, $T=0.6$ and",
   "paper_line": 1346,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1072",
   "section": "Soft Thinking as published",
   "claim": "number 0.6 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "probable tokens, \\(T = 0.6\\) and",
   "paper_text": "to the 15 most probable, $T=0.6$ and 64 soft steps. The test",
   "paper_line": 1347,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1073",
   "section": "Soft Thinking as published",
   "claim": "number 64 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "64 soft steps. The test used",
   "paper_text": "most probable, $T=0.6$ and 64 soft steps. The test used 256",
   "paper_line": 1347,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1074",
   "section": "Soft Thinking as published",
   "claim": "number 256 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "soft steps. The test used 256 GSM8K training problems",
   "paper_text": "64 soft steps. The test used 256 GSM8K training problems that",
   "paper_line": 1347,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1075",
   "section": "Soft Thinking as published",
   "claim": "number 16 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "between batches of 8 and of 16 prompts of equal length",
   "paper_text": "between batches of 8 and of 16 prompts of equal length without",
   "paper_line": 1348,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1076",
   "section": "Soft Thinking as published",
   "claim": "number 21.1 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the answer changed for 21.1% of the problems (54 of",
   "paper_text": "and the answer changed for 21.1\\,\\% of the problems (54 of",
   "paper_line": 1349,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1077",
   "section": "Soft Thinking as published",
   "claim": "number 54 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "21.1% of the problems (54 of 256;",
   "paper_text": "for 21.1\\,\\% of the problems (54 of 256; 95\\,\\% interval clustered",
   "paper_line": 1349,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1078",
   "section": "Soft Thinking as published",
   "claim": "number 256 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of the problems (54 of 256;",
   "paper_text": "21.1\\,\\% of the problems (54 of 256; 95\\,\\% interval clustered",
   "paper_line": 1349,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1079",
   "section": "Soft Thinking as published",
   "claim": "number 95 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "95% interval [16.3, 26.1],",
   "paper_text": "of the problems (54 of 256; 95\\,\\% interval clustered by batch",
   "paper_line": 1349,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1080",
   "section": "Soft Thinking as published",
   "claim": "number 16.3 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "95% interval [16.3, 26.1], computed by resampling",
   "paper_text": "interval clustered by batch $[16.3,26.1]$). This confirms the",
   "paper_line": 1349,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1081",
   "section": "Soft Thinking as published",
   "claim": "number 26.1 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "95% interval [16.3, 26.1], computed by resampling",
   "paper_text": "interval clustered by batch $[16.3,26.1]$). This confirms the prediction",
   "paper_line": 1349,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1082",
   "section": "Soft Thinking as published",
   "claim": "number 10 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text) (paper 318f8980)",
   "appears_as": "prediction of more than 10%.",
   "paper_text": "This confirms the prediction of more than 10\\,\\%.",
   "paper_line": 1350,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1083",
   "section": "Soft Thinking as published",
   "claim": "number 256 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "published one on the same 256 problems (paired differences",
   "paper_text": "arm with this one on the same 256 problems (paired differences",
   "paper_line": 1354,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1084",
   "section": "Soft Thinking as published",
   "claim": "number 5.9 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text) (paper 318f8980)",
   "appears_as": "that the fed-back tokens are identical: 5.9%",
   "paper_text": "fed-back tokens in both layouts: 5.9\\,\\% (difference 15.2 points,",
   "paper_line": 1357,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1085",
   "section": "Soft Thinking as published",
   "claim": "number 15.2 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(difference 15.2 points, [10.4, 20.2], \\(p",
   "paper_text": "layouts: 5.9\\,\\% (difference 15.2 points, $[10.4,20.2]$, $p=8\\times10^{-9}$);",
   "paper_line": 1357,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1086",
   "section": "Soft Thinking as published",
   "claim": "number 10.4 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(difference 15.2 points, [10.4, 20.2], \\(p = 8\\times10^{-9}\\)).",
   "paper_text": "(difference 15.2 points, $[10.4,20.2]$, $p=8\\times10^{-9}$);",
   "paper_line": 1357,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1087",
   "section": "Soft Thinking as published",
   "claim": "number 20.2 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(difference 15.2 points, [10.4, 20.2], \\(p = 8\\times10^{-9}\\)).",
   "paper_text": "(difference 15.2 points, $[10.4,20.2]$, $p=8\\times10^{-9}$); predicted",
   "paper_line": 1357,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1088",
   "section": "Soft Thinking as published",
   "claim": "number 8\\times10^{-9} in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "points, [10.4, 20.2], \\(p = 8\\times10^{-9}\\)). Lower, as predicted.",
   "paper_text": "15.2 points, $[10.4,20.2]$, $p=8\\times10^{-9}$); predicted lower, and it",
   "paper_line": 1357,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1089",
   "section": "Soft Thinking as published",
   "claim": "number 16 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "- 16 soft steps instead of 64:",
   "paper_text": "predicted lower, and it is; \\item 16 soft steps instead of 64: 6.6\\,\\%",
   "paper_line": 1358,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1090",
   "section": "Soft Thinking as published",
   "claim": "number 64 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "16 soft steps instead of 64: 6.6%",
   "paper_text": "\\item 16 soft steps instead of 64: 6.6\\,\\% (difference 14.5 points,",
   "paper_line": 1359,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1091",
   "section": "Soft Thinking as published",
   "claim": "number 6.6 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "soft steps instead of 64: 6.6%",
   "paper_text": "16 soft steps instead of 64: 6.6\\,\\% (difference 14.5 points,",
   "paper_line": 1359,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1092",
   "section": "Soft Thinking as published",
   "claim": "number 14.5 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(difference 14.5 points, [10.0, 19.0], \\(p",
   "paper_text": "of 64: 6.6\\,\\% (difference 14.5 points, $[10.0,19.0]$, $p=4\\times10^{-7}$);",
   "paper_line": 1359,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1093",
   "section": "Soft Thinking as published",
   "claim": "number 10.0 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(difference 14.5 points, [10.0, 19.0], \\(p = 4\\times10^{-7}\\)).",
   "paper_text": "(difference 14.5 points, $[10.0,19.0]$, $p=4\\times10^{-7}$);",
   "paper_line": 1359,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1094",
   "section": "Soft Thinking as published",
   "claim": "number 19.0 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(difference 14.5 points, [10.0, 19.0], \\(p = 4\\times10^{-7}\\)).",
   "paper_text": "(difference 14.5 points, $[10.0,19.0]$, $p=4\\times10^{-7}$); predicted",
   "paper_line": 1359,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1095",
   "section": "Soft Thinking as published",
   "claim": "number 4\\times10^{-7} in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "points, [10.0, 19.0], \\(p = 4\\times10^{-7}\\)). Lower, as predicted.",
   "paper_text": "14.5 points, $[10.0,19.0]$, $p=4\\times10^{-7}$); predicted lower, and it",
   "paper_line": 1359,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1096",
   "section": "Soft Thinking as published",
   "claim": "number 2.3 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "chain-of-thought decoding: 2.3%, at 89% accuracy",
   "paper_text": "chain-of-thought decoding: 2.3\\,\\%, at 89\\,\\% accuracy (difference",
   "paper_line": 1361,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1097",
   "section": "Soft Thinking as published",
   "claim": "number 89 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "chain-of-thought decoding: 2.3%, at 89% accuracy",
   "paper_text": "chain-of-thought decoding: 2.3\\,\\%, at 89\\,\\% accuracy (difference 18.8",
   "paper_line": 1361,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1098",
   "section": "Soft Thinking as published",
   "claim": "number 18.8 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(difference 18.8 points, [13.7, 23.6], \\(p",
   "paper_text": "89\\,\\% accuracy (difference 18.8 points, $[13.7,23.6]$, $p=10^{-11}$);",
   "paper_line": 1361,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1099",
   "section": "Soft Thinking as published",
   "claim": "number 13.7 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(difference 18.8 points, [13.7, 23.6], \\(p = 10^{-11}\\)).",
   "paper_text": "(difference 18.8 points, $[13.7,23.6]$, $p=10^{-11}$); predicted",
   "paper_line": 1361,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1100",
   "section": "Soft Thinking as published",
   "claim": "number 23.6 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(difference 18.8 points, [13.7, 23.6], \\(p = 10^{-11}\\)). Lower,",
   "paper_text": "(difference 18.8 points, $[13.7,23.6]$, $p=10^{-11}$); predicted",
   "paper_line": 1361,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1101",
   "section": "Soft Thinking as published",
   "claim": "number 10^{-11} in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "points, [13.7, 23.6], \\(p = 10^{-11}\\)). Lower, as predicted.",
   "paper_text": "18.8 points, $[13.7,23.6]$, $p=10^{-11}$); predicted lower, and it",
   "paper_line": 1361,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1102",
   "section": "Soft Thinking as published",
   "claim": "number 17.6 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the most probable token: 17.6%",
   "paper_text": "only the most probable token: 17.6\\,\\% (difference 3.5 points,",
   "paper_line": 1363,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1103",
   "section": "Soft Thinking as published",
   "claim": "number 3.5 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(difference 3.5 points, [−2.9, 10.3], \\(p",
   "paper_text": "token: 17.6\\,\\% (difference 3.5 points, $[-2.9,10.3]$, $p=0.35$);",
   "paper_line": 1363,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1104",
   "section": "Soft Thinking as published",
   "claim": "number −2.9 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(difference 3.5 points, [−2.9, 10.3], \\(p = 0.35\\)).",
   "paper_text": "17.6\\,\\% (difference 3.5 points, $[-2.9,10.3]$, $p=0.35$); predicted",
   "paper_line": 1363,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1105",
   "section": "Soft Thinking as published",
   "claim": "number 10.3 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(difference 3.5 points, [−2.9, 10.3], \\(p = 0.35\\)). The test",
   "paper_text": "(difference 3.5 points, $[-2.9,10.3]$, $p=0.35$); predicted lower,",
   "paper_line": 1363,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1106",
   "section": "Soft Thinking as published",
   "claim": "number 0.35 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "points, [−2.9, 10.3], \\(p = 0.35\\)). The test cannot tell",
   "paper_text": "3.5 points, $[-2.9,10.3]$, $p=0.35$); predicted lower, and the",
   "paper_line": 1363,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1107",
   "section": "Soft Thinking as published",
   "claim": "number 22.3 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text) (paper 318f8980)",
   "appears_as": "The full vocabulary gave 22.3% (no prediction). Most",
   "paper_text": "The full vocabulary gave 22.3\\,\\% (no prediction). Most changes",
   "paper_line": 1369,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1108",
   "section": "Soft Thinking as published",
   "claim": "number 22 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "this model answers only 22 to 30% of the",
   "paper_text": "pipeline this model answers only 22 to 30\\,\\% of the problems correctly,",
   "paper_line": 1369,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1109",
   "section": "Soft Thinking as published",
   "claim": "number 30 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "model answers only 22 to 30% of the",
   "paper_text": "this model answers only 22 to 30\\,\\% of the problems correctly,",
   "paper_line": 1370,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1110",
   "section": "Soft Thinking as published",
   "claim": "number 6.2 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "6.2% of the problems. In float64",
   "paper_text": "whether the answer is correct for 6.2\\,\\% of the problems. In float64",
   "paper_line": 1370,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1111",
   "section": "Soft Thinking as published",
   "claim": "number 1312 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "1312 and 1314 of the 1319 GSM8K",
   "paper_text": "observed runs. On 1312 and 1314 of the 1319 GSM8K",
   "paper_line": 1371,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1112",
   "section": "Soft Thinking as published",
   "claim": "number 1314 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "1312 and 1314 of the 1319 GSM8K test",
   "paper_text": "On 1312 and 1314 of the 1319 GSM8K test problems",
   "paper_line": 1371,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1113",
   "section": "Soft Thinking as published",
   "claim": "number 1319 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "1312 and 1314 of the 1319 GSM8K test problems (full",
   "paper_text": "On 1312 and 1314 of the 1319 GSM8K test problems (full vocabulary",
   "paper_line": 1371,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1114",
   "section": "Soft Thinking as published",
   "claim": "number 15 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(full vocabulary and the 15 most",
   "paper_text": "problems (full vocabulary and top-15), a perturbation of $10^{-10}$",
   "paper_line": 1371,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1115",
   "section": "Soft Thinking as published",
   "claim": "number 10^{-10} in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "tokens), a perturbation of \\(10^{-10}\\) ended below its initial",
   "paper_text": "top-15), a perturbation of $10^{-10}$ ended below its initial size,",
   "paper_line": 1372,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1116",
   "section": "Soft Thinking as published",
   "claim": "number 128 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "steps, from 2 to 128, so after 2, 4, 8 and so",
   "paper_text": "number of soft steps, from 2 to 128. It used 200 GSM8K test problems,",
   "paper_line": 1378,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1117",
   "section": "Soft Thinking as published",
   "claim": "number 128 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "2, 4, 8 and so on up to 128 steps of feedback. It",
   "paper_text": "number of soft steps, from 2 to 128. It used 200 GSM8K test problems,",
   "paper_line": 1378,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1118",
   "section": "Soft Thinking as published",
   "claim": "number 200 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "used 200 GSM8K test problems, two",
   "paper_text": "steps, from 2 to 128. It used 200 GSM8K test problems, two temperatures",
   "paper_line": 1378,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1119",
   "section": "Soft Thinking as published",
   "claim": "number 0.6 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "problems, two temperatures (0.6 and 1.2), and six steering",
   "paper_text": "problems, two temperatures (0.6 and 1.2), and six steering",
   "paper_line": 1378,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1120",
   "section": "Soft Thinking as published",
   "claim": "number 1.2 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "two temperatures (0.6 and 1.2), and six steering",
   "paper_text": "problems, two temperatures (0.6 and 1.2), and six steering strengths",
   "paper_line": 1378,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1121",
   "section": "Soft Thinking as published",
   "claim": "number -0.02 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "direction (\\(\\alpha\\) from \\(-0.02\\) to \\(0.05\\),",
   "paper_text": "hostility direction ($\\alpha$ from $-0.02$ to $0.05$). The two layouts",
   "paper_line": 1379,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1122",
   "section": "Soft Thinking as published",
   "claim": "number 0.05 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(\\(\\alpha\\) from \\(-0.02\\) to \\(0.05\\),",
   "paper_text": "($\\alpha$ from $-0.02$ to $0.05$). The two layouts agree on",
   "paper_line": 1379,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1123",
   "section": "Soft Thinking as published",
   "claim": "number 90 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "batch layouts agree on 90 to 96% of the answers after",
   "paper_text": "$0.05$). The two layouts agree on 90 to 96\\,\\% of the answers after",
   "paper_line": 1379,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1124",
   "section": "Soft Thinking as published",
   "claim": "number 96 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "layouts agree on 90 to 96% of the answers after 2",
   "paper_text": "two layouts agree on 90 to 96\\,\\% of the answers after 2",
   "paper_line": 1379,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1125",
   "section": "Soft Thinking as published",
   "claim": "number 51 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "answers after 2 steps and on 51",
   "paper_text": "answers after 2 steps and on 51 to 70\\,\\% after 128, in every",
   "paper_line": 1380,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1126",
   "section": "Soft Thinking as published",
   "claim": "number 70 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "to 70% after 128, in every configuration.",
   "paper_text": "after 2 steps and on 51 to 70\\,\\% after 128, in every configuration.",
   "paper_line": 1380,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1127",
   "section": "Soft Thinking as published",
   "claim": "number 128 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "to 70% after 128, in every configuration.",
   "paper_text": "steps and on 51 to 70\\,\\% after 128, in every configuration. Among",
   "paper_line": 1380,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1128",
   "section": "Soft Thinking as published",
   "claim": "number 10^{-10} in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(10^{-10}\\) apart, separate the two.",
   "paper_text": "same configurations, started $10^{-10}$ apart, separate the two sources",
   "paper_line": 1381,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1129",
   "section": "Soft Thinking as published",
   "claim": "number 0.02 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "steered** (\\(|\\alpha| \\le 0.02\\)). The copies change the",
   "paper_text": "weakly steered ($|\\alpha|\\le0.02$), the copies change the answer",
   "paper_line": 1384,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1130",
   "section": "Soft Thinking as published",
   "claim": "number 1.5 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "text of at most 1.5% of the problems. The answers are barely sensitive to these",
   "paper_text": "the answer text of at most 1.5\\,\\% of the problems. The loop shows little answer sensitivity",
   "paper_line": 1384,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1131",
   "section": "Soft Thinking as published",
   "claim": "number 0.05 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "**Strongly steered** (\\(\\alpha = 0.05\\)). The copies change the",
   "paper_text": "feedback. \\item At $\\alpha=0.05$ they change the answer text",
   "paper_line": 1385,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1132",
   "section": "Soft Thinking as published",
   "claim": "number 13.5 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "text of 13.5% of the problems at \\(T",
   "paper_text": "they change the answer text of 13.5\\,\\% of the problems at $T=0.6$",
   "paper_line": 1386,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1133",
   "section": "Soft Thinking as published",
   "claim": "number 0.6 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of the problems at \\(T = 0.6\\) and 27.5% at \\(T = 1.2\\),",
   "paper_text": "13.5\\,\\% of the problems at $T=0.6$ and 27.5\\,\\% at $T=1.2$, and",
   "paper_line": 1386,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1134",
   "section": "Soft Thinking as published",
   "claim": "number 27.5 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "problems at \\(T = 0.6\\) and 27.5% at \\(T = 1.2\\), and the",
   "paper_text": "the problems at $T=0.6$ and 27.5\\,\\% at $T=1.2$, and the extracted",
   "paper_line": 1386,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1135",
   "section": "Soft Thinking as published",
   "claim": "number 1.2 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.6\\) and 27.5% at \\(T = 1.2\\), and the",
   "paper_text": "$T=0.6$ and 27.5\\,\\% at $T=1.2$, and the extracted number",
   "paper_line": 1386,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1136",
   "section": "Soft Thinking as published",
   "claim": "number 4.5 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "final answer itself, of 4.5 and 9.0%. The loop itself",
   "paper_text": "and the extracted number of 4.5 and 9.0\\,\\%. The loop itself",
   "paper_line": 1386,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1137",
   "section": "Soft Thinking as published",
   "claim": "number 9.0 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "answer itself, of 4.5 and 9.0%. The loop itself is",
   "paper_text": "extracted number of 4.5 and 9.0\\,\\%. The loop itself is then",
   "paper_line": 1387,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1138",
   "section": "Soft Thinking as published",
   "claim": "number 0.5 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "accuracy has fallen to between 0.5 and 2.5% in either layout.",
   "paper_text": "accuracy has fallen to between 0.5 and 2.5\\,\\% in either layout.",
   "paper_line": 1388,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1139",
   "section": "Soft Thinking as published",
   "claim": "number 2.5 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "fallen to between 0.5 and 2.5% in either layout.",
   "paper_text": "has fallen to between 0.5 and 2.5\\,\\% in either layout. \\end{itemize}",
   "paper_line": 1388,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1140",
   "section": "Soft Thinking as published",
   "claim": "number 15 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "in concept tokens (the 15",
   "paper_text": "thinks in concept tokens (top 15, $T=0.6$) until its most probable",
   "paper_line": 1396,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1141",
   "section": "Soft Thinking as published",
   "claim": "number 0.6 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "probable tokens, \\(T = 0.6\\)) until its most probable",
   "paper_text": "concept tokens (top 15, $T=0.6$) until its most probable next",
   "paper_line": 1396,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1142",
   "section": "Soft Thinking as published",
   "claim": "number 1536 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "thinking block, or until 1536 steps, a cap on how long",
   "paper_text": "the thinking block, or until 1536 steps. It then answers by sampling",
   "paper_line": 1397,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1143",
   "section": "Soft Thinking as published",
   "claim": "number 16 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "before, the batches held 8 or 16",
   "paper_text": "the batches held 8 or 16 prompts of equal length.",
   "paper_line": 1399,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1144",
   "section": "Soft Thinking as published",
   "claim": "number 45 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "thought far less and answered 45% of a",
   "paper_text": "thought far less and answered 45\\,\\% of a check set correctly,",
   "paper_line": 1401,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1145",
   "section": "Soft Thinking as published",
   "claim": "number 83 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "set correctly, against 83% with the correct tokenizer",
   "paper_text": "check set correctly, against 83\\,\\% with the correct tokenizer",
   "paper_line": 1402,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1146",
   "section": "Soft Thinking as published",
   "claim": "number 81 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "tokenizer in bfloat16 and 81%",
   "paper_text": "correct tokenizer in bfloat16 and 81\\,\\% in float64",
   "paper_line": 1402,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1147",
   "section": "Soft Thinking as published",
   "claim": "number 27.1 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "27.1% of the soft-thinking answers",
   "paper_text": "cells, the batch layout changed 27.1\\,\\% of the soft-thinking answers",
   "paper_line": 1404,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1148",
   "section": "Soft Thinking as published",
   "claim": "number 243 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "soft-thinking answers (243 of 896; 95% interval [24.7,",
   "paper_text": "the soft-thinking answers (243 of 896; 95\\,\\% interval $[24.7,29.5]$),",
   "paper_line": 1404,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1149",
   "section": "Soft Thinking as published",
   "claim": "number 896 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "soft-thinking answers (243 of 896; 95% interval [24.7, 29.5]),",
   "paper_text": "soft-thinking answers (243 of 896; 95\\,\\% interval $[24.7,29.5]$),",
   "paper_line": 1404,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1150",
   "section": "Soft Thinking as published",
   "claim": "number 95 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "soft-thinking answers (243 of 896; 95% interval [24.7, 29.5]),",
   "paper_text": "soft-thinking answers (243 of 896; 95\\,\\% interval $[24.7,29.5]$),",
   "paper_line": 1404,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1151",
   "section": "Soft Thinking as published",
   "claim": "number 24.7 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(243 of 896; 95% interval [24.7, 29.5]), confirming the",
   "paper_text": "(243 of 896; 95\\,\\% interval $[24.7,29.5]$), confirming the prediction",
   "paper_line": 1405,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1152",
   "section": "Soft Thinking as published",
   "claim": "number 29.5 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "896; 95% interval [24.7, 29.5]), confirming the prediction",
   "paper_text": "896; 95\\,\\% interval $[24.7,29.5]$), confirming the prediction",
   "paper_line": 1405,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1153",
   "section": "Soft Thinking as published",
   "claim": "number 29.6 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "including the original run (29.6%) and the run",
   "paper_text": "including the original run (29.6\\,\\%) and the run without both",
   "paper_line": 1407,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1154",
   "section": "Soft Thinking as published",
   "claim": "number 21.9 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "combinations of this model (21.9%).",
   "paper_text": "without both cells of this model (21.9\\,\\%)",
   "paper_line": 1407,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1155",
   "section": "Soft Thinking as published",
   "claim": "number 14.5 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "DeepSeek-R1-Distill-Qwen-7B for 14.5% of",
   "paper_text": "DeepSeek-R1-Distill-Qwen-7B for 14.5\\,\\% of the problems ($[10.9,18.0]$)",
   "paper_line": 1410,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1156",
   "section": "Soft Thinking as published",
   "claim": "number 10.9 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the problems ([10.9, 18.0]) at 88 to 90% accuracy,",
   "paper_text": "14.5\\,\\% of the problems ($[10.9,18.0]$) at 88 to 90\\,\\% accuracy,",
   "paper_line": 1411,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1157",
   "section": "Soft Thinking as published",
   "claim": "number 18.0 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the problems ([10.9, 18.0]) at 88 to 90% accuracy,",
   "paper_text": "14.5\\,\\% of the problems ($[10.9,18.0]$) at 88 to 90\\,\\% accuracy,",
   "paper_line": 1411,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1158",
   "section": "Soft Thinking as published",
   "claim": "number 88 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "problems ([10.9, 18.0]) at 88 to 90% accuracy, QwQ-32B",
   "paper_text": "problems ($[10.9,18.0]$) at 88 to 90\\,\\% accuracy, and QwQ-32B",
   "paper_line": 1411,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1159",
   "section": "Soft Thinking as published",
   "claim": "number 90 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "([10.9, 18.0]) at 88 to 90% accuracy, QwQ-32B for",
   "paper_text": "problems ($[10.9,18.0]$) at 88 to 90\\,\\% accuracy, and QwQ-32B for",
   "paper_line": 1411,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1160",
   "section": "Soft Thinking as published",
   "claim": "number 19.5 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "90% accuracy, QwQ-32B for 19.5%",
   "paper_text": "at 88 to 90\\,\\% accuracy, and QwQ-32B for 19.5\\,\\%",
   "paper_line": 1411,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1161",
   "section": "Soft Thinking as published",
   "claim": "number 16.4 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "([16.4, 22.3]) at 86 to 87%, and",
   "paper_text": "and QwQ-32B for 19.5\\,\\% ($[16.4,22.3]$) at 86 to 87\\,\\%, and",
   "paper_line": 1411,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1162",
   "section": "Soft Thinking as published",
   "claim": "number 22.3 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "([16.4, 22.3]) at 86 to 87%, and DeepSeek-R1-Distill-Llama-8B",
   "paper_text": "QwQ-32B for 19.5\\,\\% ($[16.4,22.3]$) at 86 to 87\\,\\%, and DeepSeek-R1-Distill-Llama-8B",
   "paper_line": 1411,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1163",
   "section": "Soft Thinking as published",
   "claim": "number 86 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "([16.4, 22.3]) at 86 to 87%, and DeepSeek-R1-Distill-Llama-8B",
   "paper_text": "19.5\\,\\% ($[16.4,22.3]$) at 86 to 87\\,\\%, and DeepSeek-R1-Distill-Llama-8B",
   "paper_line": 1411,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1164",
   "section": "Soft Thinking as published",
   "claim": "number 87 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "([16.4, 22.3]) at 86 to 87%, and DeepSeek-R1-Distill-Llama-8B",
   "paper_text": "19.5\\,\\% ($[16.4,22.3]$) at 86 to 87\\,\\%, and DeepSeek-R1-Distill-Llama-8B",
   "paper_line": 1411,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1165",
   "section": "Soft Thinking as published",
   "claim": "number 28.9 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "DeepSeek-R1-Distill-Llama-8B for 28.9%",
   "paper_text": "DeepSeek-R1-Distill-Llama-8B for 28.9\\,\\% ($[23.4,34.4]$) at 74 to",
   "paper_line": 1412,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1166",
   "section": "Soft Thinking as published",
   "claim": "number 23.4 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "([23.4, 34.4]) at 74 to 77%. The",
   "paper_text": "DeepSeek-R1-Distill-Llama-8B for 28.9\\,\\% ($[23.4,34.4]$) at 74 to 77\\,\\%. The",
   "paper_line": 1412,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1167",
   "section": "Soft Thinking as published",
   "claim": "number 34.4 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "([23.4, 34.4]) at 74 to 77%. The two layouts",
   "paper_text": "DeepSeek-R1-Distill-Llama-8B for 28.9\\,\\% ($[23.4,34.4]$) at 74 to 77\\,\\%. The two layouts",
   "paper_line": 1412,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1168",
   "section": "Soft Thinking as published",
   "claim": "number 74 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "([23.4, 34.4]) at 74 to 77%. The two layouts disagreed",
   "paper_text": "28.9\\,\\% ($[23.4,34.4]$) at 74 to 77\\,\\%. The two layouts disagreed",
   "paper_line": 1412,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1169",
   "section": "Soft Thinking as published",
   "claim": "number 77 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "([23.4, 34.4]) at 74 to 77%. The two layouts disagreed on correctness",
   "paper_text": "28.9\\,\\% ($[23.4,34.4]$) at 74 to 77\\,\\%. The two layouts disagreed on correctness",
   "paper_line": 1412,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1170",
   "section": "Soft Thinking as published",
   "claim": "number 11.7 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "for 11.7, 14.5 and 18.0% of the",
   "paper_text": "The two layouts disagreed on correctness for 11.7, 14.5 and 18.0\\,\\% of the problems.",
   "paper_line": 1412,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1171",
   "section": "Soft Thinking as published",
   "claim": "number 14.5 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "for 11.7, 14.5 and 18.0% of the problems.",
   "paper_text": "layouts disagreed on correctness for 11.7, 14.5 and 18.0\\,\\% of the problems.",
   "paper_line": 1412,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1172",
   "section": "Soft Thinking as published",
   "claim": "number 18.0 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "for 11.7, 14.5 and 18.0% of the problems.",
   "paper_text": "layouts disagreed on correctness for 11.7, 14.5 and 18.0\\,\\% of the problems.",
   "paper_line": 1412,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1173",
   "section": "Soft Thinking as published",
   "claim": "number 10.2 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "thinking changed 10.2, 19.9 and 21.5% of the",
   "paper_text": "answers. On GSM8K the rates were 10.2, 19.9 and 21.5\\,\\% for the",
   "paper_line": 1414,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1174",
   "section": "Soft Thinking as published",
   "claim": "number 19.9 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "thinking changed 10.2, 19.9 and 21.5% of the answers",
   "paper_text": "GSM8K the rates were 10.2, 19.9 and 21.5\\,\\% for the same three",
   "paper_line": 1414,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1175",
   "section": "Soft Thinking as published",
   "claim": "number 21.5 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "changed 10.2, 19.9 and 21.5% of the answers for the",
   "paper_text": "the rates were 10.2, 19.9 and 21.5\\,\\% for the same three models.",
   "paper_line": 1414,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1176",
   "section": "Soft Thinking as published",
   "claim": "number 7.4 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text) (paper 318f8980)",
   "appears_as": "did soft thinking change more, by 7.4",
   "paper_text": "Only in DeepSeek-R1-Distill-Llama-8B did soft thinking change more, by 7.4 points",
   "paper_line": 1415,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1177",
   "section": "Soft Thinking as published",
   "claim": "number 1.9 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text) (paper 318f8980)",
   "appears_as": "points ([1.9, 12.9]; exact McNemar \\(p = 0.029\\), not corrected for the five",
   "paper_text": "by 7.4 points ($[1.9,12.9]$; exact McNemar $p=0.029$, not corrected for the five cells)",
   "paper_line": 1415,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1178",
   "section": "Soft Thinking as published",
   "claim": "number 12.9 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text) (paper 318f8980)",
   "appears_as": "points ([1.9, 12.9]; exact McNemar \\(p = 0.029\\), not corrected for the five",
   "paper_text": "by 7.4 points ($[1.9,12.9]$; exact McNemar $p=0.029$, not corrected for the five cells)",
   "paper_line": 1415,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1179",
   "section": "Soft Thinking as published",
   "claim": "number 0.029 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text) (paper 318f8980)",
   "appears_as": "points ([1.9, 12.9]; exact McNemar \\(p = 0.029\\), not corrected for the five",
   "paper_text": "by 7.4 points ($[1.9,12.9]$; exact McNemar $p=0.029$, not corrected for the five cells)",
   "paper_line": 1415,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1180",
   "section": "Soft Thinking as published",
   "claim": "number 4.7 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text) (paper 318f8980)",
   "appears_as": "combinations), and there it answered correctly 4.7 points less often",
   "paper_text": "and it answered correctly 4.7 points less often",
   "paper_line": 1416,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1181",
   "section": "Soft Thinking as published",
   "claim": "number −8.6 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text) (paper 318f8980)",
   "appears_as": "([−8.6, −0.8]; McNemar \\(p = 0.096\\)).",
   "paper_text": "often ($[-8.6,-0.8]$; McNemar $p=0.096$).",
   "paper_line": 1417,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1182",
   "section": "Soft Thinking as published",
   "claim": "number −0.8 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text) (paper 318f8980)",
   "appears_as": "([−8.6, −0.8]; McNemar \\(p = 0.096\\)).",
   "paper_text": "often ($[-8.6,-0.8]$; McNemar $p=0.096$).",
   "paper_line": 1417,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1183",
   "section": "Soft Thinking as published",
   "claim": "number 0.096 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text) (paper 318f8980)",
   "appears_as": "([−8.6, −0.8]; McNemar \\(p = 0.096\\)).",
   "paper_text": "often ($[-8.6,-0.8]$; McNemar $p=0.096$).",
   "paper_line": 1417,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1184",
   "section": "Soft Thinking as published",
   "claim": "number 11.7 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "11.7% (difference 2.7 points,",
   "paper_text": "first model's soft rate was 11.7\\,\\% (difference 2.7 points,",
   "paper_line": 1421,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1185",
   "section": "Soft Thinking as published",
   "claim": "number 2.7 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "11.7% (difference 2.7 points, [−1.6, 6.6]), a",
   "paper_text": "rate was 11.7\\,\\% (difference 2.7 points, $[-1.6,6.6]$), a separate",
   "paper_line": 1421,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1186",
   "section": "Soft Thinking as published",
   "claim": "number −1.6 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(difference 2.7 points, [−1.6, 6.6]), a separate replication",
   "paper_text": "11.7\\,\\% (difference 2.7 points, $[-1.6,6.6]$), a separate replication",
   "paper_line": 1421,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1187",
   "section": "Soft Thinking as published",
   "claim": "number 6.6 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(difference 2.7 points, [−1.6, 6.6]), a separate replication",
   "paper_text": "(difference 2.7 points, $[-1.6,6.6]$), a separate replication",
   "paper_line": 1421,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1188",
   "section": "Soft Thinking as published",
   "claim": "number 61 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "thinking cap, it changed 61% of the answers of",
   "paper_text": "the thinking cap, it changed 61\\,\\% of the answers of DeepSeek-R1-Distill-Qwen-7B",
   "paper_line": 1425,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1189",
   "section": "Soft Thinking as published",
   "claim": "number 44 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "DeepSeek-R1-Distill-Qwen-7B (44 to 48% correct) and 67%",
   "paper_text": "DeepSeek-R1-Distill-Qwen-7B (44 to 48\\,\\% correct) and 67\\,\\%",
   "paper_line": 1426,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1190",
   "section": "Soft Thinking as published",
   "claim": "number 48 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "DeepSeek-R1-Distill-Qwen-7B (44 to 48% correct) and 67% of those",
   "paper_text": "DeepSeek-R1-Distill-Qwen-7B (44 to 48\\,\\% correct) and 67\\,\\% of",
   "paper_line": 1426,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1191",
   "section": "Soft Thinking as published",
   "claim": "number 67 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(44 to 48% correct) and 67% of those of",
   "paper_text": "(44 to 48\\,\\% correct) and 67\\,\\% of those of DeepSeek-R1-Distill-Llama-8B",
   "paper_line": 1426,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1192",
   "section": "Soft Thinking as published",
   "claim": "number 39 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text) (paper 318f8980)",
   "appears_as": "DeepSeek-R1-Distill-Llama-8B (39 to 42% correct).",
   "paper_text": "DeepSeek-R1-Distill-Llama-8B (39 to 42\\,\\% correct).",
   "paper_line": 1426,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1193",
   "section": "Soft Thinking as published",
   "claim": "number 42 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text) (paper 318f8980)",
   "appears_as": "DeepSeek-R1-Distill-Llama-8B (39 to 42% correct).",
   "paper_text": "DeepSeek-R1-Distill-Llama-8B (39 to 42\\,\\% correct).",
   "paper_line": 1426,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1194",
   "section": "Soft Thinking as published",
   "claim": "number 0.01 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "model is, has stayed below 0.01 nats",
   "paper_text": "the entropy has stayed below 0.01 nats for 256 steps. An exploratory",
   "paper_line": 1434,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1195",
   "section": "Soft Thinking as published",
   "claim": "number 256 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "for 256 steps. An exploratory rerun",
   "paper_text": "stayed below 0.01 nats for 256 steps. An exploratory rerun",
   "paper_line": 1434,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1196",
   "section": "Soft Thinking as published",
   "claim": "number 4096 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "with a thinking budget of 4096 steps",
   "paper_text": "it, with a thinking budget of 4096 steps",
   "paper_line": 1435,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1197",
   "section": "Soft Thinking as published",
   "claim": "number 1536 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "instead of 1536. Cold Stop ended thinking",
   "paper_text": "its own within the original 1536 steps was reproduced exactly",
   "paper_line": 1440,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1198",
   "section": "Soft Thinking as published",
   "claim": "number 512 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "thinking in only 6 of the 512 soft rows and in",
   "paper_text": "ended thinking in only 6 of the 512 soft rows and in none of the",
   "paper_line": 1436,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1199",
   "section": "Soft Thinking as published",
   "claim": "number 512 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "none of the 512 sampled rows: the models",
   "paper_text": "soft rows and in none of the 512 sampled rows; the models nearly",
   "paper_line": 1437,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1200",
   "section": "Soft Thinking as published",
   "claim": "number 128 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "DeepSeek-R1-Distill-Qwen-7B on 128 GSM8K problems: 8.6% (soft)",
   "paper_text": "DeepSeek-R1-Distill-Qwen-7B on 128 GSM8K problems, 50.0 and 54.7\\,\\%",
   "paper_line": 1438,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1201",
   "section": "Soft Thinking as published",
   "claim": "number 8.6 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "on 128 GSM8K problems: 8.6% (soft) and 17.2%",
   "paper_text": "still changed the answers: 8.6\\,\\% (soft) and 17.2\\,\\% (sampled)",
   "paper_line": 1437,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1202",
   "section": "Soft Thinking as published",
   "claim": "number 17.2 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "problems: 8.6% (soft) and 17.2%",
   "paper_text": "answers: 8.6\\,\\% (soft) and 17.2\\,\\% (sampled) for DeepSeek-R1-Distill-Qwen-7B",
   "paper_line": 1437,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1203",
   "section": "Soft Thinking as published",
   "claim": "number 50.0 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "same model on MATH-500: 50.0 and 54.7%;",
   "paper_text": "DeepSeek-R1-Distill-Qwen-7B on 128 GSM8K problems, 50.0 and 54.7\\,\\% for it on MATH-500,",
   "paper_line": 1438,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1204",
   "section": "Soft Thinking as published",
   "claim": "number 54.7 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "model on MATH-500: 50.0 and 54.7%;",
   "paper_text": "128 GSM8K problems, 50.0 and 54.7\\,\\% for it on MATH-500, and",
   "paper_line": 1438,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1205",
   "section": "Soft Thinking as published",
   "claim": "number 64 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "- QwQ-32B on 64 GSM8K problems: 17.2 and",
   "paper_text": "and 9.4\\,\\% for QwQ-32B on 64 GSM8K problems. The soft-minus-sampled",
   "paper_line": 1439,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1206",
   "section": "Soft Thinking as published",
   "claim": "number 17.2 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "QwQ-32B on 64 GSM8K problems: 17.2 and 9.4%.",
   "paper_text": "54.7\\,\\% for it on MATH-500, and 17.2 and 9.4\\,\\% for QwQ-32B on",
   "paper_line": 1438,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1207",
   "section": "Soft Thinking as published",
   "claim": "number 9.4 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "GSM8K problems: 17.2 and 9.4%.",
   "paper_text": "it on MATH-500, and 17.2 and 9.4\\,\\% for QwQ-32B on 64 GSM8K",
   "paper_line": 1438,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1208",
   "section": "Soft Thinking as published",
   "claim": "number 1536 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "own within the original 1536 steps was",
   "paper_text": "its own within the original 1536 steps was reproduced exactly",
   "paper_line": 1440,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1209",
   "section": "Soft Thinking as published",
   "claim": "number 86 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "reasoning models that answer 86 to 90% of",
   "paper_text": "reasoning models that answer 86 to 90\\,\\% of them correctly",
   "paper_line": 60,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1210",
   "section": "Soft Thinking as published",
   "claim": "number 90 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "models that answer 86 to 90% of",
   "paper_text": "reasoning models that answer 86 to 90\\,\\% of them correctly (DeepSeek-R1-Distill-Qwen-7B,",
   "paper_line": 60,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1211",
   "section": "Soft Thinking as published",
   "claim": "number 14.5 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "problems correctly changed 14.5 and 19.5% of their answers",
   "paper_text": "(DeepSeek-R1-Distill-Qwen-7B, QwQ-32B) changed 14.5 and 19.5\\,\\%, the two layouts disagreeing on correctness",
   "paper_line": 61,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1212",
   "section": "Soft Thinking as published",
   "claim": "number 19.5 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "correctly changed 14.5 and 19.5% of their answers when",
   "paper_text": "(DeepSeek-R1-Distill-Qwen-7B, QwQ-32B) changed 14.5 and 19.5\\,\\%, the two layouts disagreeing on correctness for",
   "paper_line": 61,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1213",
   "section": "Soft Thinking as published",
   "claim": "correctness disagreement of the two layouts, smaller value, in 'Soft Thinking as published'; range ends at their extremes, 11.7 and 14.5, since report f0a09f7f (paper 4e6e2ec6)",
   "appears_as": "the two layouts disagreeing on correctness for 11.7 and 14.5% of the problems,",
   "paper_text": "19.5\\,\\%, the two layouts disagreeing on correctness for 11.7 and 14.5\\,\\% of the problems.",
   "paper_line": 61,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1214",
   "section": "Soft Thinking as published",
   "claim": "correctness disagreement of the two layouts, larger value, in 'Soft Thinking as published'; range ends at their extremes, 11.7 and 14.5, since report f0a09f7f (paper 4e6e2ec6)",
   "appears_as": "the two layouts disagreeing on correctness for 11.7 and 14.5% of the problems, and",
   "paper_text": "disagreeing on correctness for 11.7 and 14.5\\,\\% of the problems. Ordinary",
   "paper_line": 61,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1215",
   "section": "Soft Thinking as published",
   "claim": "number 10^{-10} in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "base row's by a relative \\(10^{-10}\\), far below any",
   "paper_text": "the base row's by a relative $10^{-10}$, and all copies shared the",
   "paper_line": 1444,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1216",
   "section": "Soft Thinking as published",
   "claim": "number 216 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "**DeepSeek-R1-Distill-Qwen-7B.** 216 of 256 copies ended the",
   "paper_text": "DeepSeek-R1-Distill-Qwen-7B, 216 of 256 copies ended the thinking",
   "paper_line": 1446,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1217",
   "section": "Soft Thinking as published",
   "claim": "number 256 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "**DeepSeek-R1-Distill-Qwen-7B.** 216 of 256 copies ended the thinking",
   "paper_text": "DeepSeek-R1-Distill-Qwen-7B, 216 of 256 copies ended the thinking at",
   "paper_line": 1446,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1218",
   "section": "Soft Thinking as published",
   "claim": "number 2.3 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text); rebound at paper 13145281",
   "appears_as": "initial displacement, and 2.3% changed",
   "paper_text": "the initial displacement, and 2.3\\,\\% changed the answer. These observations",
   "paper_line": 1446,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1219",
   "section": "Soft Thinking as published",
   "claim": "number 131 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the initial displacement (131 of 192",
   "paper_text": "above the initial displacement (131 of 192 and 145 of 256). Fitted",
   "paper_line": 1449,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1220",
   "section": "Soft Thinking as published",
   "claim": "number 192 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "initial displacement (131 of 192",
   "paper_text": "initial displacement (131 of 192 and 145 of 256). Fitted over",
   "paper_line": 1449,
   "paper_file": "paper/llm/main.tex"
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   "section": "Soft Thinking as published",
   "claim": "number 145 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and 145 of 256). Fitted only over",
   "paper_text": "displacement (131 of 192 and 145 of 256). Fitted over the steps",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-1222",
   "section": "Soft Thinking as published",
   "claim": "number 256 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and 145 of 256). Fitted only over the",
   "paper_text": "displacement (131 of 192 and 145 of 256). Fitted over the steps where",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Soft Thinking as published",
   "claim": "number 10^{-3} in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(10^{-3}\\), the median growth rates",
   "paper_text": "times the displacement and $10^{-3}$, the median growth rates were",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-1224",
   "section": "Soft Thinking as published",
   "claim": "number 0.011 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "median growth rates were 0.011 and 0.008 per step: slow",
   "paper_text": "the median growth rates were 0.011 and 0.008 per step. The displacement",
   "paper_line": 1450,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-1225",
   "section": "Soft Thinking as published",
   "claim": "number 0.008 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "growth rates were 0.011 and 0.008 per step: slow growth.",
   "paper_text": "growth rates were 0.011 and 0.008 per step. The displacement",
   "paper_line": 1450,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-1226",
   "section": "Soft Thinking as published",
   "claim": "number 13.5 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
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   "paper_text": "displacement alone changed 13.5 and 18.4\\,\\% of the answers,",
   "paper_line": 1451,
   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Soft Thinking as published",
   "claim": "number 18.4 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "alone changed 13.5 and 18.4% of the answers, respectively.",
   "paper_text": "displacement alone changed 13.5 and 18.4\\,\\% of the answers, respectively.",
   "paper_line": 1451,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-1228",
   "section": "Soft Thinking as published",
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   "appears_as": "before their base row did (14 in",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Soft Thinking as published",
   "claim": "number 23 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "DeepSeek-R1-Distill-Llama-8B, 23 in QwQ-32B). And the copies",
   "paper_text": "their base row (14 in R1-Llama, 23 in QwQ), and the copies of",
   "paper_line": 1453,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "shrimp-1230",
   "section": "Soft Thinking as published",
   "claim": "number 128 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "each other. The test used 128 problems for each of the",
   "paper_text": "128 problems for each 7--8B model and 96 for QwQ-32B)",
   "paper_line": 1455,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1231",
   "section": "Soft Thinking as published",
   "claim": "number 96 in 'Soft Thinking as published' (generated: post phrase matched to the paper's source text)",
   "appears_as": "smaller models and 96 for QwQ-32B.",
   "paper_text": "128 problems for each 7--8B model and 96 for QwQ-32B)",
   "paper_line": 1455,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1232",
   "section": "Glossary",
   "claim": "number 4.6692 in 'Glossary' (generated: post phrase matched to the paper's source text)",
   "appears_as": "shrink by a common factor, \\(\\delta = 4.6692\\ldots\\),",
   "paper_text": "Feigenbaum's constant is $\\delta=4.6692\\ldots$ \\cite{feigenbaum1978quantitative};",
   "paper_line": 1989,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "shrimp-1234",
   "section": "Glossary",
   "claim": "number 10^{-3} in 'Glossary' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(10^{-3}\\) in bfloat16.",
   "paper_text": "relative in float64 and about $10^{-3}$ in bfloat16. In a single forward",
   "paper_line": 1160,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0000",
   "section": "Synchronization",
   "claim": "number 12 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "layer 12, float64) have \\(\\lambda_1",
   "paper_text": "(philosophy direction, layer 12, float64), with $\\lambda_1=0.098$,",
   "paper_line": 3744,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0001",
   "section": "Synchronization",
   "claim": "number 0.098 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "float64) have \\(\\lambda_1 = 0.098\\), 0.437 and 0.196 per",
   "paper_text": "12, float64), with $\\lambda_1=0.098$, 0.437 and 0.196 per step",
   "paper_line": 3744,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0002",
   "section": "Synchronization",
   "claim": "number 0.437 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lambda_1 = 0.098\\), 0.437 and 0.196 per step over",
   "paper_text": "float64), with $\\lambda_1=0.098$, 0.437 and 0.196 per step over 3000",
   "paper_line": 3744,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0003",
   "section": "Synchronization",
   "claim": "number 0.196 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lambda_1 = 0.098\\), 0.437 and 0.196 per step over 3000",
   "paper_text": "$\\lambda_1=0.098$, 0.437 and 0.196 per step over 3000 steps, so",
   "paper_line": 3745,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0004",
   "section": "Synchronization",
   "claim": "number 3000 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and 0.196 per step over 3000",
   "paper_text": "0.437 and 0.196 per step over 3000 steps, so that $c^*=0.046$,",
   "paper_line": 3745,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0005",
   "section": "Synchronization",
   "claim": "number 0.046 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "steps, so that \\(c^* = 0.046\\), 0.177 and 0.089 (Figure",
   "paper_text": "over 3000 steps, so that $c^*=0.046$, 0.177 and 0.089 (Figure~\\ref{fig:sync};",
   "paper_line": 3745,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0006",
   "section": "Synchronization",
   "claim": "number 0.177 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "so that \\(c^* = 0.046\\), 0.177 and 0.089 (Figure",
   "paper_text": "steps, so that $c^*=0.046$, 0.177 and 0.089 (Figure~\\ref{fig:sync};",
   "paper_line": 3745,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0007",
   "section": "Synchronization",
   "claim": "number 0.089 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(c^* = 0.046\\), 0.177 and 0.089 (Figure",
   "paper_text": "that $c^*=0.046$, 0.177 and 0.089 (Figure~\\ref{fig:sync}",
   "paper_line": 3745,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0008",
   "section": "Synchronization",
   "claim": "number 0.30 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "rate, measured directly on the coupled map at seven couplings from 0 to 0.30 in",
   "paper_text": "measured directly on the coupled map at seven couplings from 0 to 0.30 in each cell, approximately follows",
   "paper_line": 3754,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0009",
   "section": "Synchronization",
   "claim": "number 0.44 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "each cell, approximately follows \\(\\lambda_1 + \\ln|1 - 2c|\\) from \\(+0.44\\) to",
   "paper_text": "approximately follows $\\lambda_1+\\ln|1-2c|$ from $+0.44$ to $-0.82$",
   "paper_line": 3755,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0010",
   "section": "Synchronization",
   "claim": "largest discrepancy of the measured transverse exponent from the prediction, 0.051 per step (paper fcf2d462)",
   "appears_as": "\\(-0.82\\): the largest discrepancy is 0.051 per step, up to four times the twins'",
   "paper_text": "the largest discrepancy is 0.051 per step, up to four times the twins' own standard errors",
   "paper_line": 3755,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0011",
   "section": "Synchronization",
   "claim": "number 0.051 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-0.82\\): the largest discrepancy is 0.051 per step, up to four times the twins'",
   "paper_text": "from $+0.44$ to $-0.82$: the largest discrepancy is 0.051 per step",
   "paper_line": 3755,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0012",
   "section": "Synchronization",
   "claim": "number 0.045 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "synchronized between \\(c = 0.045\\)",
   "paper_text": "synchronized between $c=0.045$ and 0.05 in 10,000-step runs, consistent with $c^*$",
   "paper_line": 3758,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0013",
   "section": "Synchronization",
   "claim": "number 0.05 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and 0.05, consistent with the predicted",
   "paper_text": "and 0.05 in 10,000-step runs, consistent with $c^*$",
   "paper_line": 3758,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0014",
   "section": "Synchronization",
   "claim": "number 0.18 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "copies synchronized between 0.18 and 0.19, when",
   "paper_text": "second they synchronized between 0.18 and 0.19 when ``synchronized''",
   "paper_line": 3758,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0015",
   "section": "Synchronization",
   "claim": "number 0.19 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "synchronized between 0.18 and 0.19, when",
   "paper_text": "synchronized between 0.18 and 0.19 when ``synchronized'' means",
   "paper_line": 3759,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0016",
   "section": "Synchronization",
   "claim": "number 10^{-6} in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "means a difference below \\(10^{-6}\\), consistent with \\(c^*\\);",
   "paper_text": "``synchronized'' means a difference below $10^{-6}$, consistent with $c^*$; on",
   "paper_line": 3759,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0017",
   "section": "Synchronization",
   "claim": "number 10^{-8} in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "stricter criterion of \\(10^{-8}\\) they had not synchronized",
   "paper_text": "the stricter criterion of $10^{-8}$ they had not synchronized",
   "paper_line": 3760,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0018",
   "section": "Synchronization",
   "claim": "number 0.19 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the stricter criterion of \\(10^{-8}\\) they had not synchronized by 0.19. Just below",
   "paper_text": "they had not synchronized by 0.19. Just below its predicted threshold",
   "paper_line": 3760,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0019",
   "section": "Synchronization",
   "claim": "number 0.16 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(c = 0.16\\) to 0.17, the difference",
   "paper_text": "Just below its predicted threshold, at $c=0.16$ to 0.17, the difference rose from below",
   "paper_line": 3760,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0020",
   "section": "Synchronization",
   "claim": "number 0.17 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(10^{-8}\\) to above \\(10^{-3}\\) 12 to 14 times in 10,000 steps",
   "paper_text": "the difference rose from below $10^{-8}$ to above $10^{-3}$ 12 to 14 times in 10,000 steps",
   "paper_line": 3761,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0021",
   "section": "Synchronization",
   "claim": "number 12 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(10^{-8}\\) to above \\(10^{-3}\\) 12 to 14 times in 10,000 steps",
   "paper_text": "the difference rose from below $10^{-8}$ to above $10^{-3}$ 12 to 14 times in 10,000 steps",
   "paper_line": 3761,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0022",
   "section": "Synchronization",
   "claim": "number 14 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(10^{-8}\\) to above \\(10^{-3}\\) 12 to 14 times in 10,000 steps",
   "paper_text": "the difference rose from below $10^{-8}$ to above $10^{-3}$ 12 to 14 times in 10,000 steps",
   "paper_line": 3761,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0023",
   "section": "Synchronization",
   "claim": "number 10,000 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(10^{-8}\\) to above \\(10^{-3}\\) 12 to 14 times in 10,000 steps",
   "paper_text": "the difference rose from below $10^{-8}$ to above $10^{-3}$ 12 to 14 times in 10,000 steps",
   "paper_line": 3761,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0024",
   "section": "Synchronization",
   "claim": "number -1.8 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "slopes lay between about \\(-1.8\\) and \\(-1.5\\), close to",
   "paper_text": "log-binned slopes lay between about $-1.8$ and $-1.5$, close to $-3/2$;",
   "paper_line": 3762,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0025",
   "section": "Synchronization",
   "claim": "number -1.5 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "between about \\(-1.8\\) and \\(-1.5\\), close to \\(-3/2\\).",
   "paper_text": "lay between about $-1.8$ and $-1.5$, close to $-3/2$; these descriptive",
   "paper_line": 3762,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0026",
   "section": "Synchronization",
   "claim": "third cell: synchronized between 0.15 and 0.16 (3000 steps) and between 0.12 and 0.15 (10,000 steps) on the 1e-8 criterion (paper fcf2d462)",
   "appears_as": "predicted 0.089: between 0.15 and 0.16 in 3000-step runs, and between 0.12 and 0.15",
   "paper_text": "between 0.15 and 0.16 in 3000-step runs and between 0.12 and 0.15 in 10,000-step runs on the $10^{-8}$ criterion",
   "paper_line": 3764,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0027",
   "section": "Synchronization",
   "claim": "third cell: synchronized between 0.15 and 0.16 (3000 steps) and between 0.12 and 0.15 (10,000 steps) on the 1e-8 criterion (paper fcf2d462)",
   "appears_as": "predicted 0.089: between 0.15 and 0.16 in 3000-step runs, and between 0.12 and 0.15",
   "paper_text": "between 0.15 and 0.16 in 3000-step runs and between 0.12 and 0.15 in 10,000-step runs on the $10^{-8}$ criterion",
   "paper_line": 3764,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0028",
   "section": "Synchronization",
   "claim": "number 0.089 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "predicted 0.089: between 0.15 and 0.16 in 3000-step runs, and between 0.12 and 0.15",
   "paper_text": "that $c^*=0.046$, 0.177 and 0.089 (Figure~\\ref{fig:sync}",
   "paper_line": 3745,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0029",
   "section": "Synchronization",
   "claim": "number 0.105 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(c = 0.105\\) to 0.115, where the difference",
   "paper_text": "At $c=0.105$ to 0.115, where the difference should shrink on average",
   "paper_line": 3765,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0030",
   "section": "Synchronization",
   "claim": "number 0.115 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(c = 0.105\\) to 0.115, where the difference should",
   "paper_text": "At $c=0.105$ to 0.115, where the difference should shrink on average",
   "paper_line": 3765,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0031",
   "section": "Synchronization",
   "claim": "number 10^{-14} in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "still burst from the rounding level (\\(10^{-14}\\)) to above \\(10^{-3}\\), 5 to 10",
   "paper_text": "burst from the rounding level ($10^{-14}$) to above $10^{-3}$, 5 to 10 times in 10,000 steps, consistent with attractor bubbling",
   "paper_line": 3766,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0032",
   "section": "Synchronization",
   "claim": "number 10 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "still burst from the rounding level (\\(10^{-14}\\)) to above \\(10^{-3}\\), 5 to 10",
   "paper_text": "burst from the rounding level ($10^{-14}$) to above $10^{-3}$, 5 to 10 times in 10,000 steps, consistent with attractor bubbling",
   "paper_line": 3766,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0033",
   "section": "Synchronization",
   "claim": "number 10,000 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "times in 10,000 steps, consistent with attractor bubbling.",
   "paper_text": "burst from the rounding level ($10^{-14}$) to above $10^{-3}$, 5 to 10 times in 10,000 steps, consistent with attractor bubbling",
   "paper_line": 3766,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0034",
   "section": "Synchronization",
   "claim": "rounding difference between two identical inputs in one batch, up to 9e-16 relative (paper fcf2d462)",
   "appears_as": "inputs in one batch give outputs that differ by up to \\(9\\times10^{-16}\\) relative.",
   "paper_text": "Two identical inputs in one batch give outputs that differ by up to $9\\times10^{-16}$ relative",
   "paper_line": 3768,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0035",
   "section": "Synchronization",
   "claim": "number 12 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "joint state (periods 6 to 12,",
   "paper_text": "the joint state (periods 6 to 12, verified to close within $2.2\\times10^{-13}$),",
   "paper_line": 3772,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0036",
   "section": "Synchronization",
   "claim": "number 2.2\\times10^{-13} in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "verified to close within \\(2.2\\times10^{-13}\\)), on which the two copies",
   "paper_text": "12, verified to close within $2.2\\times10^{-13}$), on which the two copies",
   "paper_line": 3772,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0037",
   "section": "Synchronization",
   "claim": "number 0.25 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "fixed map, and at \\(c = 0.25\\) they barely synchronized",
   "paper_text": "copies of a fixed map, and at $c=0.25$ they barely synchronized although",
   "paper_line": 3813,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0038",
   "section": "Synchronization",
   "claim": "number 0.25 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(c = 0.25\\) exceeds \\(c^*\\) for all",
   "paper_text": "barely synchronized although $c=0.25$ exceeds $c^*$ for all three",
   "paper_line": 3813,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0039",
   "section": "Synchronization",
   "claim": "number 12 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "philosophy direction, layer 12, float64). (a) Mean relative",
   "paper_text": "philosophy direction, layer 12, float64). (a) Mean relative",
   "paper_line": 3818,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0040",
   "section": "Synchronization",
   "claim": "number 0.165 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the second cell (\\(c = 0.165\\)): long synchronized stretches",
   "paper_text": "threshold of the second cell ($c=0.165$). (d) Bursts above the predicted",
   "paper_line": 3822,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync-0041",
   "section": "Synchronization",
   "claim": "number 0.115 in 'Synchronization' (generated: post phrase matched to the paper's source text)",
   "appears_as": "in the third cell (\\(c = 0.115\\)), consistent with attractor bubbling.",
   "paper_text": "threshold in the third cell ($c=0.115$), as in attractor bubbling.}",
   "paper_line": 3823,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0000",
   "section": "Derivative check and Hopfield proof",
   "claim": "number 12 in 'Derivative check and Hopfield proof' (generated: post phrase matched to the paper's source text)",
   "appears_as": "philosophy direction at layer 12, \\(\\alpha = 0.071674\\),",
   "paper_text": "philosophy direction at layer 12, $\\alpha=0.071674$, $\\log_{10}T=-0.115$,",
   "paper_line": 460,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0001",
   "section": "Derivative check and Hopfield proof",
   "claim": "number 0.071674 in 'Derivative check and Hopfield proof' (generated: post phrase matched to the paper's source text) (paper 602c70ac)",
   "appears_as": "at layer 12, \\(\\alpha = 0.071674\\), \\(\\log_{10}T = -0.115\\),",
   "paper_text": "direction at layer 12, $\\alpha=0.071674$, $\\log_{10}T=-0.115$, float64), in eight random unit directions",
   "paper_line": 460,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0002",
   "section": "Derivative check and Hopfield proof",
   "claim": "number -0.115 in 'Derivative check and Hopfield proof' (generated: post phrase matched to the paper's source text) (paper 602c70ac)",
   "appears_as": "0.071674\\), \\(\\log_{10}T = -0.115\\), float64), in eight random unit directions",
   "paper_text": "$\\alpha=0.071674$, $\\log_{10}T=-0.115$, float64), in eight random unit directions $u$",
   "paper_line": 460,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0003",
   "section": "Derivative check and Hopfield proof",
   "claim": "number 1.98 in 'Derivative check and Hopfield proof' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(dashed line, slope 2; fitted slopes 1.98 to 2.00 for \\(10^{-4} \\le h \\le 10^{-2}\\))",
   "paper_text": "(dashed line, slope 2; fitted slopes 1.98 to 2.00 for $10^{-4}\\le h\\le10^{-2}$)",
   "paper_line": 463,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0004",
   "section": "Derivative check and Hopfield proof",
   "claim": "number 2.00 in 'Derivative check and Hopfield proof' (generated: post phrase matched to the paper's source text)",
   "appears_as": "fitted slopes 1.98 to 2.00 for \\(10^{-4} \\le h \\le",
   "paper_text": "fitted slopes 1.98 to 2.00 for $10^{-4}\\le h\\le10^{-2}$);",
   "paper_line": 463,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0005",
   "section": "Derivative check and Hopfield proof",
   "claim": "number 10^{-4} in 'Derivative check and Hopfield proof' (generated: post phrase matched to the paper's source text)",
   "appears_as": "slopes 1.98 to 2.00 for \\(10^{-4} \\le h \\le 10^{-2}\\)). On the left",
   "paper_text": "slopes 1.98 to 2.00 for $10^{-4}\\le h\\le10^{-2}$); below $h\\approx3\\times10^{-6}$ rounding takes over",
   "paper_line": 463,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0006",
   "section": "Derivative check and Hopfield proof",
   "claim": "number 10^{-2} in 'Derivative check and Hopfield proof' (generated: post phrase matched to the paper's source text)",
   "appears_as": "for \\(10^{-4} \\le h \\le 10^{-2}\\)). On the left, a small step",
   "paper_text": "for $10^{-4}\\le h\\le10^{-2}$); below $h\\approx3\\times10^{-6}$",
   "paper_line": 463,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0007",
   "section": "Derivative check and Hopfield proof",
   "claim": "number 3\\times10^{-6} in 'Derivative check and Hopfield proof' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Rounding takes over below \\(h \\approx 3\\times10^{-6}\\)",
   "paper_text": "below $h\\approx3\\times10^{-6}$ rounding takes over and the error grows like $1/h$",
   "paper_line": 463,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0008",
   "section": "Derivative check and Hopfield proof",
   "claim": "number 1.7\\times10^{-9} in 'Derivative check and Hopfield proof' (generated: post phrase matched to the paper's source text) (paper 602c70ac)",
   "appears_as": "each direction's best central difference (open circles, \\(1.7\\times10^{-9}\\) to \\(4.8\\times10^{-9}\\))",
   "paper_text": "best central difference (open circles, $1.7\\times10^{-9}$ to $4.8\\times10^{-9}$)",
   "paper_line": 464,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0009",
   "section": "Derivative check and Hopfield proof",
   "claim": "number 4.8\\times10^{-9} in 'Derivative check and Hopfield proof' (generated: post phrase matched to the paper's source text) (paper 602c70ac)",
   "appears_as": "(open circles, \\(1.7\\times10^{-9}\\) to \\(4.8\\times10^{-9}\\)) beside the factorized derivative",
   "paper_text": "(open circles, $1.7\\times10^{-9}$ to $4.8\\times10^{-9}$) and the factorized derivative",
   "paper_line": 465,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0010",
   "section": "Derivative check and Hopfield proof",
   "claim": "number 3.8\\times10^{-14} in 'Derivative check and Hopfield proof' (generated: post phrase matched to the paper's source text) (paper 602c70ac)",
   "appears_as": "(filled orange dots, \\(3.8\\times10^{-14}\\) to \\(1.35\\times10^{-13}\\))",
   "paper_text": "(filled, $3.8\\times10^{-14}$ to $1.35\\times10^{-13}$)",
   "paper_line": 466,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0011",
   "section": "Derivative check and Hopfield proof",
   "claim": "number 1.35\\times10^{-13} in 'Derivative check and Hopfield proof' (generated: post phrase matched to the paper's source text) (paper 602c70ac)",
   "appears_as": "\\(3.8\\times10^{-14}\\) to \\(1.35\\times10^{-13}\\)). The formula has no step to choose",
   "paper_text": "(filled, $3.8\\times10^{-14}$ to $1.35\\times10^{-13}$), which has no step size",
   "paper_line": 466,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0012",
   "section": "Why the loop can be chaotic",
   "claim": "number 12 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "philosophy direction at layer 12, \\(\\alpha = 0.071674\\)),",
   "paper_text": "philosophy direction at layer 12, $\\alpha=0.071674$, $\\log_{10}T=-0.115$,",
   "paper_line": 460,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0013",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.071674 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at layer 12, \\(\\alpha = 0.071674\\)), with only the temperature",
   "paper_text": "12, $\\alpha=0.071674$), with only the temperature",
   "paper_line": 8,
   "paper_file": "paper/llm/figures/fig-readout-gain.tex"
  },
  {
   "id": "theory-0014",
   "section": "Why the loop can be chaotic",
   "claim": "number -1.27 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "peaks lie at \\(\\log_{10}T = -1.27\\) (\\(x_1\\), \\(g = 0.68\\)),",
   "paper_text": "The peaks lie at $\\log_{10}T=-1.27$ ($x_1$,",
   "paper_line": 12,
   "paper_file": "paper/llm/figures/fig-readout-gain.tex"
  },
  {
   "id": "theory-0015",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.68 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "-1.27\\) (\\(x_1\\), \\(g = 0.68\\)), \\(-0.16\\) (\\(x_0\\),",
   "paper_text": "$0.23$. Only at $1.25$ (size $0.68$) does it fall, to $0.300$.",
   "paper_line": 3619,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0016",
   "section": "Why the loop can be chaotic",
   "claim": "number -0.16 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(\\(x_1\\), \\(g = 0.68\\)), \\(-0.16\\) (\\(x_0\\), 0.059) and",
   "paper_text": "The peaks lie at $\\log_{10}T=-1.27$ ($x_1$,",
   "paper_line": 12,
   "paper_file": "paper/llm/figures/fig-readout-gain.tex"
  },
  {
   "id": "theory-0017",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.059 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.68\\)), \\(-0.16\\) (\\(x_0\\), 0.059) and 0.15 (\\(x_6\\), 0.028);",
   "paper_text": "Jacobians, has norm between 0.059 and 0.644, depending on the",
   "paper_line": 581,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0018",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.15 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-0.16\\) (\\(x_0\\), 0.059) and 0.15 (\\(x_6\\), 0.028); the vertical",
   "paper_text": "(for the 72B, entropy at most 0.15 nats up to $T=2$). In OLMo-2,",
   "paper_line": 3397,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0019",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.028 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.059) and 0.15 (\\(x_6\\), 0.028); the vertical line marks",
   "paper_text": "leading multiplier stays above $0.028$ in modulus. And the X-shaped",
   "paper_line": 4886,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0020",
   "section": "Why the loop can be chaotic",
   "claim": "number -0.115 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "temperature, \\(\\log_{10}T = -0.115\\). Where the two leading",
   "paper_text": "$\\alpha=0.071674$ and $\\log_{10}T=-0.115$, read as exact binary64 rationals",
   "paper_line": 5828,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0021",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.064 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "orbit's temperature \\(g \\le 0.064\\) at all eight states,",
   "paper_text": "weakly steered ($\\alpha\\lesssim0.064$) and the other is not, the",
   "paper_line": 3685,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0022",
   "section": "Why the loop can be chaotic",
   "claim": "number 1.2 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of \\(DF\\) lies between 1.2 and 21. Source: byte-identical",
   "paper_text": "value of $DF$ lies between 1.2 and 21 at every step, so every",
   "paper_line": 578,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0023",
   "section": "Why the loop can be chaotic",
   "claim": "number 21 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(DF\\) lies between 1.2 and 21. Source: byte-identical",
   "paper_text": "of $DF$ lies between 1.2 and 21 at every step, so every step",
   "paper_line": 578,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0024",
   "section": "Why the loop can be chaotic",
   "claim": "number -0.20 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "between \\(\\log_{10}T = -0.20\\) and 0.28. This band is an observation",
   "paper_text": "band lies between $\\log_{10}T=-0.20$ and $0.28$. This band is an observation;",
   "paper_line": 566,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0025",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.28 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = -0.20\\) and 0.28. This band",
   "paper_text": "between $\\log_{10}T=-0.20$ and $0.28$. This band is an observation",
   "paper_line": 566,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0026",
   "section": "Why the loop can be chaotic",
   "claim": "number 1547 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Below the bands, all 1547 temperatures",
   "paper_text": "Below the bands, all 1547 temperatures swept have negative exponents",
   "paper_line": 567,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0027",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.3 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "sweeps at \\(\\log_{10}T = 0.3\\), 127 of 128 temperatures",
   "paper_text": "of the sweeps at $\\log_{10}T=0.3$, 127 of 128 temperatures have",
   "paper_line": 569,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0028",
   "section": "Why the loop can be chaotic",
   "claim": "number 127 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at \\(\\log_{10}T = 0.3\\), 127 of 128 temperatures have",
   "paper_text": "sweeps at $\\log_{10}T=0.3$, 127 of 128 temperatures have a",
   "paper_line": 569,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0029",
   "section": "Why the loop can be chaotic",
   "claim": "number 128 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = 0.3\\), 127 of 128 temperatures have a",
   "paper_text": "at $\\log_{10}T=0.3$, 127 of 128 temperatures have a detected",
   "paper_line": 569,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0030",
   "section": "Why the loop can be chaotic",
   "claim": "number 101 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "period (fixed points at 101) and one has a negative",
   "paper_text": "detected period (fixed points at 101) and one has a negative exponent",
   "paper_line": 569,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0031",
   "section": "Why the loop can be chaotic",
   "claim": "number -0.42 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "entropy (at \\(\\log_{10}T = -0.42\\), \\(-0.41\\) and",
   "paper_text": "of entropy (at $\\log_{10}T=-0.42$, $-0.41$ and $-0.07$; one",
   "paper_line": 571,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0032",
   "section": "Why the loop can be chaotic",
   "claim": "number -0.41 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = -0.42\\), \\(-0.41\\) and",
   "paper_text": "entropy (at $\\log_{10}T=-0.42$, $-0.41$ and $-0.07$; one twin offset).",
   "paper_line": 571,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0033",
   "section": "Why the loop can be chaotic",
   "claim": "number -0.07 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-0.07\\); one twin offset). A",
   "paper_text": "$\\log_{10}T=-0.42$, $-0.41$ and $-0.07$; one twin offset). A further",
   "paper_line": 571,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0034",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.3 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = 0.3\\) to 1.5 finds an attracting",
   "paper_text": "unsteered 0.5B map from $\\log_{10}T=0.3$ to $1.5$ finds an attracting",
   "paper_line": 572,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0035",
   "section": "Why the loop can be chaotic",
   "claim": "number 1.5 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = 0.3\\) to 1.5 finds an attracting fixed",
   "paper_text": "map from $\\log_{10}T=0.3$ to $1.5$ finds an attracting fixed",
   "paper_line": 572,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0036",
   "section": "Why the loop can be chaotic",
   "claim": "number 25 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "attracting fixed point at all 25",
   "paper_text": "attracting fixed point at all 25 temperatures. Its entropy approaches",
   "paper_line": 573,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0037",
   "section": "Why the loop can be chaotic",
   "claim": "number 11.928 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "distribution over the vocabulary (11.928 against 11.931 nats at",
   "paper_text": "entropy approaches $\\log V$ (11.928 against 11.931 nats at $\\log_{10}T=1.5$),",
   "paper_line": 573,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0038",
   "section": "Why the loop can be chaotic",
   "claim": "number 11.931 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "vocabulary (11.928 against 11.931 nats at",
   "paper_text": "approaches $\\log V$ (11.928 against 11.931 nats at $\\log_{10}T=1.5$),",
   "paper_line": 573,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0039",
   "section": "Why the loop can be chaotic",
   "claim": "number 1.5 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = 1.5\\)), and its exponent falls",
   "paper_text": "11.931 nats at $\\log_{10}T=1.5$), and its exponent falls steadily,",
   "paper_line": 574,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0040",
   "section": "Why the loop can be chaotic",
   "claim": "number 2.14 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "exponent falls steadily, by 2.14 per decade of",
   "paper_text": "exponent falls steadily, by 2.14 per decade of temperature at",
   "paper_line": 574,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0041",
   "section": "Why the loop can be chaotic",
   "claim": "number -2.30 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "slope \\(-\\ln10 \\approx -2.30\\)",
   "paper_text": "toward the slope $-\\ln10\\approx-2.30$ expected once $p$ is uniform.",
   "paper_line": 575,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0042",
   "section": "Why the loop can be chaotic",
   "claim": "number 1.2 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of \\(DF\\) lies between 1.2 and 21 at",
   "paper_text": "value of $DF$ lies between 1.2 and 21 at every step, so every",
   "paper_line": 578,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0043",
   "section": "Why the loop can be chaotic",
   "claim": "number 21 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(DF\\) lies between 1.2 and 21 at",
   "paper_text": "of $DF$ lies between 1.2 and 21 at every step, so every step",
   "paper_line": 578,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0044",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.15 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "singular value is at least 0.15 of the first, and the second",
   "paper_text": "singular value is at least 0.15 of the first, and the second",
   "paper_line": 579,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0045",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.23 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\Sigma_p\\) is at least 0.23 of the first (minimum 0.236).",
   "paper_text": "eigenvalue of $\\Sigma_p$ is at least 0.23 of the first (minimum 0.236).",
   "paper_line": 580,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0046",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.236 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.23 of the first (minimum 0.236). Yet the",
   "paper_text": "0.23 of the first (minimum 0.236). Yet the Jacobian of the whole",
   "paper_line": 580,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0047",
   "section": "Why the loop can be chaotic",
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   "section": "Why the loop can be chaotic",
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  {
   "id": "theory-0050",
   "section": "Why the loop can be chaotic",
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   "id": "theory-0051",
   "section": "Why the loop can be chaotic",
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  {
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   "section": "Why the loop can be chaotic",
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  {
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   "section": "Why the loop can be chaotic",
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  {
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   "section": "Why the loop can be chaotic",
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  {
   "id": "theory-0055",
   "section": "Why the loop can be chaotic",
   "claim": "number 16 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
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  {
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   "section": "Why the loop can be chaotic",
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  {
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  {
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   "section": "Why the loop can be chaotic",
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  {
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   "section": "Why the loop can be chaotic",
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  {
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   "section": "Why the loop can be chaotic",
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  {
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   "section": "Why the loop can be chaotic",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "theory-0064",
   "section": "Why the loop can be chaotic",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Why the loop can be chaotic",
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  {
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   "section": "Why the loop can be chaotic",
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  {
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   "section": "Why the loop can be chaotic",
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  {
   "id": "theory-0068",
   "section": "Why the loop can be chaotic",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Why the loop can be chaotic",
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  {
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   "section": "Why the loop can be chaotic",
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  {
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   "section": "Why the loop can be chaotic",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Why the loop can be chaotic",
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   "paper_text": "differs by only $-0.07$ $[-0.23,0.12]$. With nearly no steering",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Why the loop can be chaotic",
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  {
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   "section": "Why the loop can be chaotic",
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  {
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   "section": "Why the loop can be chaotic",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Why the loop can be chaotic",
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   "paper_text": "($\\log_{10}T=0.175$--$0.225$), where it still shrinks them, but less",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Why the loop can be chaotic",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Why the loop can be chaotic",
   "claim": "number 1.26 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "next-token entropy (+1.62 nats, [1.26, 1.91]), a smaller gap",
   "paper_text": "next-token entropy ($+1.62$ nats, $[1.26,1.91]$), a smaller gap between",
   "paper_line": 712,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0079",
   "section": "Why the loop can be chaotic",
   "claim": "number 1.91 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "entropy (+1.62 nats, [1.26, 1.91]), a smaller gap",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "theory-0080",
   "section": "Why the loop can be chaotic",
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   "paper_line": 712,
   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Why the loop can be chaotic",
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   "paper_line": 713,
   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Why the loop can be chaotic",
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   "paper_file": "paper/llm/main.tex"
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   "section": "Why the loop can be chaotic",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Why the loop can be chaotic",
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   "paper_line": 713,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "theory-0085",
   "section": "Why the loop can be chaotic",
   "claim": "number 1.93 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "readout factor (+1.36, [0.91, 1.93]), each with \\(p \\le 10^{-4}\\)",
   "paper_text": "readout factor ($+1.36$, $[0.91,1.93]$), each with $p\\le10^{-4}$",
   "paper_line": 713,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "theory-0086",
   "section": "Why the loop can be chaotic",
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   "paper_file": "paper/llm/main.tex"
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  {
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   "section": "Why the loop can be chaotic",
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   "appears_as": "On its grid, 3.5% of cells were chaotic",
   "paper_text": "On its grid, 3.5\\,\\% of cells were chaotic",
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   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0088",
   "section": "Why the loop can be chaotic",
   "claim": "number 241 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text) (paper 1e8e82f4)",
   "appears_as": "3.5% of cells were chaotic (241 of 6837, all but one with a",
   "paper_text": "3.5\\,\\% of cells were chaotic (241 of 6837, all but one with a nonzero bias)",
   "paper_line": 719,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0089",
   "section": "Why the loop can be chaotic",
   "claim": "number 6837 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text) (paper 1e8e82f4)",
   "appears_as": "were chaotic (241 of 6837, all but one",
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   "paper_line": 719,
   "paper_file": "paper/llm/main.tex"
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  {
   "id": "theory-0090",
   "section": "Why the loop can be chaotic",
   "claim": "number 6.2 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "against 6.2% on the residual-steering grid",
   "paper_text": "against 6.2\\,\\% on the residual-steering grid",
   "paper_line": 720,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0091",
   "section": "Why the loop can be chaotic",
   "claim": "logit bias only: its chaotic cells lie mostly at log10 T >= 0.1 (paper 1e8e82f4)",
   "appears_as": "mostly at \\(\\log_{10}T \\ge 0.1\\) (207 of the 241 cells)",
   "paper_text": "of the plane, mostly at $\\log_{10}T\\ge0.1$ (207 of the 241 cells)",
   "paper_line": 723,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0092",
   "section": "Why the loop can be chaotic",
   "claim": "number 11 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "network Jacobian (call them 11, 10, 01 and 00, readout",
   "paper_text": "unsteered network Jacobian: arms 11, 10, 01 and 00. The hybrid",
   "paper_line": 730,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0093",
   "section": "Why the loop can be chaotic",
   "claim": "number 10 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Jacobian (call them 11, 10, 01 and 00, readout first).",
   "paper_text": "network Jacobian: arms 11, 10, 01 and 00. The hybrid arms 10 and 01",
   "paper_line": 730,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0094",
   "section": "Why the loop can be chaotic",
   "claim": "number 01 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text) (paper 1e8e82f4)",
   "appears_as": "Jacobian (call them 11, 10, 01 and 00, readout first).",
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   "paper_line": 730,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0095",
   "section": "Why the loop can be chaotic",
   "claim": "number 00 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(call them 11, 10, 01 and 00, readout first). A",
   "paper_text": "Jacobian: arms 11, 10, 01 and 00. The hybrid arms",
   "paper_line": 730,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0096",
   "section": "Why the loop can be chaotic",
   "claim": "number 11 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the fully steered version 11 reproduce the twin",
   "paper_text": "The frozen validation (arm 11 within $0.02$ of the twin exponent at every cell)",
   "paper_line": 732,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0097",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.02 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "exponent within 0.02 at every cell, holds at",
   "paper_text": "validation (arm 11 within $0.02$ of the twin exponent at every",
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   "paper_file": "paper/llm/main.tex"
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  {
   "id": "theory-0098",
   "section": "Why the loop can be chaotic",
   "claim": "number 23 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at every cell, holds at 23 of 24 cells, all within",
   "paper_text": "exponent at every cell) holds at 23 of 24 cells, all within $0.012$;",
   "paper_line": 733,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0099",
   "section": "Why the loop can be chaotic",
   "claim": "number 24 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "every cell, holds at 23 of 24 cells, all within 0.012;",
   "paper_text": "every cell) holds at 23 of 24 cells, all within $0.012$;",
   "paper_line": 733,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0100",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.012 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of 24 cells, all within 0.012; at",
   "paper_text": "23 of 24 cells, all within $0.012$; at the remaining periodic",
   "paper_line": 733,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0101",
   "section": "Why the loop can be chaotic",
   "claim": "number -12 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "which contracts at about \\(-12\\) per step, the twin",
   "paper_text": "cell, which contracts at about $-12$ per step, the twin offset",
   "paper_line": 734,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0102",
   "section": "Why the loop can be chaotic",
   "claim": "number 10 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "version 10 come within 0.1 of version",
   "paper_text": "sufficiency criterion (arm 10 within $0.1$ of arm 11 on average)",
   "paper_line": 735,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0103",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.1 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "version 10 come within 0.1 of version 11 on average,",
   "paper_text": "sufficiency criterion (arm 10 within $0.1$ of arm 11 on average) fails",
   "paper_line": 735,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0104",
   "section": "Why the loop can be chaotic",
   "claim": "number 11 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "come within 0.1 of version 11 on average, fails by overshoot:",
   "paper_text": "(arm 10 within $0.1$ of arm 11 on average) fails by overshoot:",
   "paper_line": 735,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0105",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.23 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the full steered map, by 0.23, because",
   "paper_text": "than the full steered map, by $0.23$, because steering's change",
   "paper_line": 736,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0106",
   "section": "Why the loop can be chaotic",
   "claim": "number 14 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Over 14 chaotic cells reserved",
   "paper_text": "Over 14 held-out chaotic cells, the steered readout factor",
   "paper_line": 736,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0107",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.81 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "growth by 0.81 nats per step ([0.29, 1.35]);",
   "paper_text": "raises the finite-time growth by $0.81$ nats per step ($[0.29,1.35]$).",
   "paper_line": 737,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0108",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.29 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "by 0.81 nats per step ([0.29, 1.35]); steering only",
   "paper_text": "by $0.81$ nats per step ($[0.29,1.35]$). The steered network factor",
   "paper_line": 737,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0109",
   "section": "Why the loop can be chaotic",
   "claim": "number 1.35 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.81 nats per step ([0.29, 1.35]); steering only the network",
   "paper_text": "$0.81$ nats per step ($[0.29,1.35]$). The steered network factor with the unsteered readout",
   "paper_line": 737,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0110",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.49 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "lowers it by 0.49 ([−0.63, −0.35]); the interaction",
   "paper_text": "lowers it by $0.49$ ($[-0.63,-0.35]$). The interaction is",
   "paper_line": 738,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0111",
   "section": "Why the loop can be chaotic",
   "claim": "number −0.63 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "lowers it by 0.49 ([−0.63, −0.35]); the interaction",
   "paper_text": "(steering only the network response) lowers it by $0.49$ ($[-0.63,-0.35]$).",
   "paper_line": 738,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0112",
   "section": "Why the loop can be chaotic",
   "claim": "number −0.35 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "lowers it by 0.49 ([−0.63, −0.35]); the interaction is +0.26",
   "paper_text": "lowers it by $0.49$ ($[-0.63,-0.35]$). The interaction is $+0.26$",
   "paper_line": 738,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0113",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.26 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "−0.35]); the interaction is +0.26",
   "paper_text": "($[-0.63,-0.35]$). The interaction is $+0.26$ ($[0.09,0.45]$). Below $\\log_{10}T=0$",
   "paper_line": 738,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0114",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.09 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "([0.09, 0.45]). Below \\(\\log_{10}T = 0\\)",
   "paper_text": "The interaction is $+0.26$ ($[0.09,0.45]$). Below $\\log_{10}T=0$",
   "paper_line": 738,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0115",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.45 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "([0.09, 0.45]). Below",
   "paper_text": "interaction is $+0.26$ ($[0.09,0.45]$). Below $\\log_{10}T=0$ the",
   "paper_line": 738,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0116",
   "section": "Why the loop can be chaotic",
   "claim": "number −1.03 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(−1.03 nats per step) into growth",
   "paper_text": "the contraction of the unsteered derivative ($-1.03$ nats per step) into growth",
   "paper_line": 739,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0117",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.72 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "into growth (+0.72), more than",
   "paper_text": "into growth ($+0.72$), more than the full steered map shows",
   "paper_line": 740,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0118",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.34 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "steered map shows (+0.34). Above it, the unsteered",
   "paper_text": "more than the full steered map shows ($+0.34$). Above it, the unsteered",
   "paper_line": 740,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0119",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.41 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "steered states (+0.41), and steering may act",
   "paper_text": "expands at the steered states ($+0.41$), and steering may act by",
   "paper_line": 741,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0120",
   "section": "Why the loop can be chaotic",
   "claim": "number 18 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "untied, the same crossover (18 cells of its steered",
   "paper_text": "untied, the same crossover (18 cells of its steered map at",
   "paper_line": 742,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0121",
   "section": "Why the loop can be chaotic",
   "claim": "number 14 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "map at layer 14; version 11 equals the",
   "paper_text": "of its steered map at block 14; arm 11 equals the twin exponent",
   "paper_line": 742,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0122",
   "section": "Why the loop can be chaotic",
   "claim": "number 11 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "map at layer 14; version 11 equals the twin exponent",
   "paper_text": "steered map at block 14; arm 11 equals the twin exponent within",
   "paper_line": 742,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0123",
   "section": "Why the loop can be chaotic",
   "claim": "number 10^{-4} in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "twin exponent within \\(10^{-4}\\) at every",
   "paper_text": "equals the twin exponent within $10^{-4}$ at every cell) reproduces",
   "paper_line": 742,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0124",
   "section": "Why the loop can be chaotic",
   "claim": "number 10 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "reproduces the damping: over its 10 reserved chaotic cells,",
   "paper_text": "reproduces the damping. Over its 10 held-out chaotic cells, steering",
   "paper_line": 743,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0125",
   "section": "Why the loop can be chaotic",
   "claim": "number 1.14 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "response lowers the growth by 1.14 nats per step ([−1.61,",
   "paper_text": "response lowers the growth by $1.14$ nats per step ($[-1.61,-0.64]$),",
   "paper_line": 744,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0126",
   "section": "Why the loop can be chaotic",
   "claim": "number −1.61 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "by 1.14 nats per step ([−1.61, −0.64]), and",
   "paper_text": "by $1.14$ nats per step ($[-1.61,-0.64]$), and steering only",
   "paper_line": 744,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0127",
   "section": "Why the loop can be chaotic",
   "claim": "number −0.64 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "nats per step ([−1.61, −0.64]), and",
   "paper_text": "$1.14$ nats per step ($[-1.61,-0.64]$), and steering only the readout",
   "paper_line": 744,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0128",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.23 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text) (paper 1e8e82f4)",
   "appears_as": "only the readout adds +0.23 ([−0.11, 0.63], an interval that includes",
   "paper_text": "steering only the readout adds $+0.23$ ($[-0.11,0.63]$, an interval that includes zero)",
   "paper_line": 744,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0129",
   "section": "Why the loop can be chaotic",
   "claim": "number −0.11 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text) (paper 1e8e82f4)",
   "appears_as": "the readout adds +0.23 ([−0.11, 0.63], an interval",
   "paper_text": "the readout adds $+0.23$ ($[-0.11,0.63]$, an interval that includes zero). Eight of the ten lie",
   "paper_line": 744,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0130",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.63 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text) (paper 1e8e82f4)",
   "appears_as": "adds +0.23 ([−0.11, 0.63], an interval that",
   "paper_text": "readout adds $+0.23$ ($[-0.11,0.63]$, an interval that includes zero)",
   "paper_line": 744,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0131",
   "section": "Why the loop can be chaotic",
   "claim": "number 1.33 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "states (mean +1.33). Along two more directions",
   "paper_text": "the steered states (mean $+1.33$). The crossover along two",
   "paper_line": 745,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0132",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.33 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the readout effect is +0.33 ([0.07, 0.59]) and the",
   "paper_text": "gratitude the readout effect is $+0.33$ ($[0.07,0.59]$) and the network",
   "paper_line": 746,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0133",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.07 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "readout effect is +0.33 ([0.07, 0.59]) and the network",
   "paper_text": "readout effect is $+0.33$ ($[0.07,0.59]$) and the network effect",
   "paper_line": 746,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0134",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.59 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "effect is +0.33 ([0.07, 0.59]) and the network effect",
   "paper_text": "readout effect is $+0.33$ ($[0.07,0.59]$) and the network effect $-0.14$",
   "paper_line": 746,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0135",
   "section": "Why the loop can be chaotic",
   "claim": "number −0.14 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "−0.14 ([−0.29, 0.01]); for a",
   "paper_text": "($[0.07,0.59]$) and the network effect $-0.14$ ($[-0.29,0.01]$). For a random",
   "paper_line": 746,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0136",
   "section": "Why the loop can be chaotic",
   "claim": "number −0.29 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "−0.14 ([−0.29, 0.01]); for a random direction",
   "paper_text": "the network effect $-0.14$ ($[-0.29,0.01]$). For a random direction",
   "paper_line": 746,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0137",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.01 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "−0.14 ([−0.29, 0.01]); for a random direction",
   "paper_text": "network effect $-0.14$ ($[-0.29,0.01]$). For a random direction",
   "paper_line": 746,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0138",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.77 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "vector, +0.77 ([0.47, 1.12]) and −0.09",
   "paper_text": "philosophy vector, they are $+0.77$ ($[0.47,1.12]$) and $-0.09$",
   "paper_line": 747,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0139",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.47 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "vector, +0.77 ([0.47, 1.12]) and −0.09 ([−0.22,",
   "paper_text": "vector, they are $+0.77$ ($[0.47,1.12]$) and $-0.09$ ($[-0.22,0.06]$);",
   "paper_line": 747,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0140",
   "section": "Why the loop can be chaotic",
   "claim": "number 1.12 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "vector, +0.77 ([0.47, 1.12]) and −0.09 ([−0.22, 0.06]),",
   "paper_text": "vector, they are $+0.77$ ($[0.47,1.12]$) and $-0.09$ ($[-0.22,0.06]$);",
   "paper_line": 747,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0141",
   "section": "Why the loop can be chaotic",
   "claim": "number −0.09 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "+0.77 ([0.47, 1.12]) and −0.09 ([−0.22, 0.06]), with 14",
   "paper_text": "$+0.77$ ($[0.47,1.12]$) and $-0.09$ ($[-0.22,0.06]$); 14 held-out",
   "paper_line": 747,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0142",
   "section": "Why the loop can be chaotic",
   "claim": "number −0.22 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "([0.47, 1.12]) and −0.09 ([−0.22, 0.06]), with 14 reserved",
   "paper_text": "($[0.47,1.12]$) and $-0.09$ ($[-0.22,0.06]$); 14 held-out chaotic",
   "paper_line": 747,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0143",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.06 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "1.12]) and −0.09 ([−0.22, 0.06]), with 14 reserved chaotic",
   "paper_text": "($[0.47,1.12]$) and $-0.09$ ($[-0.22,0.06]$); 14 held-out chaotic cells",
   "paper_line": 747,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0144",
   "section": "Why the loop can be chaotic",
   "claim": "number 14 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "−0.09 ([−0.22, 0.06]), with 14 reserved chaotic",
   "paper_text": "$-0.09$ ($[-0.22,0.06]$); 14 held-out chaotic cells each",
   "paper_line": 747,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0145",
   "section": "Why the loop can be chaotic",
   "claim": "number 12 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "steering lines at layer 12; dots mark chaotic cells.",
   "paper_text": "along steering lines at block 12, at five temperatures; dots",
   "paper_line": 774,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0146",
   "section": "Why the loop can be chaotic",
   "claim": "number 101 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "unsteered cells (red) on the 101 × 53 map, with 95% bootstrap",
   "paper_text": "unsteered cells (red) on the $101\\times53$ map, with 95\\,\\% bootstrap",
   "paper_line": 776,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0147",
   "section": "Why the loop can be chaotic",
   "claim": "number 53 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "cells (red) on the 101 × 53 map, with 95% bootstrap",
   "paper_text": "cells (red) on the $101\\times53$ map, with 95\\,\\% bootstrap",
   "paper_line": 776,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0148",
   "section": "Why the loop can be chaotic",
   "claim": "number 95 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the 101 × 53 map, with 95% bootstrap intervals over",
   "paper_text": "the $101\\times53$ map, with 95\\,\\% bootstrap intervals over",
   "paper_line": 776,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0149",
   "section": "Why the loop can be chaotic",
   "claim": "number 12 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "residual steering at layer 12 and under a pure logit",
   "paper_text": "residual steering at block 12 and under a pure logit bias",
   "paper_line": 781,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0150",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.01 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text) (paper 1e8e82f4)",
   "appears_as": "nearly unsteered cells, \\(\\lvert\\alpha\\rvert \\le 0.01\\) (dashed lines), chosen by steering strength alone",
   "paper_text": "nearly unsteered cells, $|\\alpha|\\le0.01$ (dashed lines; chosen by steering strength alone",
   "paper_line": 674,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0151",
   "section": "Why the loop can be chaotic",
   "claim": "number 18 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text) (paper 1e8e82f4)",
   "appears_as": "in the 18 temperature rows with at least three cells of each kind: chaotic cells",
   "paper_text": "in the 18 temperature rows with at least three cells of each kind (321 chaotic and 162 nearly unsteered cells",
   "paper_line": 675,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0152",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.87 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "relative gain shrinks differences by 0.87 to 5.49 nats per step;",
   "paper_text": "relative gain shrinks perturbations by 0.87 to 5.49 nats per step;",
   "paper_line": 677,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0153",
   "section": "Why the loop can be chaotic",
   "claim": "number 5.49 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "shrinks differences by 0.87 to 5.49 nats per step; in the chaotic",
   "paper_text": "shrinks perturbations by 0.87 to 5.49 nats per step; in the chaotic cells it grows",
   "paper_line": 677,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0154",
   "section": "Why the loop can be chaotic",
   "claim": "number 12 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text) (paper 602c70ac)",
   "appears_as": "residual steering at layer 12, which moves both factors",
   "paper_text": "residual steering at block 12, which moves both factors",
   "paper_line": 680,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0155",
   "section": "Why the loop can be chaotic",
   "claim": "number 331 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text) (paper 602c70ac)",
   "appears_as": "(black; 331 of 5353 cells, 6.2%)",
   "paper_text": "(black; 331 of 5353 cells, 6.2\\,\\%)",
   "paper_line": 681,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0156",
   "section": "Why the loop can be chaotic",
   "claim": "number 5353 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text) (paper 602c70ac)",
   "appears_as": "331 of 5353 cells, 6.2%), and under a logit",
   "paper_text": "331 of 5353 cells, 6.2\\,\\%), and under a logit bias",
   "paper_line": 681,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0157",
   "section": "Why the loop can be chaotic",
   "claim": "number 241 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text) (paper 602c70ac)",
   "appears_as": "changes only the readout (orange; 241 of 6837 cells, 3.5%)",
   "paper_text": "changes only the readout (orange; 241 of 6837 cells, 3.5\\,\\%)",
   "paper_line": 682,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0158",
   "section": "Why the loop can be chaotic",
   "claim": "number 6837 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text) (paper 602c70ac)",
   "appears_as": "(orange; 241 of 6837 cells, 3.5%). (c) Orbit-preserving",
   "paper_text": "(orange; 241 of 6837 cells, 3.5\\,\\%). (c) Orbit-preserving",
   "paper_line": 682,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0159",
   "section": "Why the loop can be chaotic",
   "claim": "number 95 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text) (paper 602c70ac)",
   "appears_as": "with 95% bootstrap intervals. Rows:",
   "paper_text": "with 95\\,\\% bootstrap intervals. Rows:",
   "paper_line": 685,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0160",
   "section": "Why the loop can be chaotic",
   "claim": "number 95 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| Contrast | Estimate (95% interval) |",
   "paper_text": "measurement & contrast & estimate (95\\,\\% interval) \\\\ \\midrule gain",
   "paper_line": 790,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0161",
   "section": "Why the loop can be chaotic",
   "claim": "number 101 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| Gain split, 101 × 53 scan | readout factor,",
   "paper_text": "interval) \\\\ \\midrule gain split, $101\\times53$ map & readout factor,",
   "paper_line": 790,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0162",
   "section": "Why the loop can be chaotic",
   "claim": "number 53 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| Gain split, 101 × 53 scan | readout factor,",
   "paper_text": "\\midrule gain split, $101\\times53$ map & readout factor, chaotic",
   "paper_line": 791,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0163",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.01 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lvert\\alpha\\rvert \\le 0.01\\) | +2.58 [1.78, 3.59]",
   "paper_text": "factor, chaotic $-$ $|\\alpha|\\le0.01$ & $+2.58$ $[1.78,3.59]$ nats/step",
   "paper_line": 792,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0164",
   "section": "Why the loop can be chaotic",
   "claim": "number 2.58 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lvert\\alpha\\rvert \\le 0.01\\) | +2.58 [1.78, 3.59] nats/step",
   "paper_text": "chaotic $-$ $|\\alpha|\\le0.01$ & $+2.58$ $[1.78,3.59]$ nats/step \\\\",
   "paper_line": 792,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0165",
   "section": "Why the loop can be chaotic",
   "claim": "number 1.78 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lvert\\alpha\\rvert \\le 0.01\\) | +2.58 [1.78, 3.59] nats/step |",
   "paper_text": "$|\\alpha|\\le0.01$ & $+2.58$ $[1.78,3.59]$ nats/step \\\\ & network",
   "paper_line": 792,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0166",
   "section": "Why the loop can be chaotic",
   "claim": "number 3.59 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\le 0.01\\) | +2.58 [1.78, 3.59] nats/step |",
   "paper_text": "$|\\alpha|\\le0.01$ & $+2.58$ $[1.78,3.59]$ nats/step \\\\ & network factor,",
   "paper_line": 792,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0167",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.01 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lvert\\alpha\\rvert \\le 0.01\\) | −0.07 [−0.23, 0.12]",
   "paper_text": "factor, chaotic $-$ $|\\alpha|\\le0.01$ & $+2.58$ $[1.78,3.59]$ nats/step",
   "paper_line": 792,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0168",
   "section": "Why the loop can be chaotic",
   "claim": "number −0.07 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lvert\\alpha\\rvert \\le 0.01\\) | −0.07 [−0.23, 0.12] nats/step",
   "paper_text": "chaotic $-$ $|\\alpha|\\le0.01$ & $-0.07$ $[-0.23,0.12]$ nats/step \\\\",
   "paper_line": 793,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0169",
   "section": "Why the loop can be chaotic",
   "claim": "number −0.23 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lvert\\alpha\\rvert \\le 0.01\\) | −0.07 [−0.23, 0.12] nats/step |",
   "paper_text": "$|\\alpha|\\le0.01$ & $-0.07$ $[-0.23,0.12]$ nats/step \\\\ & entropy,",
   "paper_line": 793,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0170",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.12 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.01\\) | −0.07 [−0.23, 0.12] nats/step |",
   "paper_text": "$|\\alpha|\\le0.01$ & $-0.07$ $[-0.23,0.12]$ nats/step \\\\ & entropy, chaotic",
   "paper_line": 793,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0171",
   "section": "Why the loop can be chaotic",
   "claim": "number 1.62 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "chaotic minus periodic | +1.62 [1.26, 1.91] nats |",
   "paper_text": "higher next-token entropy ($+1.62$ nats, $[1.26,1.91]$), a smaller",
   "paper_line": 712,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0172",
   "section": "Why the loop can be chaotic",
   "claim": "number 1.26 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "minus periodic | +1.62 [1.26, 1.91] nats |",
   "paper_text": "next-token entropy ($+1.62$ nats, $[1.26,1.91]$), a smaller gap between",
   "paper_line": 712,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0173",
   "section": "Why the loop can be chaotic",
   "claim": "number 1.91 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "periodic | +1.62 [1.26, 1.91] nats |",
   "paper_text": "entropy ($+1.62$ nats, $[1.26,1.91]$), a smaller gap between the",
   "paper_line": 712,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0174",
   "section": "Why the loop can be chaotic",
   "claim": "number −1.37 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "chaotic minus periodic | −1.37 [−1.98, −0.87] |",
   "paper_text": "between the two largest logits ($-1.37$ in units of $T$, $[-1.98,-0.87]$)",
   "paper_line": 712,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0175",
   "section": "Why the loop can be chaotic",
   "claim": "number −1.98 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "minus periodic | −1.37 [−1.98, −0.87] |",
   "paper_text": "($-1.37$ in units of $T$, $[-1.98,-0.87]$) and a larger readout",
   "paper_line": 713,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0176",
   "section": "Why the loop can be chaotic",
   "claim": "number −0.87 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "periodic | −1.37 [−1.98, −0.87] |",
   "paper_text": "($-1.37$ in units of $T$, $[-1.98,-0.87]$) and a larger readout factor",
   "paper_line": 713,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0177",
   "section": "Why the loop can be chaotic",
   "claim": "number 3.5 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "steering | chaotic share | 3.5% (241 of 6837 cells) |",
   "paper_text": "$\\alpha=0$ & chaotic share & 3.5\\,\\% (241 of 6837 cells) \\\\",
   "paper_line": 796,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0178",
   "section": "Why the loop can be chaotic",
   "claim": "number 241 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| chaotic share | 3.5% (241 of 6837 cells) |",
   "paper_text": "& chaotic share & 3.5\\,\\% (241 of 6837 cells) \\\\ residual",
   "paper_line": 796,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0179",
   "section": "Why the loop can be chaotic",
   "claim": "number 6837 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "chaotic share | 3.5% (241 of 6837 cells) |",
   "paper_text": "chaotic share & 3.5\\,\\% (241 of 6837 cells) \\\\ residual steering,",
   "paper_line": 796,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0180",
   "section": "Why the loop can be chaotic",
   "claim": "number 12 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Residual steering, layer 12 | chaotic share | 6.2%",
   "paper_text": "\\\\ residual steering, block 12 & chaotic share & 6.2\\,\\% (331",
   "paper_line": 796,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0181",
   "section": "Why the loop can be chaotic",
   "claim": "number 6.2 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "layer 12 | chaotic share | 6.2% (331 of 5353 cells) |",
   "paper_text": "block 12 & chaotic share & 6.2\\,\\% (331 of 5353 cells) \\\\",
   "paper_line": 797,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0182",
   "section": "Why the loop can be chaotic",
   "claim": "number 331 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| chaotic share | 6.2% (331 of 5353 cells) |",
   "paper_text": "& chaotic share & 6.2\\,\\% (331 of 5353 cells) \\\\ crossover,",
   "paper_line": 797,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0183",
   "section": "Why the loop can be chaotic",
   "claim": "number 5353 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "chaotic share | 6.2% (331 of 5353 cells) |",
   "paper_text": "chaotic share & 6.2\\,\\% (331 of 5353 cells) \\\\ crossover, 0.5B,",
   "paper_line": 797,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0184",
   "section": "Why the loop can be chaotic",
   "claim": "number 14 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Crossover, 0.5B, philosophy, 14 cells | readout effect",
   "paper_text": "cells) \\\\ crossover, 0.5B, 14 cells & readout effect, arm",
   "paper_line": 797,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0185",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.81 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "cells | readout effect | +0.81 [0.29, 1.35] nats/step",
   "paper_text": "effect, arm 10 $-$ arm 00 & $+0.81$ $[0.29,1.35]$ nats/step \\\\",
   "paper_line": 798,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0186",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.29 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "readout effect | +0.81 [0.29, 1.35] nats/step |",
   "paper_text": "arm 10 $-$ arm 00 & $+0.81$ $[0.29,1.35]$ nats/step \\\\ & network",
   "paper_line": 798,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0187",
   "section": "Why the loop can be chaotic",
   "claim": "number 1.35 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "readout effect | +0.81 [0.29, 1.35] nats/step |",
   "paper_text": "$-$ arm 00 & $+0.81$ $[0.29,1.35]$ nats/step \\\\ & network effect,",
   "paper_line": 798,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0188",
   "section": "Why the loop can be chaotic",
   "claim": "number −0.49 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| | network effect | −0.49 [−0.63, −0.35] nats/step",
   "paper_text": "effect, arm 01 $-$ arm 00 & $-0.49$ $[-0.63,-0.35]$ nats/step",
   "paper_line": 799,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0189",
   "section": "Why the loop can be chaotic",
   "claim": "number −0.63 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "network effect | −0.49 [−0.63, −0.35] nats/step |",
   "paper_text": "arm 01 $-$ arm 00 & $-0.49$ $[-0.63,-0.35]$ nats/step \\\\ & interaction",
   "paper_line": 799,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0190",
   "section": "Why the loop can be chaotic",
   "claim": "number −0.35 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "effect | −0.49 [−0.63, −0.35] nats/step |",
   "paper_text": "$-$ arm 00 & $-0.49$ $[-0.63,-0.35]$ nats/step \\\\ & interaction",
   "paper_line": 799,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0191",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.26 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| | interaction | +0.26 [0.09, 0.45] nats/step",
   "paper_text": "nats/step \\\\ & interaction & $+0.26$ $[0.09,0.45]$ nats/step \\\\",
   "paper_line": 799,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0192",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.09 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| interaction | +0.26 [0.09, 0.45] nats/step |",
   "paper_text": "\\\\ & interaction & $+0.26$ $[0.09,0.45]$ nats/step \\\\ crossover,",
   "paper_line": 799,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0193",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.45 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "interaction | +0.26 [0.09, 0.45] nats/step |",
   "paper_text": "interaction & $+0.26$ $[0.09,0.45]$ nats/step \\\\ crossover, gratitude",
   "paper_line": 800,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0194",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.33 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "gratitude | readout effect | +0.33 [0.07, 0.59] nats/step",
   "paper_text": "gratitude & readout effect & $+0.33$ $[0.07,0.59]$ nats/step \\\\",
   "paper_line": 801,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0195",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.07 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "readout effect | +0.33 [0.07, 0.59] nats/step |",
   "paper_text": "readout effect & $+0.33$ $[0.07,0.59]$ nats/step \\\\ & network",
   "paper_line": 801,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0196",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.59 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "readout effect | +0.33 [0.07, 0.59] nats/step |",
   "paper_text": "readout effect & $+0.33$ $[0.07,0.59]$ nats/step \\\\ & network effect",
   "paper_line": 801,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0197",
   "section": "Why the loop can be chaotic",
   "claim": "number −0.14 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "| | network effect | −0.14 [−0.29, 0.01] nats/step",
   "paper_text": "nats/step \\\\ & network effect & $-0.14$ $[-0.29,0.01]$ nats/step \\\\",
   "paper_line": 801,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0198",
   "section": "Why the loop can be chaotic",
   "claim": "number −0.29 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "network effect | −0.14 [−0.29, 0.01] nats/step |",
   "paper_text": "network effect & $-0.14$ $[-0.29,0.01]$ nats/step \\\\ crossover,",
   "paper_line": 802,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0199",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.01 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "effect | −0.14 [−0.29, 0.01] nats/step |",
   "paper_text": "network effect & $-0.14$ $[-0.29,0.01]$ nats/step \\\\ crossover, random",
   "paper_line": 802,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0200",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.77 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "direction | readout effect | +0.77 [0.47, 1.12] nats/step",
   "paper_text": "random dir. & readout effect & $+0.77$ $[0.47,1.12]$ nats/step \\\\",
   "paper_line": 803,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0201",
   "section": "Why the loop can be chaotic",
   "claim": "number 0.47 in 'Why the loop can be chaotic' (generated: post phrase matched to the paper's source text)",
   "appears_as": "readout effect | +0.77 [0.47, 1.12] nats/step |",
   "paper_text": "readout effect & $+0.77$ $[0.47,1.12]$ nats/step \\\\ & network",
   "paper_line": 803,
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   "appears_as": "readout effect | +0.77 [0.47, 1.12] nats/step |",
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   "id": "theory-0203",
   "section": "Why the loop can be chaotic",
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  {
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   "appears_as": "network effect | −0.09 [−0.22, 0.06] nats/step |",
   "paper_text": "network effect & $-0.09$ $[-0.22,0.06]$ nats/step \\\\ crossover,",
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   "id": "theory-0205",
   "section": "Why the loop can be chaotic",
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   "appears_as": "effect | −0.09 [−0.22, 0.06] nats/step |",
   "paper_text": "network effect & $-0.09$ $[-0.22,0.06]$ nats/step \\\\ crossover, 7B,",
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  {
   "id": "theory-0206",
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  {
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   "section": "Why the loop can be chaotic",
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   "paper_text": "cells & readout effect & $+0.23$ $[-0.11,0.63]$ nats/step \\\\",
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   "appears_as": "effect | +0.23 [−0.11, 0.63] nats/step |",
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   "appears_as": "effect | −1.14 [−1.61, −0.64] nats/step |",
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   "id": "theory-0219",
   "section": "Why the loop can be chaotic",
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   "id": "theory-0220",
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   "id": "theory-0236",
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   "id": "theory-0240",
   "section": "Where steering enters",
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   "id": "theory-0242",
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   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0253",
   "section": "Where steering enters",
   "claim": "number 0.22 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = -0.09\\) and 0.22,",
   "paper_text": "between $\\log_{10}T=-0.09$ and $0.22$, three fifths of them above",
   "paper_line": 1477,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0254",
   "section": "Where steering enters",
   "claim": "number 0.1 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "three fifths of them above 0.1. In the strip \\(\\lvert\\alpha\\rvert",
   "paper_text": "three fifths of them above $0.1$. In the strip $|\\alpha|<0.02$",
   "paper_line": 1477,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0255",
   "section": "Where steering enters",
   "claim": "number 0.02 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lvert\\alpha\\rvert < 0.02\\) every",
   "paper_text": "$0.1$. In the strip $|\\alpha|<0.02$ every block gives 0.8 to 2.1\\,\\%.",
   "paper_line": 1478,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0256",
   "section": "Where steering enters",
   "claim": "number 0.8 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "layer gives 0.8 to 2.1%. Llama-3.3-70B",
   "paper_text": "$|\\alpha|<0.02$ every block gives 0.8 to 2.1\\,\\%. Llama-3.3-70B behaves",
   "paper_line": 1478,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0257",
   "section": "Where steering enters",
   "claim": "number 2.1 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "layer gives 0.8 to 2.1%. Llama-3.3-70B behaves",
   "paper_text": "$|\\alpha|<0.02$ every block gives 0.8 to 2.1\\,\\%. Llama-3.3-70B behaves",
   "paper_line": 1478,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0258",
   "section": "Where steering enters",
   "claim": "number 8.0 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "direction, it is chaotic in 8.0% of a 24 × 24 map at layer",
   "paper_text": "Section~\\ref{sec:hostile}), it is chaotic in 8.0\\,\\% of a $24\\times24$ map at",
   "paper_line": 1478,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0259",
   "section": "Where steering enters",
   "claim": "number 24 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "is chaotic in 8.0% of a 24 × 24 map at layer 20 of",
   "paper_text": "Middle: Qwen2.5-7B unsteered, 24 chaotic and 24 periodic temperatures",
   "paper_line": 1281,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0260",
   "section": "Where steering enters",
   "claim": "number 24 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "chaotic in 8.0% of a 24 × 24 map at layer 20 of 80,",
   "paper_text": "Middle: Qwen2.5-7B unsteered, 24 chaotic and 24 periodic temperatures",
   "paper_line": 1281,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0261",
   "section": "Where steering enters",
   "claim": "number 20 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "a 24 × 24 map at layer 20 of 80,",
   "paper_text": "a $24\\times24$ map at block 20 of 80, down to $\\log_{10}T=-0.14$,",
   "paper_line": 1479,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0262",
   "section": "Where steering enters",
   "claim": "number 80 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "× 24 map at layer 20 of 80,",
   "paper_text": "$24\\times24$ map at block 20 of 80, down to $\\log_{10}T=-0.14$,",
   "paper_line": 1479,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0263",
   "section": "Where steering enters",
   "claim": "number -0.14 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "down to \\(\\log_{10}T = -0.14\\), against 4.3% at layer",
   "paper_text": "of 80, down to $\\log_{10}T=-0.14$, against 4.3\\,\\% at block",
   "paper_line": 1479,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0264",
   "section": "Where steering enters",
   "claim": "number 4.3 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = -0.14\\), against 4.3% at layer 35, where the",
   "paper_text": "$\\log_{10}T=-0.14$, against 4.3\\,\\% at block 35, where the",
   "paper_line": 1479,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0265",
   "section": "Where steering enters",
   "claim": "number 35 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "-0.14\\), against 4.3% at layer 35, where the chaos starts",
   "paper_text": "$\\log_{10}T=-0.14$, against 4.3\\,\\% at block 35, where the chaos starts at",
   "paper_line": 1479,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0266",
   "section": "Where steering enters",
   "claim": "number 0.01 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at \\(\\log_{10}T = 0.01\\), 4.3% at layer 50 (32",
   "paper_text": "chaos starts at $\\log_{10}T=0.01$, 4.3\\,\\% at block 50 (32 by",
   "paper_line": 1479,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0267",
   "section": "Where steering enters",
   "claim": "number 4.3 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = 0.01\\), 4.3% at layer 50 (32 by 32",
   "paper_text": "starts at $\\log_{10}T=0.01$, 4.3\\,\\% at block 50 (32 by 32 cells,",
   "paper_line": 1479,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0268",
   "section": "Where steering enters",
   "claim": "number 50 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "= 0.01\\), 4.3% at layer 50 (32 by 32 cells, a two-GPU",
   "paper_text": "$\\log_{10}T=0.01$, 4.3\\,\\% at block 50 (32 by 32 cells, a two-GPU",
   "paper_line": 1480,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0269",
   "section": "Where steering enters",
   "claim": "number 32 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.01\\), 4.3% at layer 50 (32 by 32 cells, a two-GPU",
   "paper_text": "$\\log_{10}T=0.01$, 4.3\\,\\% at block 50 (32 by 32 cells, a two-GPU map",
   "paper_line": 1480,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0270",
   "section": "Where steering enters",
   "claim": "number 32 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "4.3% at layer 50 (32 by 32 cells, a two-GPU map from",
   "paper_text": "$\\log_{10}T=0.01$, 4.3\\,\\% at block 50 (32 by 32 cells, a two-GPU map",
   "paper_line": 1480,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0271",
   "section": "Where steering enters",
   "claim": "number 0.7 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "in the size study), and 0.7% at layer 65, all",
   "paper_text": "Section~\\ref{sec:sizemain}), and 0.7\\,\\% at block 65, all above",
   "paper_line": 1480,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0272",
   "section": "Where steering enters",
   "claim": "number 65 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "study), and 0.7% at layer 65, all",
   "paper_text": "Section~\\ref{sec:sizemain}), and 0.7\\,\\% at block 65, all above $\\log_{10}T=0.19$.",
   "paper_line": 1480,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0273",
   "section": "Where steering enters",
   "claim": "number 0.19 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "above \\(\\log_{10}T = 0.19\\). These 70B labels are",
   "paper_text": "block 65, all above $\\log_{10}T=0.19$. These 70B labels are those",
   "paper_line": 1480,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0274",
   "section": "Where steering enters",
   "claim": "number 0.1 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "mostly above \\(\\log_{10}T = 0.1\\).",
   "paper_text": "chaos mostly above $\\log_{10}T=0.1$ (Section~\\ref{sec:theory}).",
   "paper_line": 1482,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0275",
   "section": "Where steering enters",
   "claim": "number 12 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "cells of layers 4, 8 and 12 have expanding readout",
   "paper_text": "chaotic cells of blocks 4, 8 and 12 have expanding readout factors",
   "paper_line": 1485,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0276",
   "section": "Where steering enters",
   "claim": "number 0.74 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "readout factors (medians +0.74,",
   "paper_text": "readout factors (medians $+0.74$, $+0.46$ and $+0.46$ nats",
   "paper_line": 1485,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0277",
   "section": "Where steering enters",
   "claim": "number 0.46 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "+0.46 and +0.46 nats per step",
   "paper_text": "factors (medians $+0.74$, $+0.46$ and $+0.46$ nats per step",
   "paper_line": 1485,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0278",
   "section": "Where steering enters",
   "claim": "number 0.46 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "+0.46 and +0.46 nats per step over 54,",
   "paper_text": "(medians $+0.74$, $+0.46$ and $+0.46$ nats per step over 54, 56",
   "paper_line": 1485,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0279",
   "section": "Where steering enters",
   "claim": "number 54 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "+0.46 nats per step over 54, 56 and 21 cells) and contracting",
   "paper_text": "$+0.46$ nats per step over 54, 56 and 21 cells) and contracting",
   "paper_line": 1486,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0280",
   "section": "Where steering enters",
   "claim": "number 56 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "nats per step over 54, 56 and 21 cells) and contracting",
   "paper_text": "$+0.46$ nats per step over 54, 56 and 21 cells) and contracting",
   "paper_line": 1486,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0281",
   "section": "Where steering enters",
   "claim": "number 21 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "per step over 54, 56 and 21 cells) and contracting",
   "paper_text": "nats per step over 54, 56 and 21 cells) and contracting network",
   "paper_line": 1486,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0282",
   "section": "Where steering enters",
   "claim": "number −0.47 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "factors (−0.47 to −0.21). At layer 16",
   "paper_text": "contracting network factors ($-0.47$ to $-0.21$). At block 16 the",
   "paper_line": 1486,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0283",
   "section": "Where steering enters",
   "claim": "number −0.21 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "factors (−0.47 to −0.21). At layer 16 the readout",
   "paper_text": "network factors ($-0.47$ to $-0.21$). At block 16 the readout",
   "paper_line": 1486,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0284",
   "section": "Where steering enters",
   "claim": "number 16 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(−0.47 to −0.21). At layer 16 the readout factor of such",
   "paper_text": "($-0.47$ to $-0.21$). At block 16 the readout factor of such",
   "paper_line": 1486,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0285",
   "section": "Where steering enters",
   "claim": "number 0.15 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "+0.15, and layer 20 gives just",
   "paper_text": "factor of such cells is only $+0.15$, and block 20 gives just 6",
   "paper_line": 1487,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0286",
   "section": "Where steering enters",
   "claim": "number 20 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "+0.15, and layer 20 gives just 6 of them. Early",
   "paper_text": "is only $+0.15$, and block 20 gives just 6 of them. Early",
   "paper_line": 1487,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0287",
   "section": "Where steering enters",
   "claim": "number 20 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "factor carries it (layer 20:",
   "paper_text": "network factor carries it (block 20: network $+1.09$, readout $-0.78$;",
   "paper_line": 1489,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0288",
   "section": "Where steering enters",
   "claim": "number 1.09 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "network +1.09, readout −0.78; Figure",
   "paper_text": "carries it (block 20: network $+1.09$, readout $-0.78$; Figure~\\ref{fig:mechanism}e).",
   "paper_line": 1489,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0289",
   "section": "Where steering enters",
   "claim": "number −0.78 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "network +1.09, readout −0.78; Figure",
   "paper_text": "20: network $+1.09$, readout $-0.78$; Figure~\\ref{fig:mechanism}e).",
   "paper_line": 1489,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0290",
   "section": "Where steering enters",
   "claim": "number 24 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "each of five layers of 24: largest Lyapunov exponent",
   "paper_text": "recipe at each of five blocks of 24: largest Lyapunov exponent",
   "paper_line": 1493,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0291",
   "section": "Where steering enters",
   "claim": "number 128 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "largest Lyapunov exponent on 128 × 128 float64 cells over",
   "paper_text": "largest Lyapunov exponent on $128\\times128$ float64 cells over",
   "paper_line": 1493,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0292",
   "section": "Where steering enters",
   "claim": "number 128 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Lyapunov exponent on 128 × 128 float64 cells over the",
   "paper_text": "largest Lyapunov exponent on $128\\times128$ float64 cells over",
   "paper_line": 1493,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0293",
   "section": "Where steering enters",
   "claim": "number 0.3 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and \\(\\log_{10}T \\in [-1, 0.3]\\). The share of chaotic",
   "paper_text": "strength and $\\log_{10}T\\in[-1,0.3]$. The share of chaotic cells",
   "paper_line": 1494,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0294",
   "section": "Where steering enters",
   "claim": "number 16 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and hostility at layer 16 at once",
   "paper_text": "float64 cells, steering at layer 16) along gratitude, hostility",
   "paper_line": 5370,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0295",
   "section": "Where steering enters",
   "claim": "number 21.7 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "makes 21.7% of a 96 × 96 plane chaotic",
   "paper_text": "block 16 of Qwen2.5-0.5B, makes 21.7\\,\\% of a $96\\times96$ plane",
   "paper_line": 1499,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0296",
   "section": "Where steering enters",
   "claim": "number 96 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "makes 21.7% of a 96 × 96 plane chaotic at \\(\\log_{10}T",
   "paper_text": "Qwen2.5-0.5B, makes 21.7\\,\\% of a $96\\times96$ plane chaotic at $\\log_{10}T=-0.1$.",
   "paper_line": 1500,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0297",
   "section": "Where steering enters",
   "claim": "number -0.1 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "chaotic at \\(\\log_{10}T = -0.1\\), while each push",
   "paper_text": "plane chaotic at $\\log_{10}T=-0.1$. The grid has no row or column",
   "paper_line": 1500,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0298",
   "section": "Where steering enters",
   "claim": "number 12.5 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of the same grid, makes 12.5% and 5.2% of its",
   "paper_text": "on the same grid: they make 12.5\\,\\% (gratitude at block 4 alone)",
   "paper_line": 1501,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0299",
   "section": "Where steering enters",
   "claim": "number 5.2 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "same grid, makes 12.5% and 5.2% of its",
   "paper_text": "(gratitude at block 4 alone) and 5.2\\,\\% (hostility at block 16",
   "paper_line": 1502,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0300",
   "section": "Where steering enters",
   "claim": "number 1561 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "line chaotic. In 1561 cells, 16.9% of the plane",
   "paper_text": "(Figure~\\ref{fig:twoblock}): 1561 cells, 16.9\\,\\% of the plane",
   "paper_line": 1503,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0301",
   "section": "Where steering enters",
   "claim": "number 16.9 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "chaotic. In 1561 cells, 16.9% of the plane and 78% of",
   "paper_text": "(Figure~\\ref{fig:twoblock}): 1561 cells, 16.9\\,\\% of the plane and 78\\,\\%",
   "paper_line": 1503,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0302",
   "section": "Where steering enters",
   "claim": "number 78 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "16.9% of the plane and 78% of its chaotic cells,",
   "paper_text": "cells, 16.9\\,\\% of the plane and 78\\,\\% of its chaotic cells, are",
   "paper_line": 1503,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0303",
   "section": "Where steering enters",
   "claim": "number 8.3 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "share is 8.3 to 16.9% of the plane,",
   "paper_text": "$\\log_{10}T=\\pm0.1$) this share is 8.3 to 16.9\\,\\% of the plane, and",
   "paper_line": 1505,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0304",
   "section": "Where steering enters",
   "claim": "number 16.9 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "share is 8.3 to 16.9% of the plane, and 7.8",
   "paper_text": "$\\log_{10}T=\\pm0.1$) this share is 8.3 to 16.9\\,\\% of the plane, and 7.8 to",
   "paper_line": 1505,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0305",
   "section": "Where steering enters",
   "claim": "number 7.8 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "16.9% of the plane, and 7.8 to 16.5% with both single",
   "paper_text": "16.9\\,\\% of the plane, and 7.8 to 16.5\\,\\% with both single",
   "paper_line": 1506,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0306",
   "section": "Where steering enters",
   "claim": "number 16.5 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of the plane, and 7.8 to 16.5% with both single pushes",
   "paper_text": "16.9\\,\\% of the plane, and 7.8 to 16.5\\,\\% with both single pushes",
   "paper_line": 1506,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0307",
   "section": "Where steering enters",
   "claim": "number 16 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(hostility at 4, gratitude at 16) the plane is",
   "paper_text": "(hostility at 4, gratitude at 16) the plane is 23.4\\,\\% chaotic,",
   "paper_line": 1506,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0308",
   "section": "Where steering enters",
   "claim": "number 23.4 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "23.4% chaotic, and at \\(\\log_{10}T",
   "paper_text": "gratitude at 16) the plane is 23.4\\,\\% chaotic, and at $\\log_{10}T=0.1$",
   "paper_line": 1507,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0309",
   "section": "Where steering enters",
   "claim": "number 0.1 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "chaotic, and at \\(\\log_{10}T = 0.1\\) both pairs give 33 and",
   "paper_text": "chaotic, and at $\\log_{10}T=0.1$ both pairs give 33 and 42\\,\\%.",
   "paper_line": 1507,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0310",
   "section": "Where steering enters",
   "claim": "number 33 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "= 0.1\\) both pairs give 33 and 42% (Figure",
   "paper_text": "$\\log_{10}T=0.1$ both pairs give 33 and 42\\,\\%. Each plane keeps",
   "paper_line": 1507,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0311",
   "section": "Where steering enters",
   "claim": "number 42 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "both pairs give 33 and 42% (Figure",
   "paper_text": "$\\log_{10}T=0.1$ both pairs give 33 and 42\\,\\%. Each plane keeps a periodic",
   "paper_line": 1507,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0312",
   "section": "Where steering enters",
   "claim": "number 96 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "largest Lyapunov exponent on 96 × 96 float64 cells over",
   "paper_text": "largest Lyapunov exponent on $96\\times96$ float64 cells over",
   "paper_line": 1513,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0313",
   "section": "Where steering enters",
   "claim": "number 96 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Lyapunov exponent on 96 × 96 float64 cells over the",
   "paper_text": "Lyapunov exponent on $96\\times96$ float64 cells over the two",
   "paper_line": 1513,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0314",
   "section": "Where steering enters",
   "claim": "number -0.1 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "strengths, at \\(\\log_{10}T = -0.1\\) (left) and 0.1 (right).",
   "paper_text": "two strengths, at $\\log_{10}T=-0.1$ (left) and $0.1$ (right).",
   "paper_line": 1514,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0315",
   "section": "Where steering enters",
   "claim": "number 0.1 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = -0.1\\) (left) and 0.1 (right). Top: gratitude",
   "paper_text": "$\\log_{10}T=-0.1$ (left) and $0.1$ (right). Top: gratitude at",
   "paper_line": 1514,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0316",
   "section": "Where steering enters",
   "claim": "number 16 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "layer 4, hostility at layer 16; bottom: the layers exchanged.",
   "paper_text": "block 4, hostility at block 16; bottom: the blocks exchanged.",
   "paper_line": 1514,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0317",
   "section": "Where steering enters",
   "claim": "number 4864 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Inside the MLP, each of the 4864 neurons writes its activation",
   "paper_text": "with residual vector $x$), the 4864 neurons write $\\sum_i h_i w_i$",
   "paper_line": 5664,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0318",
   "section": "Where steering enters",
   "claim": "number 12 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "neuron, in decoder layer 12 of Qwen2.5-0.5B-Instruct.",
   "paper_text": "MLP neuron, in decoder layer 12 of Qwen2.5-0.5B-Instruct. Each",
   "paper_line": 5662,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0319",
   "section": "Where steering enters",
   "claim": "number 896 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "own residual stream, one 896-dimensional vector per",
   "paper_text": "a network with 896-dimensional states shows the signatures of one-dimensional maps.",
   "paper_line": 3047,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0320",
   "section": "Where steering enters",
   "claim": "number 4864 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "residual vector \\(x\\)), the 4864 neurons write \\(\\sum_i",
   "paper_text": "with residual vector $x$), the 4864 neurons write $\\sum_i h_i w_i$",
   "paper_line": 5664,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0321",
   "section": "Where steering enters",
   "claim": "number 312 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the activation), and \\(312 = \\lVert v_{\\mathrm{phil}}\\rVert/\\lVert",
   "paper_text": "lower the activation), and $312=\\lVert v_{\\mathrm{phil}}\\rVert/\\lVert",
   "paper_line": 5666,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0322",
   "section": "Where steering enters",
   "claim": "number 188.99 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "v_{\\mathrm{phil}}\\rVert/\\lVert w_{832}\\rVert = 188.99/0.606\\) is a fixed scale",
   "paper_text": "v_{\\mathrm{phil}}\\rVert/\\lVert w_{832}\\rVert=188.99/0.606$ is a fixed scale for",
   "paper_line": 5667,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0323",
   "section": "Where steering enters",
   "claim": "number 832 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "fixed scale for neuron 832. Raising \\(h_{832}\\) by",
   "paper_text": "is a fixed scale for neuron 832. Raising $h_{832}$ by $312\\alpha$",
   "paper_line": 5667,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0324",
   "section": "Where steering enters",
   "claim": "number 312 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Raising \\(h_{832}\\) by \\(312\\alpha\\) for every token",
   "paper_text": "832. Raising $h_{832}$ by $312\\alpha$ for every token is the",
   "paper_line": 5667,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0325",
   "section": "Where steering enters",
   "claim": "number 312 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\alpha v\\), with \\(v = 312\\,w_{832}\\), to the layer's",
   "paper_text": "adding $\\alpha v$, with $v=312\\,w_{832}$, to the layer's output,",
   "paper_line": 5668,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0326",
   "section": "Where steering enters",
   "claim": "number 312 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "it: \\(\\sum_i h_i w_i + 312\\alpha\\,w_{832} = \\sum_{i\\neq832}",
   "paper_text": "implement it: $\\sum_i h_i w_i+312\\alpha\\,w_{832}=\\sum_{i\\neq832}h_i",
   "paper_line": 5669,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0327",
   "section": "Where steering enters",
   "claim": "number 312 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\sum_{i\\neq832} h_i w_i + (h_{832} + 312\\alpha)\\,w_{832}\\). At \\(\\lvert\\alpha\\rvert",
   "paper_text": "w_i+312\\alpha\\,w_{832}=\\sum_{i\\neq832}h_i w_i+(h_{832}+312\\alpha)\\,w_{832}$. At $|\\alpha|=0.12$",
   "paper_line": 5669,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0328",
   "section": "Where steering enters",
   "claim": "number 0.12 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lvert\\alpha\\rvert = 0.12\\) the increase is 37.4,",
   "paper_text": "w_i+(h_{832}+312\\alpha)\\,w_{832}$. At $|\\alpha|=0.12$ the increase is 37.4, against",
   "paper_line": 5669,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0329",
   "section": "Where steering enters",
   "claim": "number 37.4 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.12\\) the increase is 37.4, against a mean activation",
   "paper_text": "$|\\alpha|=0.12$ the increase is 37.4, against a mean activation",
   "paper_line": 5670,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0330",
   "section": "Where steering enters",
   "claim": "number 0.27 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "against a mean activation of 0.27 on the philosophy texts;",
   "paper_text": "against a mean activation of 0.27 on the philosophy texts; for",
   "paper_line": 5670,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0331",
   "section": "Where steering enters",
   "claim": "number 833 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "philosophy texts; for neurons 833 and 4137 the scale is 329",
   "paper_text": "philosophy texts; for neurons 833 and 4137 the scale is 329 and",
   "paper_line": 5670,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0332",
   "section": "Where steering enters",
   "claim": "number 4137 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "texts; for neurons 833 and 4137 the scale is 329 and 346.",
   "paper_text": "texts; for neurons 833 and 4137 the scale is 329 and 346. The",
   "paper_line": 5670,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0333",
   "section": "Where steering enters",
   "claim": "number 329 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "833 and 4137 the scale is 329 and 346. The tokens shown",
   "paper_text": "neurons 833 and 4137 the scale is 329 and 346. The tokens shown are",
   "paper_line": 5670,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0334",
   "section": "Where steering enters",
   "claim": "number 346 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "4137 the scale is 329 and 346. The tokens shown are only",
   "paper_text": "and 4137 the scale is 329 and 346. The tokens shown are only",
   "paper_line": 5670,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0335",
   "section": "Where steering enters",
   "claim": "number 26 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "exponents in Llama-3.1-8B (26 of 64 temperatures),",
   "paper_text": "exponents in Llama-3.1 8B (26 of 64 temperatures), Qwen2.5-7B",
   "paper_line": 5597,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0336",
   "section": "Where steering enters",
   "claim": "number 64 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "in Llama-3.1-8B (26 of 64 temperatures),",
   "paper_text": "exponents in Llama-3.1 8B (26 of 64 temperatures), Qwen2.5-7B (15",
   "paper_line": 5597,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0337",
   "section": "Where steering enters",
   "claim": "number 15 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Qwen2.5-7B (15 of 64) and OLMo-2-7B (11",
   "paper_text": "temperatures), Qwen2.5-7B (15 of 64) and OLMo-2 7B (11 of",
   "paper_line": 5597,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0338",
   "section": "Where steering enters",
   "claim": "number 64 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Qwen2.5-7B (15 of 64) and OLMo-2-7B (11 of 64),",
   "paper_text": "temperatures), Qwen2.5-7B (15 of 64) and OLMo-2 7B (11 of 64),",
   "paper_line": 5597,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0339",
   "section": "Where steering enters",
   "claim": "number 11 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(15 of 64) and OLMo-2-7B (11 of 64), while the near-zero",
   "paper_text": "Qwen2.5-7B (15 of 64) and OLMo-2 7B (11 of 64), while the near-zero",
   "paper_line": 5597,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0340",
   "section": "Where steering enters",
   "claim": "number 64 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "64) and OLMo-2-7B (11 of 64), while the near-zero columns",
   "paper_text": "temperatures), Qwen2.5-7B (15 of 64) and OLMo-2 7B (11 of 64),",
   "paper_line": 5597,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0341",
   "section": "Where steering enters",
   "claim": "number 128 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "one such cell each (of 128 and 64). A longer float64",
   "paper_text": "contain one such cell each (of 128 and 64). A longer float64 sweep",
   "paper_line": 5598,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0342",
   "section": "Where steering enters",
   "claim": "number 64 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "such cell each (of 128 and 64). A longer float64",
   "paper_text": "such cell each (of 128 and 64). A longer float64 sweep of",
   "paper_line": 5598,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0343",
   "section": "Where steering enters",
   "claim": "number 512 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the unsteered 0.5B map (512 temperatures over",
   "paper_text": "of the unsteered 0.5B map (512 temperatures over $\\log_{10}T\\in[-1,0.3]$,",
   "paper_line": 5599,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0344",
   "section": "Where steering enters",
   "claim": "number 0.3 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T \\in [-1, 0.3]\\), 1000 transient and",
   "paper_text": "temperatures over $\\log_{10}T\\in[-1,0.3]$, 1000 transient and 2000",
   "paper_line": 5599,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0345",
   "section": "Where steering enters",
   "claim": "number 1000 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T \\in [-1, 0.3]\\), 1000 transient and 2000 measured",
   "paper_text": "over $\\log_{10}T\\in[-1,0.3]$, 1000 transient and 2000 measured",
   "paper_line": 5599,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0346",
   "section": "Where steering enters",
   "claim": "number 2000 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.3]\\), 1000 transient and 2000 measured steps) finds a",
   "paper_text": "$\\log_{10}T\\in[-1,0.3]$, 1000 transient and 2000 measured steps) finds a narrow",
   "paper_line": 5599,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0347",
   "section": "Where steering enters",
   "claim": "number 0.15 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at \\(\\log_{10}T \\approx 0.15\\) to 0.21 (7 temperatures,",
   "paper_text": "chaotic band at $\\log_{10}T\\approx0.15$--$0.21$ (7 temperatures, exponents",
   "paper_line": 5600,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0348",
   "section": "Where steering enters",
   "claim": "number 0.21 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T \\approx 0.15\\) to 0.21 (7 temperatures, exponents",
   "paper_text": "at $\\log_{10}T\\approx0.15$--$0.21$ (7 temperatures, exponents",
   "paper_line": 5600,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0349",
   "section": "Where steering enters",
   "claim": "number 0.28 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.28), with a period-5 loop",
   "paper_text": "temperatures, exponents up to $0.28$), with a period-5 loop at",
   "paper_line": 5600,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0350",
   "section": "Where steering enters",
   "claim": "number 437 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "with a period-5 loop at 437 of the 512 temperatures.",
   "paper_text": "$0.28$), with a period-5 loop at 437 of the 512 temperatures. The",
   "paper_line": 5601,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0351",
   "section": "Where steering enters",
   "claim": "number 512 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "period-5 loop at 437 of the 512 temperatures. The same",
   "paper_text": "period-5 loop at 437 of the 512 temperatures. The same long",
   "paper_line": 5601,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0352",
   "section": "Where steering enters",
   "claim": "number 96 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "96 chaotic temperatures in",
   "paper_text": "temperatures. The same long sweep finds 96 chaotic temperatures in Llama-3.1",
   "paper_line": 5601,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0353",
   "section": "Where steering enters",
   "claim": "number -0.20 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "between \\(\\log_{10}T = -0.20\\) and 0.24",
   "paper_text": "Llama-3.1 8B, between $\\log_{10}T=-0.20$ and $0.24$ (exponents up to",
   "paper_line": 5602,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0354",
   "section": "Where steering enters",
   "claim": "number 0.24 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T = -0.20\\) and 0.24",
   "paper_text": "between $\\log_{10}T=-0.20$ and $0.24$ (exponents up to $0.66$),",
   "paper_line": 5602,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0355",
   "section": "Where steering enters",
   "claim": "number 0.66 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(exponents up to 0.66), interleaved with periodic",
   "paper_text": "and $0.24$ (exponents up to $0.66$), interleaved with periodic",
   "paper_line": 5602,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0356",
   "section": "Where steering enters",
   "claim": "number 52 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "windows of periods 2 to 52; within",
   "paper_text": "periodic windows of periods 2 to 52; within $\\log_{10}T\\in[-0.3,0.3]$",
   "paper_line": 5602,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0357",
   "section": "Where steering enters",
   "claim": "number -0.3 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T \\in [-0.3, 0.3]\\) its chaotic share,",
   "paper_text": "to 52; within $\\log_{10}T\\in[-0.3,0.3]$ its chaotic share, 41\\,\\%,",
   "paper_line": 5603,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0358",
   "section": "Where steering enters",
   "claim": "number 0.3 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\log_{10}T \\in [-0.3, 0.3]\\) its chaotic share, 41%,",
   "paper_text": "52; within $\\log_{10}T\\in[-0.3,0.3]$ its chaotic share, 41\\,\\%,",
   "paper_line": 5603,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0359",
   "section": "Where steering enters",
   "claim": "number 41 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.3]\\) its chaotic share, 41%, equals that of the coarse",
   "paper_text": "$\\log_{10}T\\in[-0.3,0.3]$ its chaotic share, 41\\,\\%, equals that of the coarse",
   "paper_line": 5603,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0360",
   "section": "Where steering enters",
   "claim": "number 65 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "column. Qwen2.5-7B has 65 chaotic temperatures between",
   "paper_text": "coarse column. Qwen2.5-7B has 65 chaotic temperatures between",
   "paper_line": 5603,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0361",
   "section": "Where steering enters",
   "claim": "number -0.07 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "between \\(\\log_{10}T = -0.07\\) and",
   "paper_text": "temperatures between $\\log_{10}T=-0.07$ and $0.28$ (exponents up to",
   "paper_line": 5604,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0362",
   "section": "Where steering enters",
   "claim": "number 0.28 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.28 (exponents up to 0.74),",
   "paper_text": "between $\\log_{10}T=-0.07$ and $0.28$ (exponents up to $0.74$),",
   "paper_line": 5604,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0363",
   "section": "Where steering enters",
   "claim": "number 0.74 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.28 (exponents up to 0.74), and OLMo-2-7B has 32",
   "paper_text": "and $0.28$ (exponents up to $0.74$), and OLMo-2 7B has 32 between",
   "paper_line": 5604,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0364",
   "section": "Where steering enters",
   "claim": "number 32 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.74), and OLMo-2-7B has 32 between 0.04 and 0.14 (up",
   "paper_text": "$0.74$), and OLMo-2 7B has 32 between $0.04$ and $0.14$ (up",
   "paper_line": 5604,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0365",
   "section": "Where steering enters",
   "claim": "number 0.04 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "OLMo-2-7B has 32 between 0.04 and 0.14 (up to",
   "paper_text": "and OLMo-2 7B has 32 between $0.04$ and $0.14$ (up to $0.30$).",
   "paper_line": 5604,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0366",
   "section": "Where steering enters",
   "claim": "number 0.14 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "has 32 between 0.04 and 0.14 (up to",
   "paper_text": "has 32 between $0.04$ and $0.14$ (up to $0.30$). Steering is",
   "paper_line": 5605,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0367",
   "section": "Where steering enters",
   "claim": "number 0.30 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "0.30). Steering is therefore",
   "paper_text": "between $0.04$ and $0.14$ (up to $0.30$). Steering is therefore not",
   "paper_line": 5605,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0368",
   "section": "Where steering enters",
   "claim": "number -1.5 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "exponent (clipped at \\(-1.5\\)) from float64 sweeps",
   "paper_text": "Lyapunov exponent (clipped at $-1.5$) from float64 sweeps of 512",
   "paper_line": 5643,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0369",
   "section": "Where steering enters",
   "claim": "number 512 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "from float64 sweeps of 512 temperatures (128 for the",
   "paper_text": "$-1.5$) from float64 sweeps of 512 temperatures (128 for the 70B-class",
   "paper_line": 5643,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0370",
   "section": "Where steering enters",
   "claim": "number 128 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "sweeps of 512 temperatures (128 for the 70B-class and mixture-of-experts",
   "paper_text": "sweeps of 512 temperatures (128 for the 70B-class and mixture-of-experts",
   "paper_line": 5643,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0371",
   "section": "Where steering enters",
   "claim": "number 1000 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "mixture-of-experts models; 1000 transient and 2000 measured",
   "paper_text": "mixture-of-experts models; 1000 transient and 2000 measured",
   "paper_line": 5644,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0372",
   "section": "Where steering enters",
   "claim": "number 2000 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "models; 1000 transient and 2000 measured steps). Red: no",
   "paper_text": "models; 1000 transient and 2000 measured steps). Red: no period",
   "paper_line": 5644,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0373",
   "section": "Where steering enters",
   "claim": "number 64 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "steps). Red: no period up to 64 and an exponent above \\(10^{-3}\\);",
   "paper_text": "steps). Red: no period up to 64 and an exponent above $10^{-3}$;",
   "paper_line": 5644,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0374",
   "section": "Where steering enters",
   "claim": "number 10^{-3} in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and an exponent above \\(10^{-3}\\); black crosses: neither",
   "paper_text": "to 64 and an exponent above $10^{-3}$; black crosses: neither a",
   "paper_line": 5645,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0375",
   "section": "Where steering enters",
   "claim": "number 128 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "). On the same \\(128^2\\) grid, 7.6, 8.3",
   "paper_text": "(Figure~\\ref{fig:controls}). On the same $128^2$ grid, 7.6, 8.3 and 12.5\\,\\%",
   "paper_line": 5615,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0376",
   "section": "Where steering enters",
   "claim": "number 7.6 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the same \\(128^2\\) grid, 7.6, 8.3",
   "paper_text": "(Figure~\\ref{fig:controls}). On the same $128^2$ grid, 7.6, 8.3 and 12.5\\,\\% of cells",
   "paper_line": 5615,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0377",
   "section": "Where steering enters",
   "claim": "number 8.3 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "same \\(128^2\\) grid, 7.6, 8.3",
   "paper_text": "the same $128^2$ grid, 7.6, 8.3 and 12.5\\,\\% of cells are chaotic",
   "paper_line": 5615,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0378",
   "section": "Where steering enters",
   "claim": "number 12.5 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and 12.5% of cells are chaotic for",
   "paper_text": "$128^2$ grid, 7.6, 8.3 and 12.5\\,\\% of cells are chaotic for",
   "paper_line": 5615,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0379",
   "section": "Where steering enters",
   "claim": "number 6.8 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "vector's norm, against 6.8% for philosophy and 7.5%",
   "paper_text": "philosophy vector's norm, against 6.8\\,\\% for philosophy and 7.5\\,\\%",
   "paper_line": 5616,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0380",
   "section": "Where steering enters",
   "claim": "number 7.5 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "6.8% for philosophy and 7.5% for gratitude. In all",
   "paper_text": "6.8\\,\\% for philosophy and 7.5\\,\\% for gratitude. In all five",
   "paper_line": 5617,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0381",
   "section": "Where steering enters",
   "claim": "number 0.01 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lvert\\alpha\\rvert < 0.01\\) to between 5",
   "paper_text": "from about 1\\,\\% at $|\\alpha|<0.01$ to between 5 and 22\\,\\% at",
   "paper_line": 5617,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0382",
   "section": "Where steering enters",
   "claim": "number 22 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and 22% at larger \\(\\lvert\\alpha\\rvert\\),",
   "paper_text": "$|\\alpha|<0.01$ to between 5 and 22\\,\\% at larger $|\\alpha|$, and",
   "paper_line": 5618,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0383",
   "section": "Where steering enters",
   "claim": "number 13 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "chaotic share stays between 13 and 24% at every one",
   "paper_text": "chaotic share stays between 13 and 24\\,\\% at every one of",
   "paper_line": 5622,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0384",
   "section": "Where steering enters",
   "claim": "number 24 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "share stays between 13 and 24% at every one",
   "paper_text": "share stays between 13 and 24\\,\\% at every one of 103 angles",
   "paper_line": 5622,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0385",
   "section": "Where steering enters",
   "claim": "number 103 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of 103 angles.",
   "paper_text": "and 24\\,\\% at every one of 103 angles (Figure~\\ref{fig:morph});",
   "paper_line": 766,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0386",
   "section": "Where steering enters",
   "claim": "number 9.9 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": ") gives 9.9% chaotic cells for the",
   "paper_text": "philosophy texts is 0.27) gives 9.9\\,\\% chaotic cells for the neuron",
   "paper_line": 5624,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0387",
   "section": "Where steering enters",
   "claim": "number 5.1 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "fixed before any map, 5.1% for its index neighbor",
   "paper_text": "rule fixed before any map, 5.1\\,\\% for its index neighbor",
   "paper_line": 5626,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0388",
   "section": "Where steering enters",
   "claim": "number 12.9 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "its index neighbor and 12.9% for a random neuron",
   "paper_text": "for its index neighbor and 12.9\\,\\% for a random neuron (Figure~\\ref{fig:neurons});",
   "paper_line": 5626,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0389",
   "section": "Where steering enters",
   "claim": "number 0.4 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\alpha = 0\\) the share is 0.4 to",
   "paper_text": "near $\\alpha=0$ the share is 0.4 to 1.2\\,\\%. The direction does",
   "paper_line": 5627,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0390",
   "section": "Where steering enters",
   "claim": "number 1.2 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "1.2%. The direction does select",
   "paper_text": "$\\alpha=0$ the share is 0.4 to 1.2\\,\\%. The direction does select",
   "paper_line": 5627,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0391",
   "section": "Where steering enters",
   "claim": "number 26 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "loop, but beyond it only 26 to 56% of one map's cells",
   "paper_text": "period-5 loop, but beyond it only 26 to 56\\,\\% of one map's cells",
   "paper_line": 5628,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0392",
   "section": "Where steering enters",
   "claim": "number 56 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "but beyond it only 26 to 56% of one map's cells",
   "paper_text": "loop, but beyond it only 26 to 56\\,\\% of one map's cells carry",
   "paper_line": 5628,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0393",
   "section": "Where steering enters",
   "claim": "number 26 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "the same layer give 26 and 17% chaotic cells against",
   "paper_text": "directions at the same layer give 26 and 17\\,\\% chaotic cells against",
   "paper_line": 5629,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0394",
   "section": "Where steering enters",
   "claim": "number 17 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "same layer give 26 and 17% chaotic cells against",
   "paper_text": "the same layer give 26 and 17\\,\\% chaotic cells against 28\\,\\%",
   "paper_line": 5629,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0395",
   "section": "Where steering enters",
   "claim": "number 28 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "17% chaotic cells against 28% along the concept direction;",
   "paper_text": "17\\,\\% chaotic cells against 28\\,\\% along the concept direction;",
   "paper_line": 5630,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0396",
   "section": "Where steering enters",
   "claim": "number 34 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "all three carry 34 to 44% near \\(\\alpha =",
   "paper_text": "direction; all three carry 34 to 44\\,\\% near $\\alpha=0$,",
   "paper_line": 5630,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0397",
   "section": "Where steering enters",
   "claim": "number 44 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "all three carry 34 to 44% near \\(\\alpha = 0\\), and",
   "paper_text": "direction; all three carry 34 to 44\\,\\% near $\\alpha=0$, and the",
   "paper_line": 5630,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0398",
   "section": "Where steering enters",
   "claim": "number 19 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(\\lvert\\alpha\\rvert\\). At layer 19, where a sparse autoencoder",
   "paper_text": "large $|\\alpha|$. At layer 19, where a sparse autoencoder",
   "paper_line": 5631,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0399",
   "section": "Where steering enters",
   "claim": "number 28 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "vector rebuilt there gives 28%. The decoder direction",
   "paper_text": "vector rebuilt there gives 28\\,\\%. The decoder direction",
   "paper_line": 5632,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0400",
   "section": "Where steering enters",
   "claim": "number 0.10 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "before any map; cosine 0.10 with the",
   "paper_text": "fixed before any map; cosine $0.10$ with the concept vector) gives",
   "paper_line": 5633,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0401",
   "section": "Where steering enters",
   "claim": "number 29 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "concept vector) gives 29%, a random live feature",
   "paper_text": "with the concept vector) gives 29\\,\\%, a random live feature",
   "paper_line": 5634,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0402",
   "section": "Where steering enters",
   "claim": "number 27 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "29%, a random live feature 27% and a Gaussian direction",
   "paper_text": "29\\,\\%, a random live feature 27\\,\\% and a Gaussian direction",
   "paper_line": 5634,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0403",
   "section": "Where steering enters",
   "claim": "number 39 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and a Gaussian direction 39%,",
   "paper_text": "27\\,\\% and a Gaussian direction 39\\,\\%, all at the same norm.",
   "paper_line": 5634,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0404",
   "section": "Where steering enters",
   "claim": "number 128 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "Qwen2.5-0.5B-Instruct (\\(128^2\\) float64 cells, steering",
   "paper_text": "in Qwen2.5-0.5B-Instruct ($128^2$ float64 cells, steering",
   "paper_line": 5653,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0405",
   "section": "Where steering enters",
   "claim": "number 12 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "cells, steering at layer 12, one grid and one set of",
   "paper_text": "float64 cells, steering at layer 12, one grid and one set of settings):",
   "paper_line": 5653,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0406",
   "section": "Where steering enters",
   "claim": "number 10^{-3} in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(finite-horizon exponent above \\(10^{-3}\\), no period up to 48);",
   "paper_text": "(finite-horizon exponent above $10^{-3}$, no period up to 48); color",
   "paper_line": 5655,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0407",
   "section": "Where steering enters",
   "claim": "number 48 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(10^{-3}\\), no period up to 48); color gives the exponent,",
   "paper_text": "$10^{-3}$, no period up to 48); color gives the exponent,",
   "paper_line": 5655,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0408",
   "section": "Where steering enters",
   "claim": "number 832 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "specific to philosophy (832), of its index neighbor",
   "paper_text": "philosophy on held-out texts (832), of its index neighbor (833)",
   "paper_line": 5679,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0409",
   "section": "Where steering enters",
   "claim": "number 833 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "of its index neighbor (833) and of a random neuron",
   "paper_text": "(832), of its index neighbor (833) and of a random neuron (4137),",
   "paper_line": 5680,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0410",
   "section": "Where steering enters",
   "claim": "number 4137 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "and of a random neuron (4137), each rescaled to the",
   "paper_text": "(833) and of a random neuron (4137), each rescaled to the philosophy",
   "paper_line": 5680,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0411",
   "section": "Where steering enters",
   "claim": "number 0.013 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "vector's norm (cosines with it 0.013, \\(-0.028\\) and 0.022).",
   "paper_text": "vector's norm (cosines with it 0.013, $-0.028$ and 0.022). Titles",
   "paper_line": 5680,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0412",
   "section": "Where steering enters",
   "claim": "number -0.028 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(cosines with it 0.013, \\(-0.028\\) and 0.022). Titles give",
   "paper_text": "norm (cosines with it 0.013, $-0.028$ and 0.022). Titles give the",
   "paper_line": 5680,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0413",
   "section": "Where steering enters",
   "claim": "number 0.022 in 'Where steering enters' (generated: post phrase matched to the paper's source text)",
   "appears_as": "it 0.013, \\(-0.028\\) and 0.022). Titles give the chaotic",
   "paper_text": "with it 0.013, $-0.028$ and 0.022). Titles give the chaotic share.}",
   "paper_line": 5681,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0414",
   "section": "What theory allows",
   "claim": "number 0.03 in 'What theory allows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "uniform fixed point within 0.03",
   "paper_text": "uniform fixed point within 0.03 decades of temperature, and",
   "paper_line": 4504,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0415",
   "section": "What theory allows",
   "claim": "number 1000 in 'What theory allows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "exponents by QR iteration (1000 transient and 2000 measured",
   "paper_text": "(Appendix~\\ref{sec:methods}; 1000 transient and 2000 measured",
   "paper_line": 4529,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0416",
   "section": "What theory allows",
   "claim": "number 2000 in 'What theory allows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "iteration (1000 transient and 2000 measured steps, float64)",
   "paper_text": "(Appendix~\\ref{sec:methods}; 1000 transient and 2000 measured steps, float64) at",
   "paper_line": 4529,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0417",
   "section": "What theory allows",
   "claim": "number 35 in 'What theory allows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at 35 completed cells: 28 chosen",
   "paper_text": "measured steps, float64) at 35 completed cells: 28 chosen",
   "paper_line": 4529,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0418",
   "section": "What theory allows",
   "claim": "number 28 in 'What theory allows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "at 35 completed cells: 28 chosen by percentile of",
   "paper_text": "float64) at 35 completed cells: 28 chosen by percentile of their",
   "paper_line": 4529,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0419",
   "section": "What theory allows",
   "claim": "number 30 in 'What theory allows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "their spectra were seen (of 30 requested), and seven from",
   "paper_text": "their spectra were seen (of 30 requested), and seven from",
   "paper_line": 4530,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0420",
   "section": "What theory allows",
   "claim": "number 31 in 'What theory allows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "control. At this horizon 31 have a positive",
   "paper_text": "periodic control. At this horizon 31 have a positive leading estimate",
   "paper_line": 4531,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0421",
   "section": "What theory allows",
   "claim": "number 1.008 in 'What theory allows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "have \\(D_{\\mathrm{KY}} = 1.008\\) to 1.16, consistent with",
   "paper_text": "cells have $D_{\\mathrm{KY}}=1.008$ to $1.16$, consistent with",
   "paper_line": 4533,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0422",
   "section": "What theory allows",
   "claim": "number 1.16 in 'What theory allows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(D_{\\mathrm{KY}} = 1.008\\) to 1.16, consistent with nearly",
   "paper_text": "$D_{\\mathrm{KY}}=1.008$ to $1.16$, consistent with nearly one-dimensional",
   "paper_line": 4533,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0423",
   "section": "What theory allows",
   "claim": "number -0.17 in 'What theory allows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(\\(\\log_{10}T\\) from \\(-0.17\\) to",
   "paper_text": "headline maps ($\\log_{10}T$ from $-0.17$ to $-0.04$) it is $1.03$ to",
   "paper_line": 4535,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0424",
   "section": "What theory allows",
   "claim": "number -0.04 in 'What theory allows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-0.04\\)) it is 1.03 to 1.65,",
   "paper_text": "($\\log_{10}T$ from $-0.17$ to $-0.04$) it is $1.03$ to $1.65$, rising",
   "paper_line": 4535,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0425",
   "section": "What theory allows",
   "claim": "number 1.03 in 'What theory allows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-0.04\\)) it is 1.03 to 1.65, rising with \\(\\lambda_1\\).",
   "paper_text": "$-0.17$ to $-0.04$) it is $1.03$ to $1.65$, rising with $\\lambda_1$.",
   "paper_line": 4535,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0426",
   "section": "What theory allows",
   "claim": "number 1.65 in 'What theory allows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(-0.04\\)) it is 1.03 to 1.65, rising with \\(\\lambda_1\\).",
   "paper_text": "to $-0.04$) it is $1.03$ to $1.65$, rising with $\\lambda_1$.",
   "paper_line": 4535,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0427",
   "section": "What theory allows",
   "claim": "number -0.02 in 'What theory allows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(\\(\\log_{10}T\\) from \\(-0.02\\) to 0.13), nine",
   "paper_text": "region ($\\log_{10}T$ from $-0.02$ to $0.13$), nine chaotic cells",
   "paper_line": 4536,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0428",
   "section": "What theory allows",
   "claim": "number 0.13 in 'What theory allows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "(\\(\\log_{10}T\\) from \\(-0.02\\) to 0.13), nine",
   "paper_text": "($\\log_{10}T$ from $-0.02$ to $0.13$), nine chaotic cells have",
   "paper_line": 4536,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0429",
   "section": "What theory allows",
   "claim": "number 1.37 in 'What theory allows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "have \\(D_{\\mathrm{KY}} = 1.37\\) to 2.02; at two of them",
   "paper_text": "cells have $D_{\\mathrm{KY}}=1.37$ to $2.02$; at two of them",
   "paper_line": 4536,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0430",
   "section": "What theory allows",
   "claim": "number 2.02 in 'What theory allows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "\\(D_{\\mathrm{KY}} = 1.37\\) to 2.02; at two of them the sum",
   "paper_text": "$D_{\\mathrm{KY}}=1.37$ to $2.02$; at two of them the sum of",
   "paper_line": 4536,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0431",
   "section": "What theory allows",
   "claim": "number 0.72 in 'What theory allows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "group of cells (Spearman 0.72 over 17",
   "paper_text": "each group of cells (Spearman $0.72$ over 17 philosophy cells and",
   "paper_line": 4544,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0432",
   "section": "What theory allows",
   "claim": "number 17 in 'What theory allows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "cells (Spearman 0.72 over 17",
   "paper_text": "cells (Spearman $0.72$ over 17 philosophy cells and $0.69$",
   "paper_line": 4544,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0433",
   "section": "What theory allows",
   "claim": "number 0.69 in 'What theory allows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "philosophy cells and 0.69 over 8 hostile cells, computed",
   "paper_text": "over 17 philosophy cells and $0.69$ over 8 hostile cells, computed",
   "paper_line": 4544,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0434",
   "section": "What theory allows",
   "claim": "number 16 in 'What theory allows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "cells have ratios of about 16 to 19 and",
   "paper_text": "cells have ratios of about 16 to 19 and next-token entropies",
   "paper_line": 4546,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0435",
   "section": "What theory allows",
   "claim": "number 19 in 'What theory allows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "have ratios of about 16 to 19 and",
   "paper_text": "have ratios of about 16 to 19 and next-token entropies of",
   "paper_line": 4546,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "theory-0436",
   "section": "What theory allows",
   "claim": "number 1.16 in 'What theory allows' (generated: post phrase matched to the paper's source text)",
   "appears_as": "yet \\(D_{\\mathrm{KY}} \\le 1.16\\)",
   "paper_text": "nats, yet $D_{\\mathrm{KY}}\\le1.16$. The readout supplies many",
   "paper_line": 4547,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp-001",
   "section": "Our shrimp, followed cell by cell",
   "claim": "number in the real-shrimp passages (18 Oct 2026)",
   "appears_as": "spacing \\(1.25\\times10^{-4}\\) in both steering",
   "paper_text": "spacing $1.25\\times10^{-4}$ in both strengths",
   "paper_line": 2385,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp-002",
   "section": "Our shrimp, followed cell by cell",
   "claim": "number in the real-shrimp passages (18 Oct 2026)",
   "appears_as": "from that neighbor's final state, run for 250",
   "paper_text": "runs 250 steps, followed by",
   "paper_line": 2386,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp-003",
   "section": "Our shrimp, followed cell by cell",
   "claim": "number in the real-shrimp passages (18 Oct 2026)",
   "appears_as": "examined over 300 more",
   "paper_text": "300 recorded steps with a twin",
   "paper_line": 2387,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp-004",
   "section": "Our shrimp, followed cell by cell",
   "claim": "number in the real-shrimp passages (18 Oct 2026)",
   "appears_as": "in at least four of the five places",
   "paper_text": "in at least four of its five places",
   "paper_line": 2388,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp-005",
   "section": "Our shrimp, followed cell by cell",
   "claim": "number in the real-shrimp passages (18 Oct 2026)",
   "appears_as": "Of 2173 cells computed, 1720 are on it: 822",
   "paper_text": "Of 2173 cells computed, 1720 are on the attractor: 822 with period 5",
   "paper_line": 2400,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp-006",
   "section": "Our shrimp, followed cell by cell",
   "claim": "number in the real-shrimp passages (18 Oct 2026)",
   "appears_as": "with period 10, 82 with period 20 and 11 with period 40",
   "paper_text": "371 with period 10, 82 with period 20 and 11 with period 40",
   "paper_line": 2400,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp-007",
   "section": "Our shrimp, followed cell by cell",
   "claim": "number in the real-shrimp passages (18 Oct 2026)",
   "appears_as": "periods 15, 30 and 50 inside chaotic bands, 240",
   "paper_text": "a few with periods 15, 30 and 50 inside chaotic bands, 240 chaotic",
   "paper_line": 2401,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp-008",
   "section": "Our shrimp, followed cell by cell",
   "claim": "number in the real-shrimp passages (18 Oct 2026)",
   "appears_as": "and 178 converging slowly",
   "paper_text": "and 178 converging slowly",
   "paper_line": 2402,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp-009",
   "section": "Our shrimp, followed cell by cell",
   "claim": "number in the real-shrimp passages (18 Oct 2026)",
   "appears_as": "\\((\\alpha_1, \\alpha_2) = (-0.1148, 0.109)\\)",
   "paper_text": "$(\\alpha_1,\\alpha_2)=(-0.1148,0.109)$",
   "paper_line": 2393,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp-010",
   "section": "Our shrimp, followed cell by cell",
   "claim": "number in the real-shrimp passages (18 Oct 2026)",
   "appears_as": "far as \\((-0.1252, 0.0918)\\)",
   "paper_text": "$(-0.1252,0.0918)$ and, on the left, $\\alpha_2=0.108$",
   "paper_line": 2393,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp-011",
   "section": "Our shrimp, followed cell by cell",
   "claim": "number in the real-shrimp passages (18 Oct 2026)",
   "appears_as": "up the left side to \\(\\alpha_2 = 0.108\\)",
   "paper_text": "on the left, $\\alpha_2=0.108$",
   "paper_line": 2393,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp-012",
   "section": "Our shrimp, followed cell by cell",
   "claim": "boundary gate with the lower-left leg's own curves (FM5L, docs/fm5l/lower-leg.json)",
   "appears_as": "276 of the 292 pairs of",
   "paper_text": "276 of the 292 pairs of neighboring cells with periods 5 and 10",
   "paper_line": 2410,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp-013",
   "section": "Our shrimp, followed cell by cell",
   "claim": "boundary gate with the lower-left leg's own curves (FM5L, docs/fm5l/lower-leg.json)",
   "appears_as": "and 290 to within two",
   "paper_text": "and 290 to within two",
   "paper_line": 2411,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp-014",
   "section": "Our shrimp, followed cell by cell",
   "claim": "boundary gate with the lower-left leg's own curves (FM5L, docs/fm5l/lower-leg.json)",
   "appears_as": "754 pairs in which a period-5 cell borders",
   "paper_text": "754 pairs in which a period-5 cell borders",
   "paper_line": 2411,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp-015",
   "section": "Our shrimp, followed cell by cell",
   "claim": "boundary gate with the lower-left leg's own curves (FM5L, docs/fm5l/lower-leg.json)",
   "appears_as": "717 lie within one grid step of a",
   "paper_text": "717 lie within one step of a fold curve",
   "paper_line": 2412,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp-016",
   "section": "Our shrimp, followed cell by cell",
   "claim": "number in the real-shrimp passages (18 Oct 2026)",
   "appears_as": "in steps of 0.001 in \\(\\log_{10}T\\)",
   "paper_text": "steps of 0.001 in $\\log_{10}T$",
   "paper_line": 4929,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp-017",
   "section": "Our shrimp, followed cell by cell",
   "claim": "number in the real-shrimp passages (18 Oct 2026)",
   "appears_as": "hold to within \\(10^{-7}\\)",
   "paper_text": "$|c_1|>10^{-7}$",
   "paper_line": 4931,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp-018",
   "section": "Our shrimp, followed cell by cell",
   "claim": "number in the real-shrimp passages (18 Oct 2026)",
   "appears_as": "Over the eleven",
   "paper_text": "over the eleven values of $\\log_{10}T$ from $-0.104$ to",
   "paper_line": 2446,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp-019",
   "section": "Our shrimp, followed cell by cell",
   "claim": "number in the real-shrimp passages (18 Oct 2026)",
   "appears_as": "temperatures that passed, from \\(\\log_{10}T = -0.104\\) to \\(-0.094\\), the point moves",
   "paper_text": "from $-0.104$ to $-0.094$ at which the continuation passed its gates",
   "paper_line": 2446,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp-020",
   "section": "Our shrimp, followed cell by cell",
   "claim": "number in the real-shrimp passages (18 Oct 2026)",
   "appears_as": "\\(5.6\\times10^{-3}\\), and a fourth multiplier approaches it twice",
   "paper_text": "$5.6\\times10^{-3}$, and a fourth multiplier approaches it twice",
   "paper_line": 2448,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp-021",
   "section": "Our shrimp, followed cell by cell",
   "claim": "number in the real-shrimp passages (18 Oct 2026)",
   "appears_as": "eleven temperatures (Figure 65);",
   "paper_text": "over the eleven values of $\\log_{10}T$",
   "paper_line": 2446,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp-022",
   "section": "Our shrimp, followed cell by cell",
   "claim": "number in the real-shrimp passages (18 Oct 2026)",
   "appears_as": "shells of periods 10, 20 and 40, and the edge",
   "paper_text": "shells of periods 10, 20 and 40 beyond the flips",
   "paper_line": 2393,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp-023",
   "section": "Our shrimp, followed cell by cell",
   "claim": "number in the real-shrimp passages (18 Oct 2026)",
   "appears_as": "at 13 points fixed before the computation (green: the count predicted by a section of a swallowtail",
   "paper_text": "at 13 points fixed before the computation (green: the count predicted by a section of a swallowtail",
   "paper_line": 3001,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "normbounds-001",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "number in the norm-bound passages (18 Oct 2026)",
   "appears_as": "Along the trajectories of 7936",
   "paper_text": "along the trajectories of 7936 cells of the two main maps",
   "paper_line": 544,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "normbounds-002",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "number in the norm-bound passages (18 Oct 2026)",
   "appears_as": "their medians are 2.98 and 2.57 per step over the chaotic",
   "paper_text": "their medians are 2.98 and 2.57 per step over the chaotic",
   "paper_line": 596,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "normbounds-003",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "number in the norm-bound passages (18 Oct 2026)",
   "appears_as": "median exponent of 0.30 in its chaotic cells (crossing window: 2.93, 2.62 and 0.17)",
   "paper_text": "a median exponent of 0.30 in its chaotic cells (crossing window: 2.93, 2.62 and 0.17)",
   "paper_line": 597,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "normbounds-004",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "number in the norm-bound passages (18 Oct 2026)",
   "appears_as": "\\(k = 4\\) and 5 does the average begin",
   "paper_text": "begin to separate the regimes only at $k=4$ and 5",
   "paper_line": 604,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "normbounds-005",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "number in the norm-bound passages (18 Oct 2026)",
   "appears_as": "negative in 27 and 29% of the periodic cells",
   "paper_text": "negative in 27 and 29\\,\\% of the periodic cells",
   "paper_line": 604,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "normbounds-006",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "number in the norm-bound passages (18 Oct 2026)",
   "appears_as": "\\(\\mathrm{diam}(E) = 1.2109\\)",
   "paper_text": "$\\operatorname{diam}(E)=1.2109$",
   "paper_line": 542,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "normbounds-007",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "number in the norm-bound passages (18 Oct 2026)",
   "appears_as": "where the largest of all, \\(1.54\\times10^{5}\\), was met",
   "paper_text": "largest norm, $1.54\\times10^{5}$, was met",
   "paper_line": 547,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "normbounds-008",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "number in the norm-bound passages (18 Oct 2026)",
   "appears_as": "\\(T_*(\\alpha) \\ge 5.6\\times10^{4}\\)",
   "paper_text": "$T_*(\\alpha)\\ge5.6\\times10^{4}$",
   "paper_line": 546,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "normbounds-009",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "number in the norm-bound passages (18 Oct 2026; re-anchored 19 Oct 2026 after the external-review corrections: lower estimates, 3.16 and 4.47 decades from log10 T* >= 3.44 and >= 4.75 against log10 T = 0.28, quoted as at least 3.1 and 4.4)",
   "appears_as": "thresholds that lie at least 3.1 decades (factors of ten) above the",
   "paper_text": "at least 3.1 and 4.4 decades above the highest chaotic temperature of the unsteered sweeps",
   "paper_line": 547,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "normbounds-010",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "number in the norm-bound passages (18 Oct 2026)",
   "appears_as": "sampled rows, 256 cells that did not run within the time limit, and every eighth of",
   "paper_text": "except its top four sampled rows, 256 cells that did not run within the time limit, and every eighth of the crossing window",
   "paper_line": 593,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "normbounds-011",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "number in the norm-bound passages (18 Oct 2026)",
   "appears_as": "300 transient and 60 measured steps",
   "paper_text": "300 transient and 60 measured steps",
   "paper_line": 594,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "mt-001",
   "section": "Why the two families cross in both orders",
   "claim": "number in the single-switch passage (18 Oct 2026)",
   "appears_as": "(\\(\\alpha = 0.0708\\) from \\(\\log_{10}T = -0.1440\\) to \\(-0.1396\\), and",
   "paper_text": "($\\alpha=0.0708$ from $\\log_{10}T=-0.1440$ to $-0.1396$, and",
   "paper_line": 3134,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "mt-002",
   "section": "Why the two families cross in both orders",
   "claim": "number in the single-switch passage (18 Oct 2026)",
   "appears_as": "\\(\\log_{10}T = -0.1396\\) from \\(\\alpha = 0.0690\\) to \\(0.0700\\))",
   "paper_text": "$\\log_{10}T=-0.1396$ from $\\alpha=0.0690$ to $0.0700$)",
   "paper_line": 3135,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "mt-003",
   "section": "Why the two families cross in both orders",
   "claim": "number in the single-switch passage (18 Oct 2026)",
   "appears_as": "fixed start's family was bracketed by bisection, to 1/64 of the transect spacing at three",
   "paper_text": "switch of the fixed start's family by bisection, to 1/64 of the transect spacing at three of the eight switches",
   "paper_line": 3136,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "mt-004",
   "section": "Why the two families cross in both orders",
   "claim": "number in the single-switch passage (18 Oct 2026)",
   "appears_as": "Of the eight switches, two",
   "paper_text": "Of the eight switches, two are selections",
   "paper_line": 3139,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "mt-005",
   "section": "Why the two families cross in both orders",
   "claim": "number in the single-switch passage (18 Oct 2026)",
   "appears_as": "two are intrinsic (one",
   "paper_text": "two are intrinsic (one side's",
   "paper_line": 3140,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "mt-006",
   "section": "Why the two families cross in both orders",
   "claim": "number in the single-switch passage (18 Oct 2026)",
   "appears_as": "and four remain unresolved,",
   "paper_text": "and four remain unresolved",
   "paper_line": 3141,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "mt-007",
   "section": "Why the two families cross in both orders",
   "claim": "number in the single-switch passage (18 Oct 2026)",
   "appears_as": "called none of the first seven switches a selection",
   "paper_text": "classed none of the first seven switches as",
   "paper_line": 3143,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp2-001",
   "section": "Our shrimp, followed cell by cell",
   "claim": "number in the second-temperature and boundary passages (18 Oct 2026)",
   "appears_as": "same anatomy, with 1760 cells on the attractor",
   "paper_text": "has the same anatomy (1760 cells on the",
   "paper_line": 2402,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp2-002",
   "section": "Our shrimp, followed cell by cell",
   "claim": "number in the second-temperature and boundary passages (18 Oct 2026)",
   "appears_as": "\\((+0.00085, +0.00236)\\) in",
   "paper_text": "$(+0.00085,+0.00236)$ in",
   "paper_line": 2403,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp2-003",
   "section": "Our shrimp, followed cell by cell",
   "claim": "number in the second-temperature and boundary passages (18 Oct 2026)",
   "appears_as": "by about \\((+0.00105, +0.00247)\\) over the same step",
   "paper_text": "by about $(+0.00105,+0.00247)$ over the same step",
   "paper_line": 2404,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp2-004",
   "section": "Our shrimp, followed cell by cell",
   "claim": "boundary gate with the lower-left leg's own curves (FM5L, docs/fm5l/lower-leg.json)",
   "appears_as": "and all 754 within two steps of a fold or flip curve",
   "paper_text": "all 754 within two steps of a fold or",
   "paper_line": 2412,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "realshrimp2-005",
   "section": "Our shrimp, followed cell by cell",
   "claim": "boundary gate with the lower-left leg's own curves (FM5L, docs/fm5l/lower-leg.json)",
   "appears_as": "curves alone these counts were 251, 504 and 544",
   "paper_text": "these counts were 251, 504 and 544",
   "paper_line": 2413,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "rank-001",
   "section": "Shrimps of a two-dimensional kind",
   "claim": "number in the singular-value passage (18 Oct 2026)",
   "appears_as": "is \\(1.8\\times10^{-4}\\) of the first when the cycle is started at one phase",
   "paper_text": "is $1.8\\times10^{-4}$ of the first at one starting phase",
   "paper_line": 2434,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "rank-002",
   "section": "Shrimps of a two-dimensional kind",
   "claim": "number in the singular-value passage (18 Oct 2026)",
   "appears_as": "away), and at most 0.031 of it at the",
   "paper_text": "and at most 0.031 at the others",
   "paper_line": 2435,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "rank-003",
   "section": "Shrimps of a two-dimensional kind",
   "claim": "number in the singular-value passage (18 Oct 2026)",
   "appears_as": "the first is about 65, four orders of magnitude above the eigenvalues",
   "paper_text": "while the first, at that phase, is about 65, four orders of magnitude above the eigenvalues",
   "paper_line": 2436,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "rank-004",
   "section": "Shrimps of a two-dimensional kind",
   "claim": "number in the singular-value passage (18 Oct 2026)",
   "appears_as": "away from the head, the ratio is 0.017 to 0.23",
   "paper_text": "head, the ratio is 0.017 to 0.23",
   "paper_line": 2437,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "rank2-001",
   "section": "Shrimps of a two-dimensional kind",
   "claim": "number in the singular-reduction passage (18 Oct 2026)",
   "appears_as": "At the head it is \\(-2.7\\times10^{-4}\\)",
   "paper_text": "at the head $\\lambda=-2.7\\times10^{-4}$",
   "paper_line": 2442,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "rank2-002",
   "section": "Shrimps of a two-dimensional kind",
   "claim": "number in the singular-reduction passage (18 Oct 2026)",
   "appears_as": "are orthogonal to about four parts in a million",
   "paper_text": "orthogonal to about $4\\times10^{-6}$",
   "paper_line": 2443,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "rank2-003",
   "section": "Shrimps of a two-dimensional kind",
   "claim": "number in the singular-reduction passage (18 Oct 2026)",
   "appears_as": "On an \\(11\\times11\\) grid of spacing",
   "paper_text": "on an $11\\times11$ grid of spacing $10^{-5}$ around it",
   "paper_line": 2443,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "rank2-004",
   "section": "Shrimps of a two-dimensional kind",
   "claim": "number in the singular-reduction passage (18 Oct 2026)",
   "appears_as": "\\(10^{-5}\\) around the head, \\(\\lambda\\) changes sign exactly once in every row",
   "paper_text": "$\\lambda$ changes sign exactly once in every row",
   "paper_line": 2444,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "steering-001",
   "section": "Why the loop can be chaotic",
   "claim": "lower bound of the steering-dependent threshold at every sampled steering strength (per-alpha maxima of the network norm, 7936 cells) (18 Oct 2026; source tools/norm_bounds.py runs nb/cells2, cross-a, cross-b)",
   "appears_as": "\\(T_*(\\alpha) \\ge 2.7\\times10^{3}\\)",
   "paper_text": "$T_*(\\alpha)\\ge2.7\\times10^{3}$",
   "paper_line": 545,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "steering-002",
   "section": "Why the loop can be chaotic",
   "claim": "steering strength at which the largest network norm was met (18 Oct 2026; source tools/norm_bounds.py runs nb/cells2, cross-a, cross-b)",
   "appears_as": "at \\(\\alpha = 0.06\\),",
   "paper_text": "at $\\alpha=0.06$, where the",
   "paper_line": 546,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "steering-003",
   "section": "Why the loop can be chaotic",
   "claim": "share of the readout term's variance accounted for by steering strength (stripes map, crossing window) (18 Oct 2026; source tools/norm_bounds.py runs nb/cells2, cross-a, cross-b) (paper 1e8e82f4)",
   "appears_as": "steering explains 30 and 32% of the",
   "paper_text": "steering explains 30 and 32\\,\\% and temperature 21 and 27\\,\\%",
   "paper_line": 491,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "steering-004",
   "section": "Why the loop can be chaotic",
   "claim": "share of the readout term's variance accounted for by temperature (18 Oct 2026; source tools/norm_bounds.py runs nb/cells2, cross-a, cross-b) (paper 1e8e82f4)",
   "appears_as": "and temperature 21 and 27%. For the",
   "paper_text": "steering explains 30 and 32\\,\\% and temperature 21 and 27\\,\\%",
   "paper_line": 491,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "steering-005",
   "section": "Why the loop can be chaotic",
   "claim": "share of the network term's variance accounted for by steering strength (18 Oct 2026; source tools/norm_bounds.py runs nb/cells2, cross-a, cross-b) (paper 1e8e82f4)",
   "appears_as": "steering explains 7 and 33% and temperature 47 and 4%",
   "paper_text": "steering explains 7 and 33\\,\\% on the stripes map and the crossing window and temperature 47 and 4\\,\\%",
   "paper_line": 490,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "steering-006",
   "section": "Why the loop can be chaotic",
   "claim": "share of the network term's variance accounted for by temperature (18 Oct 2026; source tools/norm_bounds.py runs nb/cells2, cross-a, cross-b) (paper 1e8e82f4)",
   "appears_as": "and temperature 47 and 4%. Neither",
   "paper_text": "window and temperature 47 and 4\\,\\%",
   "paper_line": 491,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pair-001",
   "section": "A period-doubling cascade and a proof",
   "claim": "parameter cell of the certified coexisting pair (steering strength) (Codex Task 33 release, codex/coexistence-task33/pair-certificate-release.json)",
   "appears_as": "At \\(\\alpha = 0.06468\\) and",
   "paper_text": "At $\\alpha=0.06468$ and $\\log_{10}T=-0.148$",
   "paper_line": 5846,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pair-002",
   "section": "A period-doubling cascade and a proof",
   "claim": "parameter cell of the certified coexisting pair (temperature) (Codex Task 33 release, codex/coexistence-task33/pair-certificate-release.json)",
   "appears_as": "\\(\\log_{10}T = -0.148\\), inside the strip",
   "paper_text": "At $\\alpha=0.06468$ and $\\log_{10}T=-0.148$",
   "paper_line": 5846,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pair-003",
   "section": "A period-doubling cascade and a proof",
   "claim": "numerical leading multiplier of the certified 2-cycle (Codex Task 33 release, codex/coexistence-task33/pair-certificate-release.json)",
   "appears_as": "by a factor 0.0476 per trip around the 2-cycle",
   "paper_text": "leading multiplier moduli are $0.0476$",
   "paper_line": 5858,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pair-004",
   "section": "A period-doubling cascade and a proof",
   "claim": "numerical leading multiplier of the certified 3-cycle (Codex Task 33 release, codex/coexistence-task33/pair-certificate-release.json)",
   "appears_as": "and 0.239 around the 3-cycle",
   "paper_text": "$0.0476$ and $0.239$",
   "paper_line": 5858,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pair-005",
   "section": "A period-doubling cascade and a proof",
   "claim": "proved infinity-norm bound of the eighth power of the 2-cycle's monodromy (rounded up) (Codex Task 33 release, codex/coexistence-task33/pair-certificate-release.json)",
   "appears_as": "are \\(1.9\\times10^{-8}\\) for the 2-cycle",
   "paper_text": "$7.51\\times10^{-4}$ and $1.9\\times10^{-8}$ for the 2-cycle",
   "paper_line": 5857,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pair-006",
   "section": "A period-doubling cascade and a proof",
   "claim": "proved infinity-norm bound of the eighth power of the 3-cycle's monodromy (rounded up) (Codex Task 33 release, codex/coexistence-task33/pair-certificate-release.json)",
   "appears_as": "\\(1.091\\times10^{-3}\\) for the 3-cycle",
   "paper_text": "$0.342$ and $1.091\\times10^{-3}$ for the 3-cycle",
   "paper_line": 5858,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fs-001",
   "section": "What the chaos does to inference and steering",
   "claim": "cells of the fixed-shape control (run FS, docs/fs/fs-summary.json)",
   "appears_as": "checked both on the same 448 cells",
   "paper_text": "same 448 cells",
   "paper_line": 1202,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fs-002",
   "section": "What the chaos does to inference and steering",
   "claim": "median measured/predicted passage ratios at d = 1e-15 .. 1e-7 (run FS, docs/fs/fs-summary.json)",
   "appears_as": "predicted steps is 0.87, 1.01, 1.08, 1.10 and 1.18",
   "paper_text": "medians of 0.87, 1.01, 1.08, 1.10 and 1.18",
   "paper_line": 1209,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "fs-003",
   "section": "What the chaos does to inference and steering",
   "claim": "largest share of periodic cells separated (d = 1e-3) (run FS, docs/fs/fs-summary.json)",
   "appears_as": "in up to 59% of cells",
   "paper_text": "separates 10 to 59\\,\\%",
   "paper_line": 1213,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ll-001",
   "section": "Our shrimp, followed cell by cell",
   "claim": "cells of the Newton walk into the leg (run FM5L, docs/fm5l/lower-leg.json)",
   "appears_as": "at each of the 68 cells by which the follow run",
   "paper_text": "through the 68 cells by which the follow run entered it",
   "paper_line": 2407,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ll-002",
   "section": "Our shrimp, followed cell by cell",
   "claim": "period-5 cells of the leg inside the strip (run FM5L, docs/fm5l/lower-leg.json)",
   "appears_as": "inside that strip: 39 of 39",
   "paper_text": "(39 of 39)",
   "paper_line": 2409,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ll-003",
   "section": "Our shrimp, followed cell by cell",
   "claim": "farthest lost pair from a fold or flip curve, grid steps (run FM5L, docs/fm5l/lower-leg.json)",
   "appears_as": "the farthest is 1.7 steps away",
   "paper_text": "the farthest 1.7 steps away",
   "paper_line": 2413,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ll-004",
   "section": "The lower-left leg's own curves",
   "claim": "alpha2 below which the strip is narrower than a grid step (run FM5L, docs/fm5l/lower-leg.json)",
   "appears_as": "Below \\(\\alpha_2 = 0.0934\\) the strip",
   "paper_text": "$\\alpha_2=0.0934$ the strip is narrower",
   "paper_line": 2414,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ll-005",
   "section": "The lower-left leg's own curves",
   "claim": "strip width at the leg's lowest period-5 cell in the follow run, grid steps (run FM5L, docs/fm5l/lower-leg.json)",
   "appears_as": "0.58 steps at the leg's lowest period-5 cell",
   "paper_text": "to $0.58$ at $0.0919$",
   "paper_line": 5016,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ll-006",
   "section": "The lower-left leg's own curves",
   "claim": "the leg's lowest period-5 cell in the follow run (run FM5L, docs/fm5l/lower-leg.json)",
   "appears_as": "follow run, \\(\\alpha_2 = 0.0919\\)",
   "paper_text": "$0.0919$, the leg's lowest period-5 cell in the follow run",
   "paper_line": 5016,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ll-007",
   "section": "The lower-left leg's own curves",
   "claim": "strip width at the continuation's bound, grid steps (run FM5L, docs/fm5l/lower-leg.json)",
   "appears_as": "0.015 steps at \\(\\alpha_2 = 0.080\\)",
   "paper_text": "(0.015 steps at $\\alpha_2=0.080$",
   "paper_line": 2414,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ll-008",
   "section": "The lower-left leg's own curves",
   "claim": "largest residual on the leg's curves (run FM5L, docs/fm5l/lower-leg.json)",
   "appears_as": "residual of at most \\(10^{-10}\\)",
   "paper_text": "the residual is at most $10^{-10}$",
   "paper_line": 5012,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ll-009",
   "section": "The lower-left leg's own curves",
   "claim": "largest test function on the leg's curves (run FM5L, docs/fm5l/lower-leg.json)",
   "appears_as": "at most \\(5.2\\times10^{-10}\\)",
   "paper_text": "most $5.2\\times10^{-10}$",
   "paper_line": 5013,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ll-010",
   "section": "The lower-left leg's own curves",
   "claim": "largest distance of the critical multiplier from +-1 (run FM5L, docs/fm5l/lower-leg.json)",
   "appears_as": "within \\(3.7\\times10^{-8}\\) of",
   "paper_text": "within $3.7\\times10^{-8}$ of",
   "paper_line": 5013,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ll-011",
   "section": "The lower-left leg's own curves",
   "claim": "largest other multiplier modulus (run FM5L, docs/fm5l/lower-leg.json)",
   "appears_as": "every other multiplier has modulus at most 0.21",
   "paper_text": "modulus at most $0.21$",
   "paper_line": 5014,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ll-012",
   "section": "The lower-left leg's own curves",
   "claim": "alpha1 span from fold to flip at alpha2 0.094 (run FM5L, docs/fm5l/lower-leg.json)",
   "appears_as": "within \\(1.5\\times10^{-4}\\) in \\(\\alpha_1\\)",
   "paper_text": "within $1.5\\times10^{-4}$ in $\\alpha_1$",
   "paper_line": 5026,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ll-013",
   "section": "The lower-left leg's own curves",
   "claim": "cusp flagged on the leg's fold curve (run FM5L, docs/fm5l/lower-leg.json)",
   "appears_as": "\\((-0.11938, 0.10042)\\)",
   "paper_text": "$(-0.11938,0.10042)$",
   "paper_line": 5017,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ll-014",
   "section": "The lower-left leg's own curves",
   "claim": "bend of the leg's flip curve (run FM5L, docs/fm5l/lower-leg.json)",
   "appears_as": "\\((-0.12214, 0.10135)\\)",
   "paper_text": "$(-0.12214,0.10135)$",
   "paper_line": 5018,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "ll-015",
   "section": "The lower-left leg's own curves",
   "claim": "median distances of the returning arms to the body's curves, grid steps (run FM5L, docs/fm5l/lower-leg.json)",
   "appears_as": "distance of 0.017 grid steps from the body's second fold curve, and the returning fold arm at a median of 0.055",
   "paper_text": "median distance of $0.017$ grid steps (at most $0.055$) from the body's second fold curve, and the returning fold arm at a median of $0.055$",
   "paper_line": 5020,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bh-001",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "cells with exact norms (run BH, docs/bh/bh-summary.json)",
   "appears_as": "at 24 cells fixed in advance",
   "paper_text": "the first 24 of 64 cells fixed in advance",
   "paper_line": 611,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bh-002",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "longest block length (run BH, docs/bh/bh-summary.json)",
   "appears_as": "with blocks of up to 32 steps",
   "paper_text": "32 recorded steps after 1000 transient steps",
   "paper_line": 612,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bh-003",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "median overshoot at k = 1, chaotic cells (run BH, docs/bh/bh-summary.json)",
   "appears_as": "overshoot is 2.72 per step for single steps",
   "paper_text": "2.72 per step at $k=1$",
   "paper_line": 621,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bh-004",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "median overshoot at k = 32, chaotic cells (run BH, docs/bh/bh-summary.json)",
   "appears_as": "step for single steps and 0.036 for blocks of 32 steps",
   "paper_text": "0.32 at $k=8$ and 0.036 at",
   "paper_line": 621,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bh-005",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "median overshoot at k = 32, periodic cells (run BH, docs/bh/bh-summary.json)",
   "appears_as": "and 0.12 in the periodic ones",
   "paper_text": "2.86, 0.45 and 0.12",
   "paper_line": 622,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bh-006",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "window lengths with 23 of 24 signs right (run BH, docs/bh/bh-summary.json)",
   "appears_as": "For every window length from 17 to 29 steps",
   "paper_text": "in 23 cells for every window length from 17 to 29 steps",
   "paper_line": 627,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bh-007",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "cells with the right sign (run BH, docs/bh/bh-summary.json)",
   "appears_as": "next 2000 steps in 23 of",
   "paper_text": "in 23 cells for every window length from 17",
   "paper_line": 627,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bh-008",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "steps of the long-run exponent (run BH, docs/bh/bh-summary.json)",
   "appears_as": "the exponent measured over the next 2000 steps",
   "paper_text": "of the exponent measured over the next 2000 steps",
   "paper_line": 621,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "basin-001",
   "section": "Proofs",
   "claim": "radius of the certified 2-cycle basin ball (codex/coexistence-task33/inner-basin-release.json)",
   "appears_as": "a distance of \\(2^{-681}\\)",
   "paper_text": "radius $2^{-681}$",
   "paper_line": 5865,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "basin-002",
   "section": "Proofs",
   "claim": "radius of the certified 3-cycle basin ball (codex/coexistence-task33/inner-basin-release.json)",
   "appears_as": "\\(2^{-700}\\) of the 3-cycle",
   "paper_text": "within $2^{-700}$ of",
   "paper_line": 5866,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "att-001",
   "section": "What the attractors look like",
   "claim": "strongest chaos on the row (paper: What the attractors look like)",
   "appears_as": "\\(\\alpha = 0.07248\\)), we started",
   "paper_text": "($\\alpha=0.07248$), 512 trajectories",
   "paper_line": 1012,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "att-002",
   "section": "What the attractors look like",
   "claim": "trajectories (paper: What the attractors look like)",
   "appears_as": "we started 512 trajectories",
   "paper_text": "512 trajectories started near the fixed",
   "paper_line": 1012,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "att-003",
   "section": "What the attractors look like",
   "claim": "trajectories on the period-4 orbit (paper: What the attractors look like)",
   "appears_as": "All but 14 approach one set",
   "paper_text": "all but 14 of them",
   "paper_line": 1013,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "att-004",
   "section": "What the attractors look like",
   "claim": "variance in two principal axes (paper: What the attractors look like)",
   "appears_as": "(61.6% of their variance",
   "paper_text": "(61.6\\,\\% of the variance",
   "paper_line": 1015,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "att-005",
   "section": "What the attractors look like",
   "claim": "variance in three (paper: What the attractors look like)",
   "appears_as": "77.4% with a third",
   "paper_text": "77.4\\,\\% with the third",
   "paper_line": 1015,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "att-006",
   "section": "What the attractors look like",
   "claim": "median jump in the full state (paper: What the attractors look like)",
   "appears_as": "by 0.30, more than the average distance (0.21)",
   "paper_text": "moves the state by 0.30 in all 896 dimensions",
   "paper_line": 1017,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "att-007",
   "section": "What the attractors look like",
   "claim": "Lyapunov spectrum (paper: What the attractors look like)",
   "appears_as": "0.274, −1.052, −1.486 and −1.856 per step",
   "paper_text": "$-1.486$ and $-1.856$ per step",
   "paper_line": 1020,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "att-008",
   "section": "What the attractors look like",
   "claim": "Kaplan-Yorke estimate (paper: What the attractors look like)",
   "appears_as": "dimension estimate of 1.26",
   "paper_text": "$D_{\\mathrm{KY}}=1.26$",
   "paper_line": 1020,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "att-009",
   "section": "What the attractors look like",
   "claim": "false nearest neighbors at three delays (paper: What the attractors look like)",
   "appears_as": "only 3.4% of nearest neighbors are false",
   "paper_text": "to 3.4\\,\\% with three",
   "paper_line": 1025,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "att-010",
   "section": "What the attractors look like",
   "claim": "state distance of delay neighbors (paper: What the attractors look like)",
   "appears_as": "a median 0.00037 apart",
   "paper_text": "a median $3.7\\times10^{-4}$ apart",
   "paper_line": 1026,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "att-011",
   "section": "What the attractors look like",
   "claim": "unstable multiplier of the period-3 saddle (paper: What the attractors look like)",
   "appears_as": "with multiplier −1.772",
   "paper_text": "multiplier $-1.772$",
   "paper_line": 1029,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "att-012",
   "section": "What the attractors look like",
   "claim": "band states near the manifold (paper: What the attractors look like)",
   "appears_as": "every one of the 100,600",
   "paper_text": "states of the band it reaches lies within $9.8\\times10^{-6}$",
   "paper_line": 1032,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "att-013",
   "section": "What the attractors look like",
   "claim": "manifold distance bound (paper: What the attractors look like)",
   "appears_as": "within \\(9.8\\times10^{-6}\\) of the sampled",
   "paper_text": "lies within $9.8\\times10^{-6}$ of the sampled",
   "paper_line": 1032,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "att-014",
   "section": "What the attractors look like",
   "claim": "band width (paper: What the attractors look like)",
   "appears_as": "against a band width of 0.028",
   "paper_text": "the band is 0.028 wide",
   "paper_line": 1033,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "att-015",
   "section": "What the attractors look like",
   "claim": "cell of the proved pair (paper: What the attractors look like)",
   "appears_as": "proved (\\(\\alpha = 0.06468\\))",
   "paper_text": "($\\alpha=0.06468$), every one of 9216",
   "paper_line": 1034,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync19-001",
   "section": "Why the loop can be chaotic",
   "claim": "top of the unsteered chaotic band, the reference for the high-temperature bound",
   "appears_as": "unsteered sweeps below find chaos, \\(\\log_{10}T = 0.28\\)",
   "paper_text": "highest chaotic temperature of the unsteered sweeps below ($\\log_{10}T=0.28$;",
   "paper_line": 548,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync19-002",
   "section": "Derivative check and Hopfield proof",
   "claim": "slope of the rounding reference line in Figure 7 (error growing like 1/h)",
   "appears_as": "(dotted line, slope \\(-1\\))",
   "paper_text": "the error grows like $1/h$ (dotted line)",
   "paper_line": 464,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync19-003",
   "section": "Why the loop can be chaotic",
   "claim": "window length from which the sign of the overlapping-window average agrees in 23 of the 24 cells",
   "appears_as": "windows about twenty steps long tell chaos from order",
   "paper_text": "windows of about twenty steps of the model's own loop recover the sign of the long-run exponent",
   "paper_line": 635,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync19-004",
   "section": "Why the loop can be chaotic",
   "claim": "rate at which the block bounds close on the exponent in this sample (paper 1e8e82f4)",
   "appears_as": "the \\(1/k\\) is what these 24 cells show",
   "paper_text": "roughly like $1/k$ in this sample",
   "paper_line": 622,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync19-005",
   "section": "Why the loop can be chaotic",
   "claim": "held-out chaotic cells of the crossover rows: 14 per 0.5B direction, 10 in the 7B model (Figure 13) (paper 602c70ac)",
   "appears_as": "in the 0.5B model, 14 cells each, and the philosophy direction in the 7B model, 10 cells.",
   "paper_text": "in the 0.5B model, 14 cells each, and the philosophy direction in the 7B model, 10 cells",
   "paper_line": 686,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync19-006",
   "section": "Why the loop can be chaotic",
   "claim": "crossover arm compared for steering only the readout",
   "appears_as": "(version 10 against 00)",
   "paper_text": "arm 10 within $0.1$ of arm 11 on average",
   "paper_line": 735,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync19-007",
   "section": "Cusps and shrimp-like windows",
   "claim": "width of the fourth leg near the body and far down (in alpha_1)",
   "appears_as": "narrows from \\(5.1\\times10^{-5}\\) in \\(\\alpha_1\\) near the body to \\(3.5\\times10^{-8}\\)",
   "paper_text": "narrows from $5.1\\times10^{-5}$ in $\\alpha_1$ near the body to $3.5\\times10^{-8}$, far below the grid step",
   "paper_line": 2394,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync19-008",
   "section": "Cusps and shrimp-like windows",
   "claim": "points checked along the fourth leg's center line",
   "appears_as": "At each of 128 points from the body down",
   "paper_text": "is present at all 128 points from the body down to $\\alpha_2=0.075$",
   "paper_line": 2397,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync19-009",
   "section": "Cusps and shrimp-like windows",
   "claim": "lower bound of the center-line continuation (alpha_2)",
   "appears_as": "to \\(\\alpha_2 = 0.075\\), the bound of the continuation",
   "paper_text": "down to $\\alpha_2=0.075$, the bound of the continuation",
   "paper_line": 2397,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync19-010",
   "section": "Cusps and shrimp-like windows",
   "claim": "center-line points carrying the body's family",
   "appears_as": "is present at all 128 points (period 5",
   "paper_text": "is present at all 128 points",
   "paper_line": 2397,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync19-011",
   "section": "Cusps and shrimp-like windows",
   "claim": "periods found along the center line (5 at 127 points, 20 at one)",
   "appears_as": "at 127, period 20 at one)",
   "paper_text": "(period 5 at 127, period 20 at one)",
   "paper_line": 2398,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync19-012",
   "section": "Cusps and shrimp-like windows",
   "claim": "center-line points beyond the flip with the doubled orbit or chaos behind the text",
   "appears_as": "118 of 128 carry the doubled orbit or chaos behind the same text",
   "paper_text": "118 of 128 carry the doubled orbit or chaos behind the same text",
   "paper_line": 2399,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync19-013",
   "section": "Cusps and shrimp-like windows",
   "claim": "center-line points carrying the period-5 family (verdict list)",
   "appears_as": "128 points of its center line",
   "paper_text": "is present at all 128 points",
   "paper_line": 2397,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync19-015",
   "section": "Cusps and shrimp-like windows",
   "claim": "period of the window with Type A geometry (Figure 43 caption)",
   "appears_as": "the period-5 window has the first geometry",
   "paper_text": "the language model's period-5 window has the first geometry",
   "paper_line": 3023,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync19-016",
   "section": "Cusps and shrimp-like windows",
   "claim": "center-line points that retain the followed family (127 period 5, one period 20; Figure 52a caption)",
   "appears_as": "all 128 sampled points retain the followed family, 127 with period 5 and one with period 20",
   "paper_text": "all 128 sampled points retain the followed family, 127 with period 5 and one with period 20",
   "paper_line": 2997,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync19-017",
   "section": "Summary surfaces and abstract",
   "claim": "chaotic loops whose text changed with the batch layout (0.5B, float64; lead)",
   "appears_as": "it changed the text of 173 of 192 chaotic loops",
   "paper_text": "it changed the text of 173 of 192 chaotic float64 loops",
   "paper_line": 107,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync19-018",
   "section": "Summary surfaces and abstract",
   "claim": "periodic loops whose text changed with the batch layout (0.5B, float64; lead)",
   "appears_as": "the text changed in only 7 of 192",
   "paper_text": "but of only 7 of 192 periodic ones",
   "paper_line": 107,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync19-019",
   "section": "Summary surfaces and abstract",
   "claim": "chaotic loops whose text changed with the batch layout (abstract)",
   "appears_as": "changed in 173 of the 192 chaotic loops",
   "paper_text": "in Qwen2.5-0.5B the text changed in 173 of 192 chaotic loops",
   "paper_line": 50,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync19-020",
   "section": "Summary surfaces and abstract",
   "claim": "periodic loops whose text changed with the batch layout (abstract)",
   "appears_as": "but in only 7 of the 192 periodic ones",
   "paper_text": "but in only 7 of 192 periodic ones",
   "paper_line": 50,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync19-021",
   "section": "What the chaos does to reproducibility",
   "claim": "periodic cells whose most probable tokens differ in the last 500 steps",
   "appears_as": "only 7 of the 192 do the most probable tokens differ at any step of the last 500",
   "paper_text": "at only 7 of the 192 periodic cells do the most probable tokens differ at any step of the last 500",
   "paper_line": 1192,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync19-022",
   "section": "Discussion",
   "claim": "chaotic and periodic loops whose text changed with the batch layout (0.5B)",
   "appears_as": "the text changed in 173 of 192 chaotic loops and in 7 of",
   "paper_text": "the text changed in 173 of 192 chaotic loops and in 7 of 192 periodic ones",
   "paper_line": 4003,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync19-023",
   "section": "Steering toward hostility",
   "claim": "range of the leading-token probability at the last position of the text (bands-summary.json, phase 6: 0.2347 to 0.2538)",
   "appears_as": "its probability takes values between 0.235 and 0.254",
   "paper_text": "takes values between 0.235 and 0.254 and does not repeat over the 2000 steps",
   "paper_line": 2238,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync19-024",
   "section": "Steering toward hostility",
   "claim": "largest exponent of the strongest band-chaos cell (Figure 39 caption)",
   "appears_as": "largest Lyapunov exponent is 0.091 per step: the token that wins repeats",
   "paper_text": "while the largest Lyapunov exponent is 0.091 per step: the token that wins repeats",
   "paper_line": 2283,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync19-025",
   "section": "Steering toward hostility",
   "claim": "range of the leading-token probability (Figure 39 caption)",
   "appears_as": "which stays between 0.235 and 0.254 and does not repeat over the 2000 steps, at one repetition",
   "paper_text": "which stays between 0.235 and 0.254 and does not repeat over the 2000 steps, at one",
   "paper_line": 2287,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync19-026",
   "section": "Steering toward hostility",
   "claim": "degree of the fitted return polynomial (Figure 39 caption)",
   "appears_as": "(black: a fitted polynomial of degree 8)",
   "paper_text": "(black: a fitted polynomial of degree 8)",
   "paper_line": 2289,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync19-027",
   "section": "Steering toward hostility",
   "claim": "fitted and full exponents of the strongest band-chaos cell (Figure 39 caption)",
   "appears_as": "0.647 per repetition, is within 2% of the full map's 0.636 per repetition (seven steps of about 0.091 each)",
   "paper_text": "0.647 per repetition, is within 2\\,\\% of the full map's 0.636 per repetition (seven steps of about 0.091)",
   "paper_line": 2290,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sync19-028",
   "section": "Steering toward hostility",
   "claim": "parameters of the strongest band-chaos cell (Figure 39 caption)",
   "appears_as": "\\(\\alpha = 0.0655\\), \\(\\log_{10}T = 0.18995\\); float64",
   "paper_text": "($\\alpha=0.0655$, $\\log_{10}T=0.18995$; float64, 2000 steps",
   "paper_line": 2280,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "reviewfix19-001",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "lower estimate of the decades between T*(0.06) and the highest unsteered chaotic temperature (log10 T* >= 4.75 minus 0.28 = 4.47, quoted as at least 4.4)",
   "appears_as": "at least 4.4 decades above it.",
   "paper_text": "at least 3.1 and 4.4 decades above the highest chaotic temperature",
   "paper_line": 547,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "reviewfix19-002",
   "section": "Limitations",
   "claim": "answers changed in float64 by the batch layout in the short soft-thinking pipeline: none in Qwen2.5-0.5B, 5 % in Qwen2.5-7B at T = 10^0.2",
   "appears_as": "in float64 no answer changed in the 0.5B model, and 5%",
   "paper_text": "in float64 no answer changed in the 0.5B model, and 5\\,\\% changed in the 7B model",
   "paper_line": 3919,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "codexfix19-001",
   "section": "Cusps and shrimp-like windows",
   "claim": "ratio of the full leading modulus to the rank-one truncation's eigenvalue at the head (docs/rk/rk-g-p5.jsonl: 3.605e-3 / 2.704e-4 = 13.3)",
   "appears_as": "eigenvalue is about 13 times smaller than the full map's leading eigenvalue",
   "paper_text": "That part's eigenvalue, however, is about 13 times smaller than the full leading modulus",
   "paper_line": 2439,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "codexfix19-002",
   "section": "Cusps and shrimp-like windows",
   "claim": "largest singular value of the one-period return map at the head, phase 0 (docs/rk/rk-p5-head.jsonl: 64.6)",
   "appears_as": "stretches one direction by a factor of about 65 (below)",
   "paper_text": "at one phase the norm of the return map is about 65",
   "paper_line": 2429,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "codexfix19-003",
   "section": "Cusps and shrimp-like windows",
   "claim": "largest multiplier beyond the leading pair on the 18 October curves beyond the followed domain",
   "appears_as": "they reach 0.010)",
   "paper_text": "they stay below it inside the followed domain and reach $0.010$ beyond it",
   "paper_line": 2420,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "codexfix19-004",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "cells (of 7936) where a block estimate rises between consecutive block lengths k = 1 to 5 (NB nb.json: 0, 6, 21 and 149 rises; 176 cells)",
   "appears_as": "176 of the 7936 an estimate rises between consecutive block lengths",
   "paper_text": "although in 176 of the 7936 cells an estimate rises between consecutive block lengths",
   "paper_line": 603,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "codexfix19-005",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "long-run exponent of the one disagreeing cell (run BH, bh.json a-1: -0.14638)",
   "appears_as": "negative long-run exponent (\\(-0.146\\))",
   "paper_text": "with an exponent of $-0.146$ over the 2000 later steps, whose window average falls from $+0.112$ to $+0.011$ but stays positive",
   "paper_line": 628,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "codexfix19-006",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "its overlapping-window average at 17 steps (bh.json a-1: 0.11180)",
   "appears_as": "whose window average falls from \\(+0.112\\) to",
   "paper_text": "whose window average falls from $+0.112$ to $+0.011$ but stays positive",
   "paper_line": 629,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "codexfix19-007",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "its overlapping-window average at 29 steps (bh.json a-1: 0.01133)",
   "appears_as": "\\(+0.011\\) but stays positive",
   "paper_text": "whose window average falls from $+0.112$ to $+0.011$ but stays positive",
   "paper_line": 629,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "codexfix19-008",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "long-run exponent of the cell the map labels periodic (bh.json a-1: +0.12431)",
   "appears_as": "positive long-run exponent (\\(+0.124\\))",
   "paper_text": "has an exponent of $+0.124$ over the 2000 later steps",
   "paper_line": 632,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "codexfix19-009",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "recorded steps of the exact-norm record",
   "appears_as": "do not cut the 32-step record into whole blocks",
   "paper_text": "tile the $N=32$ recorded steps",
   "paper_line": 615,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "codexfix19-010",
   "section": "Numerics and chaos labels",
   "claim": "chaos-labeled cells of the Figure 1 window never captured in 10^5 steps, of 192 (research log 18 Oct: 143)",
   "appears_as": "in the window of Figure 1, 143.",
   "paper_text": "176 and 143 cells were never captured by a periodic orbit",
   "paper_line": 852,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "codexfix19-011",
   "section": "Numerics and chaos labels",
   "claim": "longest transient before capture over both maps (report audit: captures to 97,500 steps)",
   "appears_as": "to 97,500 steps before settling",
   "paper_text": "ended on periodic orbits after 600 to 97{,}500 steps",
   "paper_line": 852,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "codexfix19-012",
   "section": "Limitations",
   "claim": "longest transient before capture over both maps",
   "appears_as": "that settled after 600 to 97,500 steps",
   "paper_text": "ended on periodic orbits after 600 to 97{,}500 steps",
   "paper_line": 852,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "codexfix19-013",
   "section": "Cusps and shrimp-like windows",
   "claim": "center-line points of the fourth leg by period (verdict list)",
   "appears_as": "128 points of its center line, 127 with period 5 and one with period 20",
   "paper_text": "bound of the continuation (period 5 at 127, period 20 at one)",
   "paper_line": 2398,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync19-001",
   "section": "Cusps and shrimp-like windows",
   "claim": "located cusps among the tangent reversals of the continued fold curves (short version) (paper d9b3d94d)",
   "appears_as": "13 of the 17 reversals of direction are located cusps (the other four, found on 18 October,",
   "paper_text": "13 of the 17 tangent reversals are located cusps (the four found on 18 October are not located)",
   "paper_line": 262,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync19-002",
   "section": "Cusps and shrimp-like windows",
   "claim": "number of continued fold curves (short version) (paper d9b3d94d)",
   "appears_as": "on the eleven fold curves we continued,",
   "paper_text": "On the eleven fold curves we continued, 13 of the 17 tangent reversals",
   "paper_line": 261,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync19-003",
   "section": "Cusps and shrimp-like windows",
   "claim": "located cusps among the tangent reversals of the continued fold curves (paper d9b3d94d)",
   "appears_as": "continued, 13 of the 17 reversals of direction are located cusps. The other four, all",
   "paper_text": "On the eleven fold curves we continued, 13 of the 17 reversals of the parameter tangent are located",
   "paper_line": 2309,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync19-004",
   "section": "Cusps and shrimp-like windows",
   "claim": "temperature of the partial fold trace with two flagged, unlocated reversals (paper d9b3d94d)",
   "appears_as": "\\(\\log_{10}T = -0.105\\). This is not a",
   "paper_text": "two on a partial trace of a fold curve of the same window at $\\log_{10}T=-0.105$",
   "paper_line": 2313,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync19-005",
   "section": "Cusps and shrimp-like windows",
   "claim": "located cusps among the tangent reversals (verdict list) (paper d9b3d94d)",
   "appears_as": "13 of the 17 reversals on the eleven curves continued (the other four, found on",
   "paper_text": "On the eleven fold curves we continued, 13 of the 17 reversals of the parameter tangent are located",
   "paper_line": 2309,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync19-006",
   "section": "Cusps and shrimp-like windows",
   "claim": "critical-multiplier bound of the 18 October rerun of the period-5 curves (paper d9b3d94d)",
   "appears_as": "legs, keeps every critical multiplier within \\(1.9\\times10^{-7}\\) of \\(\\pm1\\), and the",
   "paper_text": "keeps every critical multiplier within $1.9\\times10^{-7}$ of $\\pm1$",
   "paper_line": 4969,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync19-007",
   "section": "Cusps and shrimp-like windows",
   "claim": "largest other multiplier modulus in the 18 October rerun (paper d9b3d94d)",
   "appears_as": "largest other modulus reaches 0.86 where the lower-right leg's fold and flip curves end at",
   "paper_text": "the largest other modulus reaches $0.86$ where the lower-right leg's fold and flip",
   "paper_line": 4970,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync19-008",
   "section": "Cusps and shrimp-like windows",
   "claim": "other-multiplier bound on the second fold curve in the rerun (paper d9b3d94d)",
   "appears_as": "in the rerun, \\(1.9\\times10^{-7}\\) and 0.61)",
   "paper_text": "in the rerun, $1.9\\times10^{-7}$ and $0.61$)",
   "paper_line": 4987,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync19-009",
   "section": "Cusps and shrimp-like windows",
   "claim": "third tangent reversal of the second fold curve, flagged but not located (paper d9b3d94d)",
   "appears_as": "at \\((-0.13295, 0.08530)\\), which the continuation flags but we have not located.",
   "paper_text": "The rerun finds a third reversal, at $(-0.13295,0.08530)$",
   "paper_line": 4990,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync19-010",
   "section": "Cusps and shrimp-like windows",
   "claim": "other-multiplier bound with the curves of 18 October (rounded up) (paper d9b3d94d)",
   "appears_as": "the bound becomes 0.87, the largest second multiplier (0.86) lying where the lower-right",
   "paper_text": "these bounds become $1.9\\times10^{-7}$ and $0.87$, the largest second multiplier ($0.86$) lying",
   "paper_line": 2376,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync19-011",
   "section": "Our shrimp, followed cell by cell",
   "claim": "exponent threshold of the follow rule for slowly converging cells (paper d9b3d94d)",
   "appears_as": "but the text repeats exactly and the Lyapunov exponent is below 0.005 (an orbit converging slowly next to a fold or",
   "paper_text": "an exponent below 0.005 (a slowly converging orbit next to a fold or a flip)",
   "paper_line": 2389,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync19-013",
   "section": "Cusps and shrimp-like windows",
   "claim": "exponent threshold of the follow rule (Figure 56 note) (paper d9b3d94d)",
   "appears_as": "dark gray: no period found and an exponent below 0.005; light gray: the attractor was lost), with the fold (black)",
   "paper_text": "and an exponent below 0.005; light gray: the attractor was lost), with the fold (black)",
   "paper_line": 4955,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync19-014",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "block-bound estimates below the 60-step tangent exponent: none (paper d9b3d94d)",
   "appears_as": "No estimate fell below the tangent exponent of its own 60 measured steps at any \\(k\\)",
   "paper_text": "No estimate fell below the tangent exponent of its own 60 measured steps at any $k$",
   "paper_line": 606,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync19-015",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "cells with a k = 4 or 5 estimate below the map's 300-step exponent (paper d9b3d94d)",
   "appears_as": "(in 13 cells an estimate at \\(k = 4\\) or 5 lies below the map's exponent, which was measured over 300",
   "paper_text": "(in 13 cells a $k=4$ or 5 estimate lies below the map's exponent, which was measured over 300 steps of a separate float64 run)",
   "paper_line": 606,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync19-016",
   "section": "Why the two families cross in both orders",
   "claim": "bracket widths at the five switches where the bisection met a third loop (paper d9b3d94d)",
   "appears_as": "of the eight switches and to 1/4 or 1/2 of it at the other five, where the bisection met a",
   "paper_text": "to 1/4 or 1/2 of it at the other five, where the bisection met a third loop",
   "paper_line": 3136,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync19-017",
   "section": "Shrimps of a two-dimensional kind",
   "claim": "second-to-first singular-value ratio at four points near the head (paper d9b3d94d)",
   "appears_as": "\\(1.8\\times10^{-4}\\) at four points \\(5\\times10^{-5}\\) away), and at most 0.031 of it at the",
   "paper_text": "($1.7$ to $1.8\\times10^{-4}$ at four points $5\\times10^{-5}$ away)",
   "paper_line": 2435,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync19-018",
   "section": "Cusps and shrimp-like windows",
   "claim": "lowest period-5 cell of the lower-left leg in the follow run (Figure 53 note) (paper d9b3d94d)",
   "appears_as": "the leg's lowest period-5 cell in the follow run is at 0.0919.",
   "paper_text": "the leg's lowest period-5 cell in the follow run is at $0.0919$",
   "paper_line": 5037,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync19-019",
   "section": "Evidence grading",
   "claim": "doses at which the fixed-shape test's primary criterion held (paper d9b3d94d)",
   "appears_as": "the primary dose criterion held at every dose from \\(10^{-15}\\) to \\(10^{-7}\\)",
   "paper_text": "the primary dose criterion holds at every dose from $10^{-15}$ to $10^{-7}$",
   "paper_line": 5899,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync19-020",
   "section": "Contributions reasoning2",
   "claim": "number of periodic orbits with computer-assisted proofs (paper d9b3d94d); corrected after arxiv-v1 at paper 1b718635",
   "appears_as": "Computer-assisted proofs cover four periodic orbits (the period-8 orbit, a coexisting",
   "paper_text": "computer-assisted proofs for only four orbits at three parameter points (the period-8 orbit, a coexisting period-2 and period-3 pair, and the 3-cycle at the start of the cascade)",
   "paper_line": 6509,
   "paper_file": "paper/llm/main.tex",
   "paper_commit": "1b71863581386048c50d41b1f8137a6ba6adec25"
  },
  {
   "id": "resync19-021",
   "section": "Numerics and chaos labels",
   "claim": "number of periodic orbits with computer-assisted proofs (certification panel) (paper d9b3d94d); rebound at paper 13145281; corrected after arxiv-v1 at paper 1b718635",
   "appears_as": "why we certified only four periodic orbits.",
   "paper_text": "computer-assisted proofs for only four orbits at three parameter points",
   "paper_line": 6509,
   "paper_file": "paper/llm/main.tex",
   "paper_commit": "1b71863581386048c50d41b1f8137a6ba6adec25"
  },
  {
   "id": "resync19-022",
   "section": "Cascade and proof",
   "claim": "periods of the coexisting certified orbits (certification panel) (paper d9b3d94d); rebound at paper 13145281; corrected after arxiv-v1 at paper 1b718635",
   "appears_as": "for two coexisting attracting orbits of periods 2 and 3 at a second setting",
   "paper_text": "two coexisting attracting orbits of periods 2 and 3",
   "paper_line": 92,
   "paper_file": "paper/llm/main.tex",
   "paper_commit": "1b71863581386048c50d41b1f8137a6ba6adec25"
  },
  {
   "id": "resync19-023",
   "section": "Evidence grading",
   "claim": "latest frozen test outside the search census (paper d9b3d94d)",
   "appears_as": "tests frozen later, up to the fixed-shape control of 18 October, are identified as such where",
   "paper_text": "tests frozen later, up to the fixed-shape control of 18 October, are identified as such where they are reported",
   "paper_line": 5797,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync19-024",
   "section": "Saddle-node bottleneck",
   "claim": "Newton residual of the seed orbit in the curve-finding method (step 1; paper e2d2bd0c)",
   "appears_as": "solves \\(F^p(x) = x\\) to a residual of about \\(10^{-14}\\)",
   "paper_text": "refines the orbit to residuals near $10^{-14}$",
   "paper_line": 4387,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync19-025",
   "section": "Saddle-node bottleneck",
   "claim": "residual gate of every drawn curve point (paper d9b3d94d)",
   "appears_as": "\\(10^{-10}\\) and the critical multiplier, recomputed from the dense monodromy,",
   "paper_text": "its residual is at most $10^{-10}$ and the critical",
   "paper_line": 4398,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync19-026",
   "section": "Saddle-node bottleneck",
   "claim": "gate on the critical multiplier of every drawn curve point (paper d9b3d94d)",
   "appears_as": "is real and within \\(10^{-7}\\) of \\(+1\\) or \\(-1\\)",
   "paper_text": "real and within $10^{-7}$ of $\\pm1$",
   "paper_line": 4399,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync19-027",
   "section": "Saddle-node bottleneck",
   "claim": "cost of one curve point for the 0.5B model (paper d9b3d94d)",
   "appears_as": "Each curve point costs about 50 seconds on one H100 GPU for the 0.5B model",
   "paper_text": "For the 0.5B model one curve point takes about 50\\,s",
   "paper_line": 4404,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync19-028",
   "section": "Cusps and shrimp-like windows",
   "claim": "agreement of the computed kite corners A and B with Gallas's (paper d9b3d94d)",
   "appears_as": "The computed corners A and B agree with Gallas's to six significant digits.",
   "paper_text": "The computed corners A and B agree with Gallas's to six significant digits.",
   "paper_line": 3014,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-001",
   "section": "Steering as a probe",
   "claim": "dimension of the residual stream of Qwen2.5-0.5B-Instruct (paper e2d2bd0c)",
   "appears_as": "one 896-dimensional vector per token",
   "paper_text": "($V=151{,}936$, $d=896$)",
   "paper_line": 314,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-002",
   "section": "Steering as a probe",
   "claim": "number of short texts and of steps behind the philosophy direction (paper e2d2bd0c)",
   "appears_as": "direction comes from 16 short texts and three steps.",
   "paper_text": "Our main direction, philosophy, is built in three steps from 16 short texts",
   "paper_line": 329,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-003",
   "section": "Steering as a probe",
   "claim": "number of philosophical sentences (paper e2d2bd0c)",
   "appears_as": "Eight philosophical sentences, such as",
   "paper_text": "eight philosophical sentences, such as",
   "paper_line": 330,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-004",
   "section": "Steering as a probe",
   "claim": "number of neutral sentences (paper e2d2bd0c)",
   "appears_as": "and eight neutral ones, such as",
   "paper_text": "and eight neutral ones, such as",
   "paper_line": 332,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-005",
   "section": "Steering as a probe",
   "claim": "layer whose output is read for the direction (paper e2d2bd0c)",
   "appears_as": "the residual-stream vector after decoder layer 12",
   "paper_text": "residual-stream vector after decoder layer 12 (of 24, counted from 0) is read at its last token",
   "paper_line": 334,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-006",
   "section": "Steering as a probe",
   "claim": "number of decoder layers, counted from 0 (paper e2d2bd0c)",
   "appears_as": "(of 24, counted from 0) is read at the text's last token.",
   "paper_text": "after decoder layer 12 (of 24, counted from 0)",
   "paper_line": 334,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-007",
   "section": "Steering as a probe",
   "claim": "length of the direction: mean residual norm at layer 12 over the 16 texts (paper e2d2bd0c)",
   "appears_as": "(189, the mean over the 16 texts).",
   "paper_text": "rescaled to the mean residual norm at that layer over the 16 texts, $\\lVert v\\rVert=189$",
   "paper_line": 336,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-008",
   "section": "Steering as a probe",
   "claim": "push of alpha = 0.07 as a fraction of a typical residual vector (paper e2d2bd0c)",
   "appears_as": "\\(\\alpha = 0.07\\) adds 7% of one.",
   "paper_text": "$\\alpha=0.07$ adds 7\\,\\% of one",
   "paper_line": 337,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-009",
   "section": "Steering as a probe",
   "claim": "norm of the raw difference of the group means (paper e2d2bd0c)",
   "appears_as": "the two groups has length 8.1, so",
   "paper_text": "The raw difference has norm 8.1, so",
   "paper_line": 337,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-010",
   "section": "Steering as a probe",
   "claim": "strength that reproduces the natural contrast between the two groups (paper e2d2bd0c)",
   "appears_as": "\\(\\alpha \\approx 0.043\\) reproduces the natural",
   "paper_text": "$\\alpha\\approx0.043$ reproduces the natural contrast between the two groups of texts",
   "paper_line": 338,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-011",
   "section": "Steering as a probe",
   "claim": "steering range of Figure 1 (paper 070d66e0)",
   "appears_as": "the values of Figure 1, 0.0625 to",
   "paper_text": "the values of Figure~\\ref{fig:cross512}, 0.0625 to 0.0775, push 1.5 to 1.8 times as far",
   "paper_line": 338,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-012",
   "section": "Steering as a probe",
   "claim": "upper end of Figure 1's steering range (paper 070d66e0)",
   "appears_as": "0.0775, push 1.5 to 1.8 times as far.",
   "paper_text": "the values of Figure~\\ref{fig:cross512}, 0.0625 to 0.0775, push 1.5 to 1.8 times as far",
   "paper_line": 338,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-013",
   "section": "Steering as a probe",
   "claim": "how far Figure 1's steering values push relative to the natural contrast (alpha ~ 0.043); stated in the paper since a865b0b8, previously DERIVED (0.0625/0.043 = 1.45, 0.0775/0.043 = 1.80) (paper 070d66e0)",
   "appears_as": "push 1.5 to 1.8 times as far",
   "paper_text": "push 1.5 to 1.8 times as far",
   "paper_line": 339,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-014",
   "section": "Steering as a probe",
   "claim": "where the push is added during the loop (paper 1e8e82f4)",
   "appears_as": "the residual stream after layer 12 at every position: at",
   "paper_text": "is added to the residual stream after layer 12 at every position: at each token of the prompt and at the fed-back soft token",
   "paper_line": 339,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-015",
   "section": "Steering as a probe",
   "claim": "layers of the two directions of the period-5 shrimp's plane (paper e2d2bd0c)",
   "appears_as": "4 and hostility at layer 16 for the two-layer plane of the period-5 shrimp.",
   "paper_text": "gratitude at block~4 and hostility at block~16",
   "paper_line": 2987,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-016",
   "section": "Our shrimp, followed cell by cell",
   "claim": "resolution of the fixed-start map of the period-5 window (run HP5) (paper e2d2bd0c)",
   "appears_as": "A finer fixed-start map of the window, 512 × 512 cells (Figure 62a)",
   "paper_text": "From the fixed start, a $512\\times512$ map of the window",
   "paper_line": 2381,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-017",
   "section": "Our shrimp, followed cell by cell",
   "claim": "share of the followed domain where the fixed start reaches the window's family (HP5) (paper e2d2bd0c)",
   "appears_as": "In 59% of them the fixed start reaches the window's family",
   "paper_text": "shows the window's family in 59\\,\\% of the cells of the followed domain",
   "paper_line": 2382,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-018",
   "section": "Our shrimp, followed cell by cell",
   "claim": "share of the followed domain where the fixed start reaches another periodic attractor (HP5) (paper e2d2bd0c)",
   "appears_as": "in 24% it reaches another periodic attractor",
   "paper_text": "in 24\\,\\% the fixed start reaches another periodic attractor",
   "paper_line": 2382,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-019",
   "section": "Our shrimp, followed cell by cell",
   "claim": "periods of the coexisting attractor and its doublings reached by the fixed start (paper e2d2bd0c)",
   "appears_as": "the coexisting period-4 attractor and its doublings (periods 4, 8, 16 and 32)",
   "paper_text": "mostly the coexisting period-4 attractor and its doublings (periods 4, 8, 16 and 32)",
   "paper_line": 2383,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-020",
   "section": "Our shrimp, followed cell by cell",
   "claim": "share of the followed domain where the fixed start's largest exponent exceeds 1e-3, counted as chaos (HP5) (paper 3c2498da)",
   "appears_as": "in 12% its largest exponent exceeds",
   "paper_text": "12\\,\\% a largest exponent above $10^{-3}$ (chaos; at 33 cells it overrides a detected period)",
   "paper_line": 2384,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-021",
   "section": "Our shrimp, followed cell by cell",
   "claim": "share of the followed domain where the fixed start reaches neither (HP5) (paper 3c2498da)",
   "appears_as": "and in 5% neither. Where it",
   "paper_text": "and in 5\\,\\% neither",
   "paper_line": 2384,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-022",
   "section": "Our shrimp, followed cell by cell",
   "claim": "the coexisting attractor reached in parts of the legs (short version) (paper e2d2bd0c)",
   "appears_as": "coexisting period-4 attractor instead, so even in a fine fixed-start map the shrimp appears torn across a broad",
   "paper_text": "the coexisting period-4 attractor that the fixed start reaches in parts of the legs",
   "paper_line": 2990,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-023",
   "section": "Our shrimp, followed cell by cell",
   "claim": "resolution of panel (a) of Figure 52 (HP5) (paper e2d2bd0c)",
   "appears_as": "(a) A 512 × 512 map of the window from the fixed start",
   "paper_text": "A $512\\times512$ map of the window from the fixed start (run HP5;",
   "paper_line": 2988,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-024",
   "section": "Our shrimp, followed cell by cell",
   "claim": "steps of the HP5 map in alpha_1 and alpha_2 (Figure 52 note) (paper e2d2bd0c)",
   "appears_as": "(steps \\(2.4\\times10^{-5}\\) in \\(\\alpha_1\\) and \\(3.8\\times10^{-5}\\) in \\(\\alpha_2\\))",
   "paper_text": "steps $2.4\\times10^{-5}$ in $\\alpha_1$ and $3.8\\times10^{-5}$ in $\\alpha_2$)",
   "paper_line": 2988,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-025",
   "section": "Our shrimp, followed cell by cell",
   "claim": "the window's family: periods that are multiples of five (Figure 52 note) (paper e2d2bd0c)",
   "appears_as": "cells whose period is a multiple of five, the window's family",
   "paper_text": "cells whose period is a multiple of five, the window's family",
   "paper_line": 2989,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-026",
   "section": "Our shrimp, followed cell by cell",
   "claim": "coexisting period-4 attractor shown pale (Figure 52 note) (paper e2d2bd0c)",
   "appears_as": "(among them the coexisting period-4 attractor that the fixed start reaches in parts of the legs, across which the shrimp appears torn)",
   "paper_text": "the coexisting period-4 attractor that the fixed start reaches in parts of the legs",
   "paper_line": 2990,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-027",
   "section": "Our shrimp, followed cell by cell",
   "claim": "grid spacing of the follow run whose domain edge is drawn in cyan (Figure 52 note) (paper e2d2bd0c)",
   "appears_as": "followed cell by cell from the body on a grid of spacing \\(1.25\\times10^{-4}\\)",
   "paper_text": "followed cell by cell from the body on a grid of spacing $1.25\\times10^{-4}$",
   "paper_line": 2996,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-028",
   "section": "The lower-left leg's own curves",
   "claim": "exponent threshold of the follow rule (Figure 53 note; legend as in the paper's Figure shrimptemperature a, since Figure 52a no longer shows the followed domain) (paper e2d2bd0c)",
   "appears_as": "dark gray: no period found and an exponent below 0.005; light gray: the attractor was lost), with the fold (black) and flip (red, dashed) curves of",
   "paper_text": "and an exponent below 0.005; light gray: the attractor was lost), with the fold (black) and flip (red, dashed) curves",
   "paper_line": 4955,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "resync20-029",
   "section": "Reproducibility",
   "claim": "cells with neither label in the batch-layout test (Figure 23 note) (paper e2d2bd0c)",
   "appears_as": "the median of the 64 cells with neither label (gray)",
   "paper_text": "the median of the 64 cells with neither label (gray)",
   "paper_line": 1464,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-001",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "period of the second shrimp-shaped window (paper e2d2bd0c)",
   "appears_as": "shrimp-shaped window that the article studies: the period-6 loop",
   "paper_text": "holds a second shrimp-shaped window: the period-6 loop",
   "paper_line": 2518,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-002",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "length of the window's token loop (paper e2d2bd0c)",
   "appears_as": "six tokens repeated forever.",
   "paper_text": "with the same six-token text but",
   "paper_line": 2542,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-003",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "seed cell of the period-6 orbit (most contracting cell of the HR9 scan) (paper e2d2bd0c)",
   "appears_as": "\\((\\alpha, \\log_{10}T) = (0.073097, -0.15204)\\)",
   "paper_text": "At a strongly contracting cell of the map, $(\\alpha,\\log_{10}T)=(0.073097,-0.15204)$",
   "paper_line": 2520,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-004",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "primitive period of the seed orbit (paper e2d2bd0c)",
   "appears_as": "float64 converges to a primitive period-6 orbit",
   "paper_text": "converges to a primitive period-6 orbit",
   "paper_line": 2521,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-005",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Newton residual of the seed orbit (paper e2d2bd0c)",
   "appears_as": "three (residual \\(1.6\\times10^{-14}\\))",
   "paper_text": "(residual $1.6\\times10^{-14}$)",
   "paper_line": 2521,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-006",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "modulus of the seed orbit's complex leading pair (paper e2d2bd0c)",
   "appears_as": "form a complex pair of modulus 0.016",
   "paper_text": "multipliers form a complex pair of modulus $0.016$",
   "paper_line": 2522,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-007",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "cells of the followed attractor: the body and its legs, continued through a narrow neck into a smaller window (paper 7526a62e)",
   "appears_as": "attractor fills 4224 cells. They cover the shrimp's body and its legs, and below the body they continue through a",
   "paper_text": "the attractor fills 4224 cells. They cover the shrimp's body and its legs, and below the body they continue through a narrow neck into a smaller, distorted window",
   "paper_line": 2523,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-008",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "followed cells with period 6 (paper e2d2bd0c)",
   "appears_as": "Period 6 holds in 1946 of them",
   "paper_text": "period 6 holds 1946",
   "paper_line": 2524,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-009",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "doubled periods along the edges (paper e2d2bd0c)",
   "appears_as": "the doubled periods 12, 24 and",
   "paper_text": "periods 12, 24 and 48 hold 945 along the edges",
   "paper_line": 2525,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-010",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "followed cells with periods 12, 24 and 48 (paper e2d2bd0c)",
   "appears_as": "48 in 945, along the edges",
   "paper_text": "periods 12, 24 and 48 hold 945 along the edges",
   "paper_line": 2525,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-011",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "followed cells with other periods (paper e2d2bd0c)",
   "appears_as": "other periods in 35;",
   "paper_text": "other periods 35",
   "paper_line": 2525,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-012",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "followed cells with chaos behind the repeating text (paper 602c70ac)",
   "appears_as": "chaos behind the repeating text in 811, cells where the most probable",
   "paper_text": "chaos behind the repeating text in 811 (an exactly repeating text, no period up to 64 and an exponent of at least 0.005)",
   "paper_line": 2525,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-013",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "slow followed cells (paper 602c70ac)",
   "appears_as": "and slow cells in 487, the same but with an",
   "paper_text": "slow cells in 487 (the same with an exponent below 0.005",
   "paper_line": 2526,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-014",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "continuation from the body in four directions (paper 7526a62e)",
   "appears_as": "Continued from the body in four directions, up and down in \\(\\alpha\\) and in \\(T\\), each time along a",
   "paper_text": "Continued from the body in four directions, up and down in $\\alpha$ and in $T$, the period-6 orbit ends at a fold above and on the right",
   "paper_line": 2527,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-015",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "residual and multiplier gates of the curve points (within 1e-7 on the body and kite curves) (paper 3c2498da)",
   "appears_as": "\\(10^{-10}\\), critical multiplier real and within \\(10^{-7}\\) of \\(\\pm1\\) on the body and kite curves; four points of",
   "paper_text": "(residual at most $10^{-10}$, critical multiplier real and within $10^{-7}$ of $\\pm1$ on the body and kite curves; four points of the extended leg curves reach $2.9\\times10^{-7}$)",
   "paper_line": 2528,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-016",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "boundary gate within the window of Figure 57a, periods 6 and 12: all 232 pairs within two grid steps (paper 3c2498da)",
   "appears_as": "for all 232 neighboring pairs of cells with periods 6 and 12",
   "paper_text": "curves for all 232 neighboring pairs of periods 6 and 12",
   "paper_line": 2532,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-017",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "boundary check within the window of Figure 57a, period 6 and the lost followed attractor: all 459 pairs (paper 17353aec)",
   "appears_as": "and for all 459 pairs of a period-6 cell and a cell where the",
   "paper_text": "and all 459 pairs of a period-6 cell and a cell where the followed attractor was lost",
   "paper_line": 2532,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-018",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "median distance of both boundary gates within the window of Figure 57a (paper 3c2498da)",
   "appears_as": "(median distance 0.19 steps for both kinds)",
   "paper_text": "(median distances 0.19 steps)",
   "paper_line": 2532,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-020",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "resolution of the close-up map (run HR10) (paper e2d2bd0c)",
   "appears_as": "A 640 × 640 fixed-start map centered on the body",
   "paper_text": "$640\\times640$ fixed-start map centered on the body",
   "paper_line": 2535,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-021",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "steps of the close-up map in alpha (paper e2d2bd0c)",
   "appears_as": "with steps of \\(4.4\\times10^{-6}\\) in",
   "paper_text": "(steps $4.4\\times10^{-6}$ in $\\alpha$ and $1.25\\times10^{-5}$ in",
   "paper_line": 2535,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-022",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "steps of the close-up map in log10 T, relative to Figure 1 (paper e2d2bd0c)",
   "appears_as": "\\(\\alpha\\) and \\(1.25\\times10^{-5}\\) in \\(\\log_{10}T\\), about seven times finer than Figure 1",
   "paper_text": "$1.25\\times10^{-5}$ in $\\log_{10}T$, about seven times finer than",
   "paper_line": 2535,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-023",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "chaotic share of the close-up map (paper e2d2bd0c)",
   "appears_as": "is 66.5% chaotic",
   "paper_text": "66.5\\,\\% of its cells chaotic",
   "paper_line": 2536,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-024",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "the crossing R of the two flip curves (paper e2d2bd0c)",
   "appears_as": "\\((0.072912, -0.154104)\\) (the cyan diamond in Figure 48b)",
   "paper_text": "near $(0.072912,-0.154104)$",
   "paper_line": 2540,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-025",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Newton residuals of the two orbits at R (paper e2d2bd0c)",
   "appears_as": "(residuals \\(3\\times10^{-14}\\) and \\(2\\times10^{-13}\\))",
   "paper_text": "(residuals $3\\times10^{-14}$ and $2\\times10^{-13}$)",
   "paper_line": 2542,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-026",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "the two orbits at R write the same six-token text (paper e2d2bd0c)",
   "appears_as": "Both write the same six-token text",
   "paper_text": "with the same six-token text but",
   "paper_line": 2542,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-027",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "distance of the two orbits at R (paper e2d2bd0c)",
   "appears_as": "6.4% of the mean state norm apart",
   "paper_text": "6.4\\,\\% of the mean state norm apart",
   "paper_line": 2543,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-028",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "cyclic alignments tried for the distance (paper e2d2bd0c)",
   "appears_as": "so we try all six cyclic alignments",
   "paper_text": "the best of the six cyclic alignments",
   "paper_line": 2543,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-029",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "leading multipliers of the two orbits at the approximate crossing R (no exclusive cause given) (paper 17353aec)",
   "appears_as": "have leading multipliers \\(-0.9952\\) and \\(-1.0005\\): close to \\(-1\\), but not within that tolerance.",
   "paper_text": "leading multipliers are $-0.9952$ and $-1.0005$ at this approximate crossing of the two traced curves",
   "paper_line": 2544,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-030",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "check on the critical multiplier of the drawn curve points (paper 17353aec)",
   "appears_as": "drawn point of both curves passed the check of step 4, within \\(10^{-7}\\) of \\(-1\\)",
   "paper_text": "critical multiplier real and within $10^{-7}$ of $\\pm1$",
   "paper_line": 2528,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-031",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "leading multipliers of the two orbits at R (paper 17353aec)",
   "appears_as": "leading multipliers \\(-0.9952\\) and \\(-1.0005\\)",
   "paper_text": "Their leading multipliers are $-0.9952$ and $-1.0005$",
   "paper_line": 2543,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-032",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "distances from R to the nearest saved points of the two traced curves, in steps of the grid of Figure 1 (paper 17353aec)",
   "appears_as": "Figure 1, the nearest saved points of the two curves lie 1.7 and 0.3 steps away.",
   "paper_text": "whose nearest saved points lie 1.7 and 0.3 steps of the grid of Figure~\\ref{fig:cross512} away",
   "paper_line": 2544,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-033",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "distance from R to the nearest saved point of the second curve, in steps of the grid of Figure 1 (paper 17353aec)",
   "appears_as": "the nearest saved points of the two curves lie 1.7 and 0.3 steps away",
   "paper_text": "whose nearest saved points lie 1.7 and 0.3 steps of the grid of Figure~\\ref{fig:cross512} away",
   "paper_line": 2544,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-035",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "figure of Gallas (1994) with the kite C-A-R-B (paper e2d2bd0c)",
   "appears_as": "([Gallas, 1994](#ref-gallas-1994), Fig. 7)",
   "paper_text": "\\cite[Fig.~7]{gallas1994dissecting}",
   "paper_line": 2547,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-036",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "body point near R where the lower flip curve's orbit attracts (paper e2d2bd0c)",
   "appears_as": "at \\((0.0730, -0.1539)\\), the orbit of",
   "paper_text": "at $(0.0730,-0.1539)$, the orbit of the lower flip curve is attracting",
   "paper_line": 2547,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-037",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "leading multiplier of that orbit there (paper e2d2bd0c)",
   "appears_as": "(leading multiplier \\(-0.797\\))",
   "paper_text": "(leading multiplier $-0.797$)",
   "paper_line": 2548,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-038",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "located cusps of the period-6 fold curves besides the kite's cusp C (paper 070d66e0)",
   "appears_as": "Besides C, the fold curves have five more located cusps (Table 16)",
   "paper_text": "the fold curves have five more located cusps (Table~\\ref{tab:p6cusps})",
   "paper_line": 2563,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-039",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "four of the five further cusps, in two pairs near the ends of the upper-left and lower-left legs (paper 7526a62e)",
   "appears_as": "the ends of the upper-left and lower-left legs lie four of them, in two pairs",
   "paper_text": "four in two pairs near the ends of the upper-left and lower-left legs",
   "paper_line": 2563,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-040",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "located cusps counted earlier (the period-6 cusps are not among them) (paper e2d2bd0c)",
   "appears_as": "These six cusps are not among the thirteen counted in",
   "paper_text": "At the thirteen located cusps",
   "paper_line": 4870,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-041",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "grid of the continued orbit over the body (run DSS6) (paper e2d2bd0c)",
   "appears_as": "31 × 31 grid over the body",
   "paper_text": "On a $31\\times31$ grid of the continued orbit over the body",
   "paper_line": 2569,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-042",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "parameter ranges of the DSS6 grid (paper e2d2bd0c)",
   "appears_as": "(\\(\\alpha\\) from 0.0724 to 0.0738, \\(\\log_{10}T\\) from \\(-0.1545\\) to \\(-0.1500\\))",
   "paper_text": "($\\alpha$ from 0.0724 to 0.0738, $\\log_{10}T$ from $-0.1545$ to $-0.1500$;",
   "paper_line": 2569,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-043",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "cells of the DSS6 grid at which Newton continuation converged (of 582 reached before the time limit) (paper 1e8e82f4)",
   "appears_as": "converged at 529 of them",
   "paper_text": "the run reached 582 of the 961 cells before its time limit, and 529 of them converged",
   "paper_line": 2570,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-044",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "smallest leading modulus on the DSS6 grid and its cell (paper 070d66e0)",
   "appears_as": "grid, 0.0063, at the cell \\((0.073053, -0.15120)\\) on the line of strongest contraction",
   "paper_text": "$0.0063$ at the cell $(0.073053,-0.15120)$ on the line of strongest contraction",
   "paper_line": 2571,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-045",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "the nearly imaginary leading pair at that cell (paper e2d2bd0c)",
   "appears_as": "\\(0.0004 \\pm 0.0063i\\)",
   "paper_text": "$0.0004\\pm0.0063i$",
   "paper_line": 2572,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-046",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "modulus of the third multiplier there (paper e2d2bd0c)",
   "appears_as": "modulus 0.0051. Three multipliers of nearly equal small modulus",
   "paper_text": "with a third multiplier of modulus $0.0051$",
   "paper_line": 2572,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-047",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "cells with a complex leading pair (paper e2d2bd0c)",
   "appears_as": "bends to the upper left. All nine",
   "paper_text": "and all nine cells with a complex leading pair lie on its upper part",
   "paper_line": 2575,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-048",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "arguments of the complex leading pairs (paper e2d2bd0c)",
   "appears_as": "with arguments of 43 to 135 degrees",
   "paper_text": "(arguments 43 to 135 degrees, moduli 0.006 to 0.038)",
   "paper_line": 2575,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-049",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "moduli of the complex leading pairs (paper e2d2bd0c)",
   "appears_as": "moduli of 0.006 to 0.038",
   "paper_text": "(arguments 43 to 135 degrees, moduli 0.006 to 0.038)",
   "paper_line": 2575,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-050",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "cells where the real or conjugate top-two pair has a negative real product (of 289) (paper 3c2498da)",
   "appears_as": "conjugate, and their product is then real, negative at 143 of these cells.",
   "paper_text": "and their real product is negative at 143",
   "paper_line": 2576,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-051",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "neighboring solved pairs across which the real leading multiplier changes sign (paper 3c2498da)",
   "appears_as": "and we infer no determinant-zero curve from them. The real leading multiplier changes sign across 45 neighboring",
   "paper_text": "The real leading multiplier changes sign across 45 neighboring solved pairs",
   "paper_line": 2578,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-052",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "sign-change pairs passing the endpoint test (leading and next moduli within a factor three at both ends) (paper 3c2498da)",
   "appears_as": "of each pair: only two of the 45 pairs have them within a factor three of each other at both ends.",
   "paper_text": "only two have leading and next moduli within a factor three at both ends",
   "paper_line": 2579,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-053",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "the endpoint test cannot tell a zero crossing from an exchange of dominance (paper 3c2498da)",
   "appears_as": "looks only at the two cells, it cannot tell a multiplier crossing zero from an exchange of dominance;",
   "paper_text": "this endpoint test does not tell a multiplier crossing zero from an exchange of dominance",
   "paper_line": 2580,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-054",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "verdict: the three numerical criteria along the body (paper e2d2bd0c)",
   "appears_as": "With these qualifications the period-6 window meets the three numerical criteria along its body",
   "paper_text": "With these qualifications the period-6 window meets the three numerical criteria along its body",
   "paper_line": 2647,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-055",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "verdict: the kite and its cusp C located, five more cusps (paper 7526a62e)",
   "appears_as": "the kite of Gallas's cell and its cusp C located (five more located cusps close the ends of the legs and the small",
   "paper_text": "with the kite of Gallas's cell and its cusp C located (five more cusps close the ends of the legs and the small window beyond the neck)",
   "paper_line": 2647,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-056",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "resolution of panel (a) of the period-6 figure (paper e2d2bd0c)",
   "appears_as": "(a) A 640 × 640 map of the window, centered on the body",
   "paper_text": "(a) A $640\\times640$ map of the window, centered on the body",
   "paper_line": 2692,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-057",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "orbits found at the crossing (figure note) (paper e2d2bd0c)",
   "appears_as": "where two distinct period-6 orbits are found (a pseudo-crossing)",
   "paper_text": "where two distinct period-6 orbits are found (a pseudo-crossing)",
   "paper_line": 2694,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-058",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "cusps marked in panel (c) of Figure 57 (paper 070d66e0)",
   "appears_as": "gold stars: the six located cusps (Table 16)",
   "paper_text": "gold stars: the six located cusps (Table~\\ref{tab:p6cusps})",
   "paper_line": 2696,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-059",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "cusp table (Table 16), upper 1: position, c, det J (paper 00183cec)",
   "appears_as": "| upper 1 | \\((0.0678765, -0.1513104)\\) | \\(+6.10\\times10^{3}\\) | \\(4.59\\times10^{4}\\) |",
   "paper_text": "upper 1 & $(0.0678765, -0.1513104)$ & $+6.10\\times10^{3}$ & $4.59\\times10^{4}$",
   "paper_line": 2960,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-060",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "cusp table (Table 16), upper 2: position, c, det J (paper 00183cec)",
   "appears_as": "| upper 2 | \\((0.0682059, -0.1503283)\\) | \\(-8.01\\times10^{3}\\) | \\(2.20\\times10^{5}\\) |",
   "paper_text": "upper 2 & $(0.0682059, -0.1503283)$ & $-8.01\\times10^{3}$ & $2.20\\times10^{5}$",
   "paper_line": 2961,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-061",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "cusp table (Table 16), neck: position, c, det J (paper 070d66e0)",
   "appears_as": "| neck | \\((0.0748392, -0.1595956)\\) | \\(-4.02\\times10^{4}\\) | \\(4.47\\times10^{3}\\) |",
   "paper_text": "neck & $(0.0748392, -0.1595956)$ & $-4.02\\times10^{4}$ & $4.47\\times10^{3}$",
   "paper_line": 2964,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-062",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "cusp brackets: magnitude of the oriented quadratic coefficient at the twelve bracketing curve points, 0.17 to 39.11 (paper cda9ca04)",
   "appears_as": "of magnitude between 0.17 and 39.11 at the twelve bracketing curve points, falls to at most \\(9.5\\times10^{-5}\\)",
   "paper_text": "of magnitude between 0.17 and 39.11 at the twelve bracketing curve points, falls to at most $9.5\\times10^{-5}$ in modulus",
   "paper_line": 2950,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-063",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "critical multiplier at the located cusps (paper e2d2bd0c)",
   "appears_as": "the critical multiplier equals \\(+1\\) to within \\(8.2\\times10^{-9}\\)",
   "paper_text": "the critical multiplier equals $+1$ to within $8.2\\times10^{-9}$",
   "paper_line": 2951,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-064",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "largest next modulus at the located cusps (paper e2d2bd0c)",
   "appears_as": "and the next has modulus at most 0.74",
   "paper_text": "and the next has modulus at most 0.74",
   "paper_line": 2952,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-065",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "period of the window (subsection summary) (paper e2d2bd0c)",
   "appears_as": "shrimp-shaped window that the article studies, of period 6.",
   "paper_text": "holds a second shrimp-shaped window: the period-6 loop",
   "paper_line": 2518,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-066",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "located cusps besides the kite's cusp C (subsection summary) (paper 7526a62e)",
   "appears_as": "corners, A and B, are crossings of curves that belong to different orbits, like R. Five more located cusps close the",
   "paper_text": "Besides C, the fold curves have five more located cusps",
   "paper_line": 2562,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-067",
   "section": "Cusps and shrimp-like windows",
   "claim": "the second shrimp-shaped window (section introduction) (paper e2d2bd0c)",
   "appears_as": "a shrimp-shaped window of period 6 in the plane of Figure 1,",
   "paper_text": "a second shrimp-shaped window of the full map, consistent with Gallas's organization",
   "paper_line": 2649,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-068",
   "section": "Cusps and shrimp-like windows",
   "claim": "the second shrimp-shaped window, with the kite and its cusp C (section summary) (paper 7526a62e)",
   "appears_as": "shrimp-shaped window of period 6, lies in the plane of Figure 1 itself.",
   "paper_text": "with the kite of Gallas's cell and its cusp C located",
   "paper_line": 2647,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-069",
   "section": "Cusps and shrimp-like windows",
   "claim": "the period-6 window in the verdict list (paper e2d2bd0c)",
   "appears_as": "- in the plane of Figure 1 itself, the shrimp of the article: a period-6 window that meets the three",
   "paper_text": "the period-6 window meets the three numerical criteria along its body",
   "paper_line": 2647,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-070",
   "section": "Cusps and shrimp-like windows",
   "claim": "the kite of the period-6 window and its cusp (list of findings) (paper 7526a62e)",
   "appears_as": "numerical criteria along its body, with the kite of Gallas's",
   "paper_text": "with the kite of Gallas's cell and its cusp C located",
   "paper_line": 2647,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-071",
   "section": "Cusps and shrimp-like windows",
   "claim": "what remains open for the period-6 window (list of what was not found) (paper 070d66e0)",
   "appears_as": "- the far parts of the period-6 window's legs, which remain unresolved;",
   "paper_text": "The far parts of its legs remain unresolved.",
   "paper_line": 2651,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hedge-001",
   "section": "Summary surfaces and abstract",
   "claim": "share of sampled chaotic labels of two maps that persist to 10^5 steps (paper 070d66e0)",
   "appears_as": "random samples, 74 and 92% of the chaotic cells of two maps stay chaotic for",
   "paper_text": "74 and 92\\,\\% of the labels of two maps persist to $10^5$ steps",
   "paper_line": 170,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hedge-002",
   "section": "Summary surfaces and abstract",
   "claim": "horizon of the persistence test (paper 070d66e0)",
   "appears_as": "\\(10^5\\) steps, and the exponents, measured from twin trajectories, agree with",
   "paper_text": "74 and 92\\,\\% of the labels of two maps persist to $10^5$ steps",
   "paper_line": 170,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-001",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "temperature of the branch continued in alpha (run KITE-LA) (paper 070d66e0)",
   "appears_as": "temperature \\(\\log_{10}T = -0.15395\\), starting from its flip",
   "paper_text": "Continued in $\\alpha$ at fixed $\\log_{10}T=-0.15395$ from the first orbit's flip",
   "paper_line": 2551,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-002",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "first fold of the S-shaped branch (paper 070d66e0)",
   "appears_as": "stays attracting up to a fold at \\(\\alpha = 0.072992\\)",
   "paper_text": "the orbit stays attracting up to a fold at $\\alpha=0.072992$",
   "paper_line": 2552,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-003",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "second fold of the S-shaped branch (paper 070d66e0)",
   "appears_as": "to a second fold at \\(0.072793\\)",
   "paper_text": "the branch returns along the saddle to a second fold at $0.072793$",
   "paper_line": 2552,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-004",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "flip of the second orbit on the branch line (paper 070d66e0)",
   "appears_as": "which stays attracting until it flips near \\(0.07301\\)",
   "paper_text": "and it continues on the second orbit, which flips near $0.07301$",
   "paper_line": 2553,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-005",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "coexistence interval of the two attracting orbits at log10 T = -0.15395 (paper 070d66e0)",
   "appears_as": "coexist for \\(\\alpha\\) between 0.072907 and 0.072992",
   "paper_text": "at that temperature the two attracting orbits coexist for $\\alpha$ between 0.072907 and 0.072992",
   "paper_line": 2554,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-006",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "flip of the first orbit on the branch line: the lower end of the coexistence interval, since the second orbit attracts from its fold at 0.072793 to its flip near 0.07301 (research log, KITE-LA: stable from the flip, alpha 0.072907) (paper 070d66e0)",
   "appears_as": "the first orbit is attracting from its flip at 0.072907",
   "paper_text": "at that temperature the two attracting orbits coexist for $\\alpha$ between 0.072907 and 0.072992",
   "paper_line": 2554,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-007",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "fold of the second orbit continued upward in log10 T (run KITE-UT) (paper 070d66e0)",
   "appears_as": "attracting up to its own fold at \\(\\log_{10}T = -0.153657\\)",
   "paper_text": "is attracting up to its own fold at $-0.153657$",
   "paper_line": 2555,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-008",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "position of the kite's cusp C (paper 070d66e0)",
   "appears_as": "at \\((0.0730186, -0.1532803)\\): cubic coefficient",
   "paper_text": "the kite's cusp C, located at $(0.0730186,-0.1532803)$",
   "paper_line": 2556,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-009",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "cubic coefficient and unfolding determinant at C (paper 070d66e0)",
   "appears_as": "\\(c = -1.33\\times10^{4}\\), unfolding determinant \\(\\det K = -2624\\)",
   "paper_text": "(cubic coefficient $c=-1.33\\times10^{4}$, unfolding determinant $\\det K=-2624$",
   "paper_line": 2557,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-010",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "critical multiplier at C (7.62e-9 rounded up; was 7.6e-9 before Codex Task 38 S4) (paper 3c2498da)",
   "appears_as": "critical multiplier within \\(7.7\\times10^{-9}\\) of",
   "paper_text": "critical multiplier within $7.7\\times10^{-9}$ of $+1$",
   "paper_line": 2557,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-011",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "next modulus at C; C lies on the side of R toward the body (paper 17353aec)",
   "appears_as": "\\(+1\\), next modulus 0.00095.",
   "paper_text": "next modulus $0.00095$), on the side of R toward the body",
   "paper_line": 2558,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-012",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "corner A of the kite (paper 070d66e0)",
   "appears_as": "A \\(= (0.072991, -0.153984)\\) on the lower flip curve",
   "paper_text": "Its two branches meet the two flip curves at A $=(0.072991,-0.153984)$ and B $=(0.072900,-0.153707)$",
   "paper_line": 2558,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-013",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "corner B of the kite (paper 070d66e0)",
   "appears_as": "B \\(= (0.072900, -0.153707)\\) on the upper-left one",
   "paper_text": "Its two branches meet the two flip curves at A $=(0.072991,-0.153984)$ and B $=(0.072900,-0.153707)$",
   "paper_line": 2558,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-014",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "resolution of the kite map relative to Figure 57a (HR11) (paper 070d66e0)",
   "appears_as": "cells 7.5 times finer in \\(\\alpha\\) and 4.6 times finer in \\(\\log_{10}T\\) than in Figure 48a",
   "paper_text": "with cells 7.5 times finer in $\\alpha$ and 4.6 times finer in $\\log_{10}T$ than in Figure~\\ref{fig:p6shrimp}a",
   "paper_line": 2704,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-015",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "grid of the kite map (Figure 58a) (paper 070d66e0)",
   "appears_as": "(a) A 512 × 512 float64 map of the lower-left end of the body",
   "paper_text": "(a) A $512\\times512$ float64 map of the lower-left end of the body",
   "paper_line": 2704,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-016",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "temperature of the branch line drawn in Figure 58a (paper 070d66e0)",
   "appears_as": "Green: the line \\(\\log_{10}T = -0.15395\\) of the branch",
   "paper_text": "Green: the line $\\log_{10}T=-0.15395$ of the branch",
   "paper_line": 2708,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-017",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "cusp table (Table 16), C: position, c, det J (paper 070d66e0)",
   "appears_as": "| C | \\((0.0730186, -0.1532803)\\) | \\(-1.33\\times10^{4}\\) | \\(-2.62\\times10^{3}\\) |",
   "paper_text": "C & $(0.0730186, -0.1532803)$ & $-1.33\\times10^{4}$ & $-2.62\\times10^{3}$",
   "paper_line": 2959,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-018",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "cusp table (Table 16), lower 1: position, c, det J (paper 00183cec)",
   "appears_as": "| lower 1 | \\((0.0694974, -0.1602656)\\) | \\(-2.25\\times10^{3}\\) | \\(2.09\\times10^{4}\\) |",
   "paper_text": "lower 1 & $(0.0694974, -0.1602656)$ & $-2.25\\times10^{3}$ & $2.09\\times10^{4}$",
   "paper_line": 2962,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-019",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "cusp table (Table 16), lower 2: position, c, det J (paper 00183cec)",
   "appears_as": "| lower 2 | \\((0.0695513, -0.1601114)\\) | \\(+2.01\\times10^{3}\\) | \\(2.20\\times10^{4}\\) |",
   "paper_text": "lower 2 & $(0.0695513, -0.1601114)$ & $+2.01\\times10^{3}$ & $2.20\\times10^{4}$",
   "paper_line": 2963,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-020",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "cusps with c < 0 (signs of the c column of Table 16: C, upper 2, lower 1, neck) (paper 00183cec)",
   "appears_as": "near a cusp with \\(c < 0\\) (C, upper 2, lower 1 and the neck)",
   "paper_text": "C & $(0.0730186, -0.1532803)$ & $-1.33\\times10^{4}$",
   "paper_line": 2959,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-021",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "cusps with c > 0 (signs of the c column of Table 16: upper 1, lower 2) (paper 00183cec)",
   "appears_as": "near one with \\(c > 0\\) (upper 1 and lower 2)",
   "paper_text": "upper 1 & $(0.0678765, -0.1513104)$ & $+6.10\\times10^{3}$",
   "paper_line": 2960,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-022",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "located cusps in the Table 16 note (paper 070d66e0)",
   "appears_as": "Table 16: the six located cusps of the period-6 window (float64)",
   "paper_text": "The six located cusps of the period-6 window (float64)",
   "paper_line": 2948,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-023",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "located cusps besides C (Figure 57 note: pairs near the ends of both lower legs) (paper 070d66e0)",
   "appears_as": "pairs near the ends of the upper-left and lower-left legs (the lower pair's stars overlap at this scale)",
   "paper_text": "pairs near the ends of the upper-left and lower-left legs (the lower pair's stars overlap at this scale)",
   "paper_line": 2696,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-024",
   "section": "Cusps and shrimp-like windows",
   "claim": "the kite and its located cusp (section summary) (paper 7526a62e)",
   "appears_as": "kite of Gallas's cell, where two attracting orbits coexist, and the kite's located",
   "paper_text": "with the kite of Gallas's cell and its cusp C located",
   "paper_line": 2647,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-001",
   "section": "Changing the prompt",
   "claim": "number of prompt variants mapped (run PV) (paper 070d66e0)",
   "appears_as": "cells with the philosophy direction at layer 12, under 22 variants (Figure 21)",
   "paper_text": "22 variants (Figure~\\ref{fig:prompts})",
   "paper_line": 5686,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-002",
   "section": "Changing the prompt",
   "claim": "plane and grid of the prompt maps (paper 070d66e0)",
   "appears_as": "\\(\\alpha\\) from \\(-0.12\\) to 0.12 and \\(\\log_{10}T\\) from \\(-1\\) to 0.3, in 128 × 128 float64",
   "paper_text": "the standard plane ($\\alpha$ from $-0.12$ to $0.12$, $\\log_{10}T$ from $-1$ to $0.3$; $128\\times128$ float64 cells, philosophy direction at layer 12)",
   "paper_line": 5684,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-003",
   "section": "Changing the prompt",
   "claim": "number of prompt variants, the base prompt among them (short version) (paper 17353aec)",
   "appears_as": "Under 22 variants, the base prompt among",
   "paper_text": "22 variants (Figure~\\ref{fig:prompts})",
   "paper_line": 5686,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-004",
   "section": "Changing the prompt",
   "claim": "range of the chaotic share over the tested prompt variants (every prompt tested) (paper 602c70ac)",
   "appears_as": "Every prompt we tested gives chaos with periodic windows: 5.9 to 14.9% of",
   "paper_text": "Every prompt we tested gives chaos with periodic windows: 5.9 to 14.9\\,\\% of the plane is chaotic",
   "paper_line": 5692,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-005",
   "section": "Changing the prompt",
   "claim": "chaotic share for the base prompt (paper 070d66e0)",
   "appears_as": "(7.0% for the base prompt)",
   "paper_text": "(7.0\\,\\% for the base prompt)",
   "paper_line": 5693,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-006",
   "section": "Changing the prompt",
   "claim": "range of the maps' largest exponents (paper 070d66e0)",
   "appears_as": "with largest exponents of 0.62 to 0.85",
   "paper_text": "with largest exponents of 0.62 to 0.85 per step",
   "paper_line": 5693,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-007",
   "section": "Changing the prompt",
   "claim": "effect of removing the user message on the chaotic share (paper 070d66e0)",
   "appears_as": "Removing the user message doubles the chaotic share",
   "paper_text": "Removing the user message doubles the chaotic share",
   "paper_line": 5694,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-008",
   "section": "Changing the prompt",
   "claim": "chaotic share for the prompts that are one random vector (paper 070d66e0)",
   "appears_as": "is one random vector gives 8 to 10%.",
   "paper_text": "even a prompt that is one random vector gives 8 to 10\\,\\%",
   "paper_line": 5694,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-009",
   "section": "Changing the prompt",
   "claim": "Jaccard overlap with the base prompt, over the 18 prompts other than the base (not the random starts) (paper 2b81de3f)",
   "appears_as": "cells of each of the other 18 prompts overlap those of the base prompt by 1 to 37% by this measure; the",
   "paper_text": "the chaotic cells of each of the other 18 prompts overlap those of the base prompt by 1 to 37\\,\\% (Jaccard index)",
   "paper_line": 5695,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-010",
   "section": "Changing the prompt",
   "claim": "agreement of the random-start chaos/non-chaos threshold labels with the base run (paper 3c2498da)",
   "appears_as": "the chaos/non-chaos threshold labels agree with the base run at 98.9 to 99.0% of the cells",
   "paper_text": "the chaos/non-chaos threshold labels agree with the base run at 98.9 to 99.0\\,\\% of the cells",
   "paper_line": 5697,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-011",
   "section": "Changing the prompt",
   "claim": "number of random starts (paper 3c2498da)",
   "appears_as": "For the three random starts,",
   "paper_text": "For the three random starts",
   "paper_line": 5697,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-012",
   "section": "Changing the prompt",
   "claim": "prompts counted in the frequency map (random-start runs left out) (paper 070d66e0)",
   "appears_as": "fraction of the prompts in which that cell is chaotic, over 19 prompts: all 22 runs",
   "paper_text": "fraction of the 19 prompt variants (the random-start runs left out) in which it is chaotic",
   "paper_line": 5724,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-013",
   "section": "Changing the prompt",
   "claim": "share of cells chaotic for at least one prompt (paper 070d66e0)",
   "appears_as": "48.3% of the cells are chaotic for at",
   "paper_text": "48.3\\,\\% of the cells are chaotic for at least one prompt",
   "paper_line": 5700,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-014",
   "section": "Changing the prompt",
   "claim": "share of cells chaotic for half of the prompts or more (paper 070d66e0)",
   "appears_as": "but only 3.0% for half of them or more",
   "paper_text": "but only 3.0\\,\\% for half of them or more",
   "paper_line": 5701,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-015",
   "section": "Changing the prompt",
   "claim": "peak of the mean chaotic fraction per temperature row (paper 070d66e0)",
   "appears_as": "peaks at 38% near \\(\\log_{10}T = 0.15\\)",
   "paper_text": "peaks at 38\\,\\% near $\\log_{10}T=0.15$",
   "paper_line": 5702,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-016",
   "section": "Changing the prompt",
   "claim": "mean chaotic fraction per row in the cold band (paper 070d66e0)",
   "appears_as": "\\(\\log_{10}T = 0.15\\), against 0.8%",
   "paper_text": "against 0.8\\,\\% below $\\log_{10}T=-0.5$",
   "paper_line": 5702,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-017",
   "section": "Changing the prompt",
   "claim": "edge of the cold band (paper 070d66e0)",
   "appears_as": "below \\(\\log_{10}T = -0.5\\).",
   "paper_text": "against 0.8\\,\\% below $\\log_{10}T=-0.5$",
   "paper_line": 5702,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-018",
   "section": "Changing the prompt",
   "claim": "peak of the random-vector prompts' mean profile (paper 070d66e0)",
   "appears_as": "peaks near \\(\\log_{10}T = 0.03\\)",
   "paper_text": "their mean profile peaks near $\\log_{10}T=0.03$, that of the text prompts near $0.16$",
   "paper_line": 5703,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-019",
   "section": "Changing the prompt",
   "claim": "peak of the text prompts' mean profile (paper 070d66e0)",
   "appears_as": "and that of the text prompts near 0.16",
   "paper_text": "their mean profile peaks near $\\log_{10}T=0.03$, that of the text prompts near $0.16$",
   "paper_line": 5703,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-020",
   "section": "Changing the prompt",
   "claim": "cells per temperature row (128 x 128 grid) (paper 070d66e0)",
   "appears_as": "the share of its 128 cells that are chaotic",
   "paper_text": "$128\\times128$ float64 cells, philosophy direction at layer 12",
   "paper_line": 5685,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-021",
   "section": "Changing the prompt",
   "claim": "grid and plane of Figure 21 (paper 070d66e0)",
   "appears_as": "128 × 128 cells over \\(\\alpha \\in [-0.12, 0.12]\\) and \\(\\log_{10}T \\in [-1, 0.3]\\)",
   "paper_text": "$128\\times128$ cells over $\\alpha\\in[-0.12,0.12]$ and $\\log_{10}T\\in[-1,0.3]$",
   "paper_line": 5711,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-022",
   "section": "Changing the prompt",
   "claim": "variants in Figure 21a (paper 00183cec)",
   "appears_as": "The chaotic share of the plane for each of the 22 variants",
   "paper_text": "The chaotic share of the plane for each of the 22 variants (19 prefixes, and the base prefix with the loop started from three random vectors)",
   "paper_line": 5711,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-023",
   "section": "Changing the prompt",
   "claim": "maps shown in Figure 21b (paper 070d66e0)",
   "appears_as": "(b) Eight of the maps, each titled with its chaotic share",
   "paper_text": "(b) Eight of the maps",
   "paper_line": 5714,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-024",
   "section": "Changing the prompt",
   "claim": "prompts counted in Figure 22a (paper 070d66e0)",
   "appears_as": "the fraction of the 19 prompt variants (the random-start runs left out)",
   "paper_text": "fraction of the 19 prompt variants (the random-start runs left out) in which it is chaotic",
   "paper_line": 5724,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-025",
   "section": "Changing the prompt",
   "claim": "random-vector prompts in Figure 22b (paper 1e8e82f4)",
   "appears_as": "the text prompts (blue) and the three random-vector prompts (orange, dashed)",
   "paper_text": "for all prompts, the text prompts and the three random-vector prompts",
   "paper_line": 5725,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-026",
   "section": "Changing the prompt",
   "claim": "prompts that are one random vector (paper 070d66e0)",
   "appears_as": "Three prompts that are each a single random vector",
   "paper_text": "three prompts that are a single random vector, with no text at all",
   "paper_line": 5689,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-027",
   "section": "Changing the prompt",
   "claim": "length of the long system prompt (paper 070d66e0)",
   "appears_as": "a system prompt three times as",
   "paper_text": "a system prompt three times as long and a two-turn conversation",
   "paper_line": 5689,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-028",
   "section": "Changing the prompt",
   "claim": "random orders of the system prompt's words (paper 00183cec)",
   "appears_as": "The system prompt's words in two random orders",
   "paper_text": "the system prompt's words in two random orders, the user message's two tokens reversed, and both changes together",
   "paper_line": 5687,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-029",
   "section": "Changing the prompt",
   "claim": "tokens of the user message, reversed (paper 00183cec)",
   "appears_as": "user message's two tokens reversed",
   "paper_text": "the system prompt's words in two random orders, the user message's two tokens reversed, and both changes together",
   "paper_line": 5687,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-030",
   "section": "Changing the prompt",
   "claim": "random start vectors with the base prompt (paper 070d66e0)",
   "appears_as": "The base prompt, with the loop started from three random vectors",
   "paper_text": "and the base prompt with the loop started from three random vectors",
   "paper_line": 5691,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-031",
   "section": "Changing the prompt",
   "claim": "the other 0.5B results use one prompt (short version; not \"every other\") (paper 17353aec)",
   "appears_as": "All the other 0.5B results in this note use one prompt",
   "paper_text": "Every 0.5B result above uses one prompt",
   "paper_line": 5684,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-032",
   "section": "Steering as a probe",
   "claim": "number of prompt variants, all tested (steering as a probe) (paper 2b81de3f)",
   "appears_as": "The prompt plays a similar part: under each of the 22 variants",
   "paper_text": "22 variants (Figure~\\ref{fig:prompts})",
   "paper_line": 5686,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-033",
   "section": "Limitations",
   "claim": "number of prompt variants (Limitations) (paper 00183cec)",
   "appears_as": "The maps use one prompt, apart from the 22 prompt",
   "paper_text": "The maps use one prompt, apart from the 22 prompt variants of the 0.5B standard plane",
   "paper_line": 5741,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "expoff-001",
   "section": "Numerics and chaos labels",
   "claim": "the twin starts from a random direction in 896 dimensions at the end of the transient, so the averaging window includes its alignment (paper 2b81de3f)",
   "appears_as": "896 dimensions at the end of the transient, so the averaging window, the measured steps over which the exponent",
   "paper_text": "The twin starts from a random direction in 896 dimensions at the end of the transient, so the averaging window includes its alignment",
   "paper_line": 847,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "expoff-002",
   "section": "Numerics and chaos labels",
   "claim": "the finite-window estimate of a periodic cell differs from ln|mu1|/p (both signs occur: +0.0035, -0.0073) (paper 3c2498da)",
   "appears_as": "finite-window estimate differs a little, in either direction, from the exact value",
   "paper_text": "so the finite-window estimate of a periodic cell differs from $\\ln|\\mu_1|/p$ of its orbit",
   "paper_line": 848,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "expoff-003",
   "section": "Numerics and chaos labels",
   "claim": "map exponents at two adjacent cells inside the kite (paper 00183cec)",
   "appears_as": "Figure 49, the map gives \\(-0.2786\\) and \\(-0.0885\\) per step and the period-6 orbits found",
   "paper_text": "the map gives $-0.2786$ and $-0.0885$ per step",
   "paper_line": 850,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "expoff-004",
   "section": "Numerics and chaos labels",
   "claim": "exponents of the Newton-converged period-6 orbits at the same cells, and the offsets (paper 00183cec)",
   "appears_as": "by Newton's method give \\(-0.2821\\) and \\(-0.0813\\), offsets of \\(+0.0035\\) and \\(-0.0073\\).",
   "paper_text": "the Newton-converged period-6 orbits $-0.2821$ and $-0.0813$, offsets of $+0.0035$ and $-0.0073$",
   "paper_line": 850,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "expoff-005",
   "section": "Numerics and chaos labels",
   "claim": "periodic cells are classified by period; the gray scale carries the offset (paper 00183cec)",
   "appears_as": "Periodic cells are classified by their period, not by this exponent; the offset shows only",
   "paper_text": "Periodic cells are classified by their period, not by this exponent; the gray scale of the maps carries the offset",
   "paper_line": 851,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-025",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "why Newton from the other orbit fails at (0.0730, -0.1539): the point lies just beyond its fold (branch C-A) (paper 00183cec)",
   "appears_as": "converge there, and the kite below shows why: the point lies just beyond that orbit's fold, the kite's branch C–A",
   "paper_text": "the point lies just beyond that orbit's fold, on the branch C--A of the kite",
   "paper_line": 2549,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-026",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "the straight edge inside the kite (Figure 58 note) is a basin boundary of the fixed start, not a bifurcation, where checked (paper 4e6e2ec6)",
   "appears_as": "Inside the kite, the straight edge where the gray changes abruptly (near \\(\\log_{10}T = -0.15353\\)) is a basin boundary of the fixed start, not a bifurcation, where we checked it",
   "paper_text": "the straight edge where the gray changes abruptly (near $\\log_{10}T=-0.15353$) is a basin boundary of the fixed start, not a bifurcation, where we checked it",
   "paper_line": 2714,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-027",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "leading multipliers of the two attracting orbits on both sides of the straight edge (Figure 58 note) (paper 00183cec)",
   "appears_as": "(leading multipliers 0.18 and 0.60 to 0.61)",
   "paper_text": "(leading multipliers $0.18$ and $0.60$ to $0.61$)",
   "paper_line": 2716,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-001",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "grid of the hook map and its resolution relative to Figure 58a (paper 00183cec)",
   "appears_as": "A 640 × 640 map of that end, with cells 3.1 and 2.5 times finer than in Figure 49a",
   "paper_text": "A $640\\times640$ map of the upper end of the kite (Figure~\\ref{fig:p6hook}; cells 3.1 and 2.5 times finer than in Figure~\\ref{fig:p6kite}a)",
   "paper_line": 2722,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-002",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "the wedge's lower edge: where the fixed start switches to the other attracting orbit (paper 00183cec)",
   "appears_as": "fixed start switches to the other attracting orbit. That lower edge is not a bifurcation.",
   "paper_text": "below by a smooth curve where the fixed start switches to the other attracting orbit",
   "paper_line": 2724,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-003",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "pair 1: both orbits exist and attract across the lower edge, with their multipliers (paper 00183cec)",
   "appears_as": "both sides. At adjacent cells across the wedge's lower edge, both orbits exist and attract (multipliers 0.18 and 0.60",
   "paper_text": "at adjacent cells across that curve both orbits exist and attract (multipliers $0.18$ and $0.60$ to $0.61$; pair 1)",
   "paper_line": 2725,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-004",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "pair 2: two attracting period-6 orbits at both cells across a tongue's edge, with their multipliers (paper 00183cec)",
   "appears_as": "attracting period-6 orbits exist at both cells (multipliers \\(-0.72\\) and \\(-0.11\\); pair 2)",
   "paper_text": "two other attracting period-6 orbits exist at both cells (multipliers $-0.72$ and $-0.11$; pair 2)",
   "paper_line": 2727,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-005",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "inside several tongues the fixed start's outcome alternates from cell to cell, a structure not resolved at this grid spacing (paper 2b81de3f)",
   "appears_as": "fixed start's outcome alternates from cell to cell, a structure not resolved at this grid spacing (Figure 50b).",
   "paper_text": "so the fixed start's outcome alternates from cell to cell, a structure not resolved at this grid spacing",
   "paper_line": 2728,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-006",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "grid and range of the hook map (Figure 59 note) (paper 00183cec)",
   "appears_as": "(a) A 640 × 640 map of \\(\\alpha \\in [0.07291, 0.07303]\\) and \\(\\log_{10}T \\in [-0.1540, -0.1533]\\)",
   "paper_text": "(a) A $640\\times640$ map of $\\alpha\\in[0.07291,0.07303]$ and $\\log_{10}T\\in[-0.1540,-0.1533]$",
   "paper_line": 2738,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-034",
   "section": "Changing the prompt",
   "claim": "the 22 variants: 19 prompts, and the base prompt with three random starts (paper 00183cec)",
   "appears_as": "cells with the philosophy direction at layer 12, under 22 variants (Figure 21): 19",
   "paper_text": "22 variants (19 prefixes, and the base prefix with the loop started from three random vectors)",
   "paper_line": 5712,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-035",
   "section": "Changing the prompt",
   "claim": "the scrambled variants include both changes together (paper 00183cec)",
   "appears_as": "user message's two tokens reversed (`\"!Hello\"`), and both changes together",
   "paper_text": "the user message's two tokens reversed, and both changes together",
   "paper_line": 5687,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-036",
   "section": "Changing the prompt",
   "claim": "composition of the 22 variants (Figure 21 note) (paper 00183cec)",
   "appears_as": "(19 prompts, and the base prompt with the loop started from three random vectors)",
   "paper_text": "(19 prefixes, and the base prefix with the loop started from three random vectors)",
   "paper_line": 5712,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-001",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "chaotic six-band cells passing the pooled coding test (short version) (paper 3c2498da)",
   "appears_as": "coding passes its test in 48 of the 58 chaotic cells tested.",
   "paper_text": "48 of the 58 chaotic six-band cells of a $48\\times48$ map of the window have an error ratio below 5\\,\\%",
   "paper_line": 2844,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-002",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "distinct window words (short version) (paper 17353aec)",
   "appears_as": "its period doublings carry the words of the period-doubling cascade, and 23 distinct window words appear in all.",
   "paper_text": "23 distinct window words W",
   "paper_line": 2859,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-003",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "selected cells where the Newton check reproduces the scan's label (short version) (paper 17353aec)",
   "appears_as": "Float64 Newton solves at 23 selected cells, covering 12 of the words, reproduce the label at 16 and leave five cells",
   "paper_text": "reproduce the scan's label at 16 cells",
   "paper_line": 2871,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-004",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "unconfirmed cells just below the kite (short version) (paper 17353aec)",
   "appears_as": "reproduce the label at 16 and leave five cells",
   "paper_text": "at the remaining 5 cells, just below the kite, no phase is clean",
   "paper_line": 2872,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-005",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "six bands visited in turn, returning every six steps (paper 00183cec)",
   "appears_as": "The loop then visits six thin bands of the state space in turn, one per token, and returns to each band every six",
   "paper_text": "the loop visits six thin bands of the state space in turn, one per token, and returns to each band every six steps",
   "paper_line": 2835,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-006",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "grid of the return-map test (paper 3c2498da)",
   "appears_as": "We tested this on a 48 × 48 map of the window of Figure 48a",
   "paper_text": "48 of the 58 chaotic six-band cells of a $48\\times48$ map of the window",
   "paper_line": 2844,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-007",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "transient and recorded steps per cell of the return-map test (paper 00183cec)",
   "appears_as": "transient and 3000 recorded steps per cell (Figure 56a)",
   "paper_text": "1000 transient and 3000 recorded steps per cell",
   "paper_line": 2883,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-008",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "chaotic six-band cells of the return-map test (paper 3c2498da)",
   "appears_as": "Of the 58 chaotic cells of the map that write the six-token text, the",
   "paper_text": "48 of the 58 chaotic six-band cells of a $48\\times48$ map of the window",
   "paper_line": 2844,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-009",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "largest pooled error ratio among passing cells (not a bound on each phase) (paper 3c2498da)",
   "appears_as": "The largest passing ratio is 4.7%, and 23",
   "paper_text": "the largest passing ratio is 4.7\\,\\%",
   "paper_line": 2845,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-010",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "cells with no misplaced visit (paper 17353aec)",
   "appears_as": "passing ratio is 4.7%, and 23",
   "paper_text": "23 cells have no misplaced visit",
   "paper_line": 2845,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-011",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "cells failing the coding test, and the three in one column (paper 17353aec)",
   "appears_as": "The other 10 cells fail the coding test: three in one column beside the body's left",
   "paper_text": "The other 10 cells fail the coding test: three in one column beside the body's left flip curve and seven below the kite",
   "paper_line": 2846,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-012",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "failing cells whose return map rises and falls more than once (Figure 63h-k) (paper 3c2498da)",
   "appears_as": "of the scatter of the points: it rises and falls more than once (Figure 56h–k).",
   "paper_text": "In 7 of them the return map has more than one resolved turning point: it rises and falls more than once (Figure~\\ref{fig:p6returnmaps}h--k)",
   "paper_line": 2847,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-013",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "Singer's theorem with its endpoint alternative, as the paper states it (paper 3c2498da)",
   "appears_as": "\\(C^3\\) unimodal interval map with negative Schwarzian derivative, at most one attracting periodic orbit can have an",
   "paper_text": "For a $C^3$ unimodal interval map with negative Schwarzian derivative, at most one attracting periodic orbit can have an immediate basin that avoids the interval's endpoints \\cite{singer1978stable}",
   "paper_line": 2848,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-014",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "the extra turning points are consistent with the coexisting kite orbits (not shown to cause them) (paper 3c2498da)",
   "appears_as": "orbit fits. The extra turning points below the kite are consistent with a scalar explanation of the coexistence inside",
   "paper_text": "the extra turning points below the kite are consistent with a scalar explanation of the coexistence inside it",
   "paper_line": 2850,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-015",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "visits per band of a period-6k orbit (paper 3c2498da)",
   "appears_as": "A periodic orbit of period 6k visits each band k",
   "paper_text": "A periodic orbit of period $6k$ visits each band $k$ times",
   "paper_line": 2853,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-016",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "maximal rotation in the kneading order (paper 00183cec)",
   "appears_as": "Rotated to the largest sequence in this order, the",
   "paper_text": "rotated to the largest sequence in the order of kneading theory",
   "paper_line": 2853,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-017",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "words of the doubling cascade (paper 00183cec)",
   "appears_as": "6), R (12), RLR (24) and RLRRRLR (48).",
   "paper_text": "the empty word (period 6), R (12), RLR (24) and RLRRRLR (48)",
   "paper_line": 2860,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-018",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "periodic six-band cells that receive a window word after the majority vote and the MSS filter (paper 17353aec)",
   "appears_as": "word. After the vote and the filter, 44,577 periodic six-band cells on the 640 × 640 grid of Figure 48a receive",
   "paper_text": "After a majority vote over the band phases whose coding is usable (at least three) and an explicit filter that keeps only MSS words, 44{,}577 periodic six-band cells on the $640\\times640$ grid of Figure~\\ref{fig:p6shrimp}a receive",
   "paper_line": 2857,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-019",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "distinct window words (paper 17353aec)",
   "appears_as": "23 distinct window words W (Figure 57); the filter rejects 240 further cells whose",
   "paper_text": "receive 23 distinct window words W (Figure~\\ref{fig:words})",
   "paper_line": 2858,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-020",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "words of windows in the surrounding chaos (paper 3c2498da)",
   "appears_as": "among them RL (period 18), RLRR (30), and",
   "paper_text": "among them RL (period 18), RLRR (30), and RLRRR and RLLRL, two distinct windows of period 36 that only their words tell apart",
   "paper_line": 2861,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-021",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "two distinct period-36 windows (paper 00183cec)",
   "appears_as": "RLLRL, two distinct windows of period 36 that only their words tell apart.",
   "paper_text": "among them RL (period 18), RLRR (30), and RLRRR and RLLRL, two distinct windows of period 36 that only their words tell apart",
   "paper_line": 2861,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-022",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "sign of the leading multiplier predicted from the parity of R in W|X (paper 3c2498da)",
   "appears_as": "\\((-1)^{n_R}\\), with \\(n_R\\) the number of R's in W|X: positive next to the boundary where the orbit is born",
   "paper_text": "the sign of the orbit's leading multiplier, $(-1)^{n_R}$ with $n_R$ the number of R's in W|X",
   "paper_line": 2863,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-023",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "leading multiplier of the word R on side L (Table 17) (paper 00183cec)",
   "appears_as": "(\\(-0.770\\)), and on side R at another",
   "paper_text": "R & L & 12 & $(0.0731628, -0.1539703)$ & $-0.770$ & 5 & confirmed",
   "paper_line": 2924,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-024",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "leading multiplier of the word R on side R (Table 17) (paper 00183cec)",
   "appears_as": "with two R's and a positive multiplier (\\(+0.078\\)) (Table 17)",
   "paper_text": "R & R & 12 & $(0.0733030, -0.1538200)$ & $+0.078$ & 5 & confirmed",
   "paper_line": 2925,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-025",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "cells labeled C (phases disagree on the last symbol; not located superstable curves) (paper 3c2498da)",
   "appears_as": "The scan assigns C to 153 cells whose usable phases do not agree sufficiently on the last symbol.",
   "paper_text": "The scan assigns C to 153 cells whose usable phases do not agree sufficiently on the last symbol",
   "paper_line": 2865,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-026",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "selection of the checked cells (at least three coded cells in the half of the scan then complete) and their number (paper 17353aec)",
   "appears_as": "three coded cells in that half, the cell nearest the center of the label's largest patch. That gives 23 cells, which",
   "paper_text": "(the cell nearest the center of the label's largest patch: 23 cells, covering 12 of the 23 words",
   "paper_line": 2869,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-027",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "cells where the Newton check, scored by the subsequent clean-phase rule, reproduces the scan's label (paper 3c2498da)",
   "appears_as": "the clean phases give. By that rule the Newton solves reproduce the scan's label at 16 cells, and each confirmed word",
   "paper_text": "reproduce the scan's label at 16 cells",
   "paper_line": 2871,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-028",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "selected C cells with complex leading pairs (paper 3c2498da)",
   "appears_as": "The two C cells have complex leading pairs.",
   "paper_text": "the two C cells have complex leading pairs",
   "paper_line": 2871,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-029",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "unconfirmed cells and their four words (paper 17353aec)",
   "appears_as": "remaining 5 cells, just below the kite, no phase is clean, so their four words (RLL on both sides, RLLLRLL, RLLLRLR",
   "paper_text": "at the remaining 5 cells, just below the kite, no phase is clean, so their four words (RLL on both sides, RLLLRLL, RLLLRLR and RLLLRRR) remain unconfirmed",
   "paper_line": 2872,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-030",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "eligible periodic six-band cells that receive no word (paper 17353aec)",
   "appears_as": "In total, 1,469 of the 46,046",
   "paper_text": "In total, 1{,}469 of the 46{,}046 eligible periodic six-band cells receive no word (3.2\\,\\%)",
   "paper_line": 2875,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-031",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "cells without a word within Euclidean distance two grid cells of the eligible domain's edge (paper 17353aec)",
   "appears_as": "eligible periodic six-band cells receive no word (3.2%), the 240 rejected by the filter among them; 922 of them (63%)",
   "paper_text": "922 of them (63\\,\\%) lie within Euclidean distance two grid cells of the eligible domain's edge",
   "paper_line": 2876,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-032",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "steps per cell (Figure 63 note) (paper 00183cec)",
   "appears_as": "philosophy direction at layer 12, float64; 1000 transient and 3000 recorded steps per cell). (a) The cells of a 48 × 48 map of the window of Figure 48a",
   "paper_text": "float64; 1000 transient and 3000 recorded steps per cell). (a) The cells of a $48\\times48$ map of the window of Figure~\\ref{fig:p6shrimp}a",
   "paper_line": 2883,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-033",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "panels b-g: six green cells (Figure 63 note) (paper 00183cec)",
   "appears_as": "(b–g) Six-step return maps at six green cells",
   "paper_text": "(b--g) Six-step return maps at six green cells",
   "paper_line": 2885,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-034",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "panels h-k: four red cells (Figure 63 note) (paper 00183cec)",
   "appears_as": "(h–k) Return maps at four red cells (letters in (a)) with more than one turning point",
   "paper_text": "(h--k) Return maps at four red cells (letters in (a)) with more than one turning point",
   "paper_line": 2887,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-035",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "grid of the word map (Figure 64 note) (paper 00183cec)",
   "appears_as": "Figure 57: symbolic words of the period-6 shrimp's windows (640 × 640 float64 cells, the grid of Figure 48a)",
   "paper_text": "Symbolic words of the period-6 shrimp's windows ($640\\times640$ float64 cells, the grid of Figure~\\ref{fig:p6shrimp}a)",
   "paper_line": 2895,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-036",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "the empty word at a = 0 (Figure 64 note) (paper 00183cec)",
   "appears_as": "(the body's empty word is that of its fixed point, at \\(a = 0\\))",
   "paper_text": "(the body's empty word is that of its fixed point, at $a=0$)",
   "paper_line": 2901,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-037",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "soft-token period six times the word period (Figure 64 note) (paper 00183cec)",
   "appears_as": "labels give the period of the soft-token orbit, six times the word's period",
   "paper_text": "labels give the period of the soft-token orbit, six times the word's period",
   "paper_line": 2902,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-038",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "selection rule of the checked cells: at least three cells in the eight of the scan's 16 bands (strips of grid rows) then complete (Table 17 note) (paper 17353aec)",
   "appears_as": "side of Figure 57 with at least three cells in the eight of the scan's 16 strips of rows then complete",
   "paper_text": "center of the largest patch of each window word and side of Figure~\\ref{fig:words} with at least three cells in the eight of the scan's 16 bands then complete",
   "paper_line": 2909,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-039",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "cosine bound of a clean phase (Table 17 note) (paper 00183cec)",
   "appears_as": "with every \\(\\lvert\\cos\\rvert \\ge 0.5\\)",
   "paper_text": "with every $|\\cos|\\ge0.5$",
   "paper_line": 2912,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-040",
   "section": "What was and was not found",
   "claim": "chaotic six-band cells passing the coding test (found list) (paper 3c2498da)",
   "appears_as": "a coding test passed by 48",
   "paper_text": "48 of the 58 chaotic six-band cells of a $48\\times48$ map of the window have an error ratio below 5\\,\\%",
   "paper_line": 2844,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-041",
   "section": "What was and was not found",
   "claim": "distinct window words (found list) (paper 17353aec)",
   "appears_as": "window words of the doubling cascade and of the quadratic family, 23 distinct words in",
   "paper_text": "23 distinct window words W",
   "paper_line": 2859,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-042",
   "section": "What was and was not found",
   "claim": "selected cells where the Newton check reproduces the scan's label (found list) (paper 17353aec)",
   "appears_as": "label at 16 ([Symbolic dynamics of the period-6 shrimp](#symbolic-dynamics));",
   "paper_text": "reproduce the scan's label at 16 cells",
   "paper_line": 2871,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-043",
   "section": "What was and was not found",
   "claim": "symbolic sequences determined for the period-6 window only (not-found list) (paper 00183cec)",
   "appears_as": "and the symbolic sequences of windows other than the period-6 window;",
   "paper_text": "Symbolic sequences are determined for the period-6 window only",
   "paper_line": 3935,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-044",
   "section": "Not claimed",
   "claim": "symbolic sequences determined for the period-6 window only (Not claimed) (paper 00183cec)",
   "appears_as": "tails and periodicity hubs were not traced, and symbolic sequences were determined",
   "paper_text": "Symbolic sequences are determined for the period-6 window only",
   "paper_line": 3935,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-101",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "word table (Table 17), (empty), side C: period, position, mu1, clean phases, result (paper 00183cec)",
   "appears_as": "| (empty) | C | 6 | \\((0.0730707, -0.1520673)\\) | \\(-0.002+0.024i\\) | 0 | complex pair |",
   "paper_text": "(empty) & C & 6 & $(0.0730707, -0.1520673)$ & $-0.002+0.024i$ & 0 & complex pair",
   "paper_line": 2920,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-102",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "word table (Table 17), (empty), side L: period, position, mu1, clean phases, result (paper 00183cec)",
   "appears_as": "| (empty) | L | 6 | \\((0.0731584, -0.1527559)\\) | \\(+0.189\\) | 6 | confirmed |",
   "paper_text": "(empty) & L & 6 & $(0.0731584, -0.1527559)$ & $+0.189$ & 6 & confirmed",
   "paper_line": 2921,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-103",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "word table (Table 17), (empty), side R: period, position, mu1, clean phases, result (paper 00183cec)",
   "appears_as": "| (empty) | R | 6 | \\((0.0732285, -0.1533944)\\) | \\(-0.686\\) | 6 | confirmed |",
   "paper_text": "(empty) & R & 6 & $(0.0732285, -0.1533944)$ & $-0.686$ & 6 & confirmed",
   "paper_line": 2922,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-104",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "word table (Table 17), R, side C: period, position, mu1, clean phases, result (paper 00183cec)",
   "appears_as": "| R | C | 12 | \\((0.0732548, -0.1537825)\\) | \\(-0.001+0.004i\\) | 0 | complex pair |",
   "paper_text": "R & C & 12 & $(0.0732548, -0.1537825)$ & $-0.001+0.004i$ & 0 & complex pair",
   "paper_line": 2923,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-105",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "word table (Table 17), R, side L: period, position, mu1, clean phases, result (paper 00183cec)",
   "appears_as": "| R | L | 12 | \\((0.0731628, -0.1539703)\\) | \\(-0.770\\) | 5 | confirmed |",
   "paper_text": "R & L & 12 & $(0.0731628, -0.1539703)$ & $-0.770$ & 5 & confirmed",
   "paper_line": 2924,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-106",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "word table (Table 17), R, side R: period, position, mu1, clean phases, result (paper 00183cec)",
   "appears_as": "| R | R | 12 | \\((0.0733030, -0.1538200)\\) | \\(+0.078\\) | 5 | confirmed |",
   "paper_text": "R & R & 12 & $(0.0733030, -0.1538200)$ & $+0.078$ & 5 & confirmed",
   "paper_line": 2925,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-107",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "word table (Table 17), RL, side L: period, position, mu1, clean phases, result (paper 00183cec)",
   "appears_as": "| RL | L | 18 | \\((0.0730488, -0.1543333)\\) | \\(-0.184\\) | 3 | confirmed |",
   "paper_text": "RL & L & 18 & $(0.0730488, -0.1543333)$ & $-0.184$ & 3 & confirmed",
   "paper_line": 2926,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-108",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "word table (Table 17), RL, side R: period, position, mu1, clean phases, result (paper 00183cec)",
   "appears_as": "| RL | R | 18 | \\((0.0727465, -0.1528936)\\) | \\(+0.266\\) | 2 | confirmed |",
   "paper_text": "RL & R & 18 & $(0.0727465, -0.1528936)$ & $+0.266$ & 2 & confirmed",
   "paper_line": 2927,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-109",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "word table (Table 17), RLL, side L: period, position, mu1, clean phases, result (paper 00183cec)",
   "appears_as": "| RLL | L | 24 | \\((0.0732110, -0.1542582)\\) | \\(-0.481\\) | 0 | *no clean phase* |",
   "paper_text": "RLL & L & 24 & $(0.0732110, -0.1542582)$ & $-0.481$ & 0 & \\emph{no clean phase}",
   "paper_line": 2928,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-110",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "word table (Table 17), RLL, side R: period, position, mu1, clean phases, result (paper 00183cec)",
   "appears_as": "| RLL | R | 24 | \\((0.0731847, -0.1542707)\\) | \\(+0.278\\) | 0 | *no clean phase* |",
   "paper_text": "RLL & R & 24 & $(0.0731847, -0.1542707)$ & $+0.278$ & 0 & \\emph{no clean phase}",
   "paper_line": 2929,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-111",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "word table (Table 17), RLR, side L: period, position, mu1, clean phases, result (paper 00183cec)",
   "appears_as": "| RLR | L | 24 | \\((0.0731540, -0.1540454)\\) | \\(+0.178\\) | 4 | confirmed |",
   "paper_text": "RLR & L & 24 & $(0.0731540, -0.1540454)$ & $+0.178$ & 4 & confirmed",
   "paper_line": 2930,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-112",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "word table (Table 17), RLR, side R: period, position, mu1, clean phases, result (paper 00183cec)",
   "appears_as": "| RLR | R | 24 | \\((0.0727772, -0.1524053)\\) | \\(-0.526\\) | 3 | confirmed |",
   "paper_text": "RLR & R & 24 & $(0.0727772, -0.1524053)$ & $-0.526$ & 3 & confirmed",
   "paper_line": 2931,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-113",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "word table (Table 17), RLRR, side L: period, position, mu1, clean phases, result (paper 00183cec)",
   "appears_as": "| RLRR | L | 30 | \\((0.0731408, -0.1543208)\\) | \\(-0.051\\) | 3 | confirmed |",
   "paper_text": "RLRR & L & 30 & $(0.0731408, -0.1543208)$ & $-0.051$ & 3 & confirmed",
   "paper_line": 2932,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-114",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "word table (Table 17), RLRR, side R: period, position, mu1, clean phases, result (paper 00183cec)",
   "appears_as": "| RLRR | R | 30 | \\((0.0731408, -0.1542707)\\) | \\(+0.139\\) | 4 | confirmed |",
   "paper_text": "RLRR & R & 30 & $(0.0731408, -0.1542707)$ & $+0.139$ & 4 & confirmed",
   "paper_line": 2933,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-115",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "word table (Table 17), RLLRL, side L: period, position, mu1, clean phases, result (paper 00183cec)",
   "appears_as": "| RLLRL | L | 36 | \\((0.0740260, -0.1569249)\\) | \\(+0.168\\) | 4 | confirmed |",
   "paper_text": "RLLRL & L & 36 & $(0.0740260, -0.1569249)$ & $+0.168$ & 4 & confirmed",
   "paper_line": 2934,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-116",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "word table (Table 17), RLLRL, side R: period, position, mu1, clean phases, result (paper 00183cec)",
   "appears_as": "| RLLRL | R | 36 | \\((0.0730444, -0.1543584)\\) | \\(-0.439\\) | 3 | confirmed |",
   "paper_text": "RLLRL & R & 36 & $(0.0730444, -0.1543584)$ & $-0.439$ & 3 & confirmed",
   "paper_line": 2935,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-117",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "word table (Table 17), RLRRR, side L: period, position, mu1, clean phases, result (paper 00183cec)",
   "appears_as": "| RLRRR | L | 36 | \\((0.0731671, -0.1542457)\\) | \\(+0.146\\) | 3 | confirmed |",
   "paper_text": "RLRRR & L & 36 & $(0.0731671, -0.1542457)$ & $+0.146$ & 3 & confirmed",
   "paper_line": 2936,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-118",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "word table (Table 17), RLRRR, side R: period, position, mu1, clean phases, result (paper 00183cec)",
   "appears_as": "| RLRRR | R | 36 | \\((0.0731628, -0.1541956)\\) | \\(-0.063\\) | 3 | confirmed |",
   "paper_text": "RLRRR & R & 36 & $(0.0731628, -0.1541956)$ & $-0.063$ & 3 & confirmed",
   "paper_line": 2937,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-119",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "word table (Table 17), RLLLRLL, side L: period, position, mu1, clean phases, result (paper 00183cec)",
   "appears_as": "| RLLLRLL | L | 48 | \\((0.0731803, -0.1543083)\\) | \\(+0.169\\) | 0 | *no clean phase* |",
   "paper_text": "RLLLRLL & L & 48 & $(0.0731803, -0.1543083)$ & $+0.169$ & 0 & \\emph{no clean phase}",
   "paper_line": 2938,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-120",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "word table (Table 17), RLLLRLR, side L: period, position, mu1, clean phases, result (paper 00183cec)",
   "appears_as": "| RLLLRLR | L | 48 | \\((0.0732066, -0.1543834)\\) | \\(-0.251\\) | 0 | *no clean phase* |",
   "paper_text": "RLLLRLR & L & 48 & $(0.0732066, -0.1543834)$ & $-0.251$ & 0 & \\emph{no clean phase}",
   "paper_line": 2939,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-121",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "word table (Table 17), RLLLRRR, side L: period, position, mu1, clean phases, result (paper 00183cec)",
   "appears_as": "| RLLLRRR | L | 48 | \\((0.0733074, -0.1541581)\\) | \\(+0.035\\) | 0 | *no clean phase* |",
   "paper_text": "RLLLRRR & L & 48 & $(0.0733074, -0.1541581)$ & $+0.035$ & 0 & \\emph{no clean phase}",
   "paper_line": 2940,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-122",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "word table (Table 17), RLRRRLR, side L: period, position, mu1, clean phases, result (paper 00183cec)",
   "appears_as": "| RLRRRLR | L | 48 | \\((0.0731146, -0.1541080)\\) | \\(-0.085\\) | 4 | confirmed |",
   "paper_text": "RLRRRLR & L & 48 & $(0.0731146, -0.1541080)$ & $-0.085$ & 4 & confirmed",
   "paper_line": 2941,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-123",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "word table (Table 17), RLRRRLR, side R: period, position, mu1, clean phases, result (paper 00183cec)",
   "appears_as": "| RLRRRLR | R | 48 | \\((0.0731102, -0.1541080)\\) | \\(+0.226\\) | 5 | confirmed |",
   "paper_text": "RLRRRLR & R & 48 & $(0.0731102, -0.1541080)$ & $+0.226$ & 5 & confirmed",
   "paper_line": 2942,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "expoff-006",
   "section": "Numerics and chaos labels",
   "claim": "the offsets are consistent with the alignment transient, whose contribution has not been isolated (paper 3c2498da)",
   "appears_as": "These offsets are consistent with that alignment transient, but its contribution has not",
   "paper_text": "by amounts consistent with that transient (its contribution has not been isolated)",
   "paper_line": 849,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-037",
   "section": "Changing the prompt",
   "claim": "agreement of the periods detected within the run between the random-start runs and the base run (paper 17353aec)",
   "appears_as": "agree at only 86.5 to 93.1% of the cells, so within this horizon, the finite number of steps",
   "paper_text": "the periods detected within the run agree at only 86.5 to 93.1\\,\\%",
   "paper_line": 5698,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-038",
   "section": "Changing the prompt",
   "claim": "chaos threshold of the prompt maps: largest exponent above 1e-3 alone (paper 3c2498da)",
   "appears_as": "chaotic when its largest exponent exceeds \\(10^{-3}\\), with no check for a period.",
   "paper_text": "here chaotic means a largest exponent above $10^{-3}$ alone",
   "paper_line": 5693,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-039",
   "section": "Changing the prompt",
   "claim": "cells per map where the exponent-only indicator overlaps a detected period (paper 3c2498da)",
   "appears_as": "decides, and this finite-window indicator overlaps a detected period at 3 to 18 cells per",
   "paper_text": "this finite-window indicator overlaps a detected period at 3 to 18 cells per map",
   "paper_line": 5693,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-040",
   "section": "Changing the prompt",
   "claim": "colors and gray of the eight maps (Figure 21 note) (paper 3c2498da)",
   "appears_as": "(colors: the largest exponent where it exceeds \\(10^{-3}\\); gray: the other cells, darker where more contracting, among them a few unresolved nonperiodic cells",
   "paper_text": "(colors: the largest exponent where it exceeds $10^{-3}$; gray: the other cells, darker where more contracting, among them a few unresolved nonperiodic cells)",
   "paper_line": 5714,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hp5-001",
   "section": "Our shrimp, followed cell by cell",
   "claim": "threshold of the HP5 chaos share; cells where it overrides a detected period (paper 3c2498da)",
   "appears_as": "\\(10^{-3}\\), which counts as chaos here even at 33 cells where a period is also detected",
   "paper_text": "12\\,\\% a largest exponent above $10^{-3}$ (chaos; at 33 cells it overrides a detected period)",
   "paper_line": 2384,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hp5-002",
   "section": "Our shrimp, followed cell by cell",
   "claim": "colors of panel (a): exponent above 1e-3, overriding a detected period at 33 cells (Figure 52 note) (paper 3c2498da)",
   "appears_as": "cells whose largest exponent exceeds \\(10^{-3}\\) colored by its value (this overrides a detected period at 33 cells of the followed domain)",
   "paper_text": "cells whose largest exponent exceeds $10^{-3}$ by its value (this overrides a detected period at 33 cells of the followed domain)",
   "paper_line": 2991,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-072",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "largest multiplier deviation: four points of the extended leg curves (paper 3c2498da)",
   "appears_as": "the curves extended along the legs reach \\(2.9\\times10^{-7}\\))",
   "paper_text": "four points of the extended leg curves reach $2.9\\times10^{-7}$",
   "paper_line": 2529,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-073",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "boundary gate within the window of Figure 57a: every pair within two grid steps (paper 3c2498da)",
   "appears_as": "they agree for every pair of neighboring cells across the edge: the edge lies within two grid steps of the curves",
   "paper_text": "Within the window of Figure~\\ref{fig:p6shrimp}a, the edge of the followed domain lies within two grid steps of the curves for all 232 neighboring pairs",
   "paper_line": 2531,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-074",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "boundary gate over the whole followed domain, periods 6 and 12 (paper 3c2498da)",
   "appears_as": "Over the whole followed domain the shares fall to 388",
   "paper_text": "over the whole followed domain the shares fall to 388 of 916",
   "paper_line": 2533,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-075",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "boundary gate over the whole followed domain, period 6 and a lost attractor, and the two medians (paper 3c2498da)",
   "appears_as": "of 916 and 1,720 of 1,888 (medians 4.3 and 0.24 steps)",
   "paper_text": "388 of 916 and 1{,}720 of 1{,}888 (medians 4.3 and 0.24 steps)",
   "paper_line": 2533,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-076",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "solved cells where the two largest-modulus multipliers form a real or conjugate pair (paper 3c2498da)",
   "appears_as": "\\(\\mu_2\\), form a pair of their own? At 289 solved cells they do:",
   "paper_text": "At 289 solved cells the two largest-modulus multipliers form a real or complex-conjugate pair",
   "paper_line": 2576,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-077",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "solved cells where the leading real multiplier is followed by a complex-conjugate pair (paper 3c2498da)",
   "appears_as": "At the other 240, the leading real",
   "paper_text": "at the other 240 the leading real multiplier is followed by a complex-conjugate pair",
   "paper_line": 2577,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "p6-078",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "no real two-dimensional determinant from the first two; no determinant-zero curve inferred (paper 3c2498da)",
   "appears_as": "even real: the first two alone define no real two-dimensional determinant",
   "paper_text": "so the first two alone define no real two-dimensional determinant, and we infer no determinant-zero curve from them",
   "paper_line": 2577,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-007",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "random-start map of the hook box: grid, no hook or tongues, comparison at the nearest fixed-start cell (paper 2b81de3f)",
   "appears_as": "mapped at 128 × 128 cells, shows neither the hook nor the tongues, and only 38% of its cells keep their exponent to",
   "paper_text": "the same box at $128\\times128$ cells shows neither the hook nor the tongues, and only 38\\,\\% of its cells keep their exponent within 0.02 of the nearest cell of the fixed-start map",
   "paper_line": 2730,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-008",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "share of random-start cells within 0.02 of the nearest cell of the fixed-start map (paper 2b81de3f)",
   "appears_as": "within 0.02 of the nearest cell of the fixed-start map.",
   "paper_text": "only 38\\,\\% of its cells keep their exponent within 0.02",
   "paper_line": 2731,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-009",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "the random start: a random token's embedding (paper 3c2498da)",
   "appears_as": "From the embedding of one randomly chosen token as the start, the box of Figure 50a,",
   "paper_text": "From a random token's embedding as the start, the same box",
   "paper_line": 2730,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-010",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "the hook and tongues are basin crossings of the fixed start, not bifurcations (paper 3c2498da)",
   "appears_as": "These edges are set by where the fixed start lies relative to the basins, as basin",
   "paper_text": "these edges are set by where the fixed start lies relative to the basins, as basin boundaries should be, not by bifurcations",
   "paper_line": 2731,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-045",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "cells passing the pooled coding test, and its 5% threshold (paper 3c2498da)",
   "appears_as": "six-band cells, 48 have an error ratio below 5% and pass the coding test.",
   "paper_text": "48 of the 58 chaotic six-band cells of a $48\\times48$ map of the window have an error ratio below 5\\,\\%",
   "paper_line": 2844,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-046",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "largest single-phase ratio in a passing cell (paper 3c2498da)",
   "appears_as": "passing cell reaches 21.7%.",
   "paper_text": "a single phase of a passing cell reaches 21.7\\,\\%",
   "paper_line": 2845,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-047",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "failing cells below the kite, and those with more than one resolved turning point (paper 17353aec)",
   "appears_as": "flip curve and seven below the kite. In 7 of them the return map has more than one resolved turning point",
   "paper_text": "flip curve and seven below the kite. In 7 of them the return map has more than one resolved turning point",
   "paper_line": 2847,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-048",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "failing cells without a resolved second turning point (10 - 7 = 3, DERIVED from the paper's counts) (paper 17353aec)",
   "appears_as": "In the other 3 the coding fails",
   "paper_text": "The other 10 cells fail the coding test: three in one column beside the body's left flip curve and seven below the kite. In 7 of them",
   "paper_line": 2846,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-049",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "the extra turning points establish neither a global scalar reduction nor its Schwarzian sign (paper 3c2498da)",
   "appears_as": "global scalar reduction, one interval map for the whole attractor, nor the sign of its Schwarzian derivative.",
   "paper_text": "but they establish neither a global scalar reduction nor its Schwarzian sign",
   "paper_line": 2851,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-050",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "cells rejected by the MSS-admissibility filter (paper 3c2498da)",
   "appears_as": "the filter rejects 240 further cells whose",
   "paper_text": "the filter rejects 240 further cells whose labels are not MSS words",
   "paper_line": 2859,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-051",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "share of eligible periodic six-band cells that receive no word (paper 17353aec)",
   "appears_as": "receive no word (3.2%)",
   "paper_text": "receive no word (3.2\\,\\%)",
   "paper_line": 2876,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-052",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "the 240 MSS-rejected cells are among the 1,469 without a word (44,577 + 1,469 = 46,046) (paper 17353aec)",
   "appears_as": "the 240 rejected by the filter among them",
   "paper_text": "the 240 rejected by the filter among them",
   "paper_line": 2876,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-053",
   "section": "What was and was not found",
   "claim": "chaotic six-band cells of the coding test (found list) (paper 3c2498da)",
   "appears_as": "of the 58 chaotic six-band cells tested, extra turning points just below the kite",
   "paper_text": "48 of the 58 chaotic six-band cells of a $48\\times48$ map of the window have an error ratio below 5\\,\\%",
   "paper_line": 2844,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-054",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "green cells: pooled misplaced visits below 5% of the rarer symbol (Figure 63 note) (paper 3c2498da)",
   "appears_as": "that pass the pooled coding test (green: misplaced visits below 5% of the rarer symbol's, pooled over the usable phases)",
   "paper_text": "that pass the pooled coding test (green: misplaced visits below 5\\,\\% of the rarer symbol's, pooled over the usable phases)",
   "paper_line": 2884,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-055",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "cosine bound of the subsequent clean-phase rule (paper 3c2498da)",
   "appears_as": "\\(\\lvert\\cos\\rvert \\ge 0.5\\) (the scalar product above, taken between unit directions)",
   "paper_text": "separates along the band, with every $|\\cos|\\ge0.5$), reproduce the scan",
   "paper_line": 2871,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-056",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "the labels: W matched to the superstable itinerary WC, X the inferred last branch symbol (paper 3c2498da)",
   "appears_as": "first k − 1 letters, is matched to the quadratic family's superstable itinerary WC and names the window.",
   "paper_text": "W is matched to the quadratic family's superstable itinerary WC and names the window",
   "paper_line": 2855,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-057",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "C cells: small, nonzero complex leading pairs at the two selected cells (paper 3c2498da)",
   "appears_as": "two selected C cells, Newton calculations report small, nonzero complex leading pairs:",
   "paper_text": "at the two selected C cells, Newton calculations report small, nonzero complex leading pairs",
   "paper_line": 2866,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bh-009",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "cells (of 24) where the sign of the block bound B_k agrees with the 2000-step exponent, k = 1, 2 and 4 (paper 17353aec)",
   "appears_as": "the next 2000 steps in only 13 of the 24 cells for blocks of 1, 2 and 4 steps, and in 22",
   "paper_text": "The sign of $B_k$ agrees with the sign of that exponent in 13 of the 24 cells for $k=1$, 2 and 4",
   "paper_line": 624,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "bh-010",
   "section": "Stability belongs to the loop, not to the step",
   "claim": "cells (of 24) where the sign of the block bound B_k agrees with the 2000-step exponent, k = 16 (paper 17353aec)",
   "appears_as": "for blocks of 16. Lengths",
   "paper_text": "and in 22 at $k=16$",
   "paper_line": 624,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "reset-draw",
   "section": "Reproducibility",
   "claim": "problems of the reset test: newly drawn additions (paper 17353aec)",
   "appears_as": "It used 128 newly drawn additions,",
   "paper_text": "on 128 newly drawn additions",
   "paper_line": 1323,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "reset-05b-r",
   "section": "Reproducibility",
   "claim": "answers changed with the reset, Qwen2.5-0.5B, bfloat16 on an H100: 1 of 128 (0.8%) (paper 318f8980)",
   "appears_as": "without the reset and in 1 (0.8%)",
   "paper_text": "in 1 (0.8\\,\\%) with reset in the 0.5B model",
   "paper_line": 1335,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "reset-T05b",
   "section": "Reproducibility",
   "claim": "temperature of the 0.5B reset test (paper 17353aec)",
   "appears_as": "Qwen2.5-0.5B (at \\(T = 1\\))",
   "paper_text": "the 0.5B pipeline at $T=1$ on 128 newly drawn additions",
   "paper_line": 1323,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "reset-T7b",
   "section": "Reproducibility",
   "claim": "temperature of the 7B reset test (paper 17353aec)",
   "appears_as": "Qwen2.5-7B (at \\(T = 10^{0.2}\\))",
   "paper_text": "in Qwen2.5-7B at $T=10^{0.2}$",
   "paper_line": 1335,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "reset-first",
   "section": "Reproducibility",
   "claim": "first run of the 0.5B reset test on a workstation GPU: answers changed, free 88 of 128 (69%) against reset 7 (5.5%) (paper 318f8980)",
   "appears_as": "(69%) in the free condition and in 7 (5.5%) in the reset condition, a difference",
   "paper_text": "In bfloat16 the answer changed in 88 of the 128 problems (69\\,\\%) in the free arm and in 7 (5.5\\,\\%) in the reset arm",
   "paper_line": 1328,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hc-001",
   "section": "Numerics and chaos labels",
   "claim": "protocol of the longer horizon check (paper 17353aec)",
   "appears_as": "A longer horizon check (1000 transient and 2000 measured",
   "paper_text": "with 1000 transient and 2000 measured steps at two twin offsets",
   "paper_line": 5754,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "indep-007",
   "section": "Numerics and chaos labels",
   "claim": "the independent implementation reproduces the exponents of two chaotic cells and of the certified period-8 orbit (paper 17353aec)",
   "appears_as": "reproduces the exponents of two chaotic cells and of the certified period-8 orbit",
   "paper_text": "its 300-step exponents at two chaotic cells of Figure~\\ref{fig:cross512}",
   "paper_line": 4231,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-011",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "steering strength at which the lower edge was bisected (paper 17353aec)",
   "appears_as": "At \\(\\alpha = 0.072975\\) we bisected the wedge's lower edge in \\(\\log_{10}T\\) to",
   "paper_text": "At $\\alpha=0.072975$ we bisected the wedge's lower edge in $\\log_{10}T$ to the float64 limit",
   "paper_line": 2748,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-012",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "the lower edge, bisected to the float64 limit (paper 17353aec)",
   "appears_as": "the limit of float64 arithmetic, at \\(\\log_{10}T = -0.1535299666043828\\).",
   "paper_text": "at $\\log_{10}T=-0.1535299666043828$",
   "paper_line": 2749,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-013",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Newton residual of the saddle found from the lingering state (paper 17353aec)",
   "appears_as": "converges (residual \\(2\\times10^{-14}\\)) to a saddle with a single multiplier outside the unit circle,",
   "paper_text": "converges (residual $2\\times10^{-14}$) to a saddle with a single multiplier outside the unit circle",
   "paper_line": 2751,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-014",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "the saddle's unstable multiplier and next modulus; first relative distance (paper 17353aec)",
   "appears_as": "\\(\\mu_u = 1.2625\\), real, with the next modulus \\(7.8\\times10^{-4}\\), at relative distances \\(3.5\\times10^{-3}\\) and",
   "paper_text": "$\\mu_u=1.2625$, real, with the next modulus $7.8\\times10^{-4}$, at relative distances $3.5\\times10^{-3}$ and $4.7\\times10^{-3}$",
   "paper_line": 2752,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-015",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "relative distances of the saddle from the two attracting orbits (paper 17353aec)",
   "appears_as": "\\(4.7\\times10^{-3}\\) from the two attracting orbits.",
   "paper_text": "at relative distances $3.5\\times10^{-3}$ and $4.7\\times10^{-3}$ from the two attracting orbits",
   "paper_line": 2752,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-016",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "predicted lingering time per factor e: 6/ln mu_u (paper 17353aec)",
   "appears_as": "Its unstable multiplier predicts \\(6/\\ln\\mu_u = 25.74\\) steps",
   "paper_text": "$6/\\ln\\mu_u=25.74$ steps for every factor $e$ by which the offset shrinks",
   "paper_line": 2757,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-017",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "temperatures per side of the edge (paper 17353aec)",
   "appears_as": "We then started the loop at 17 temperatures on each side of the edge, at distances \\(\\delta\\) from",
   "paper_text": "At 17 temperatures on each side of the edge, a distance $\\delta$ from $10^{-6}$ to $10^{-14}$ in $\\log_{10}T$ away",
   "paper_line": 2758,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-018",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "range of the distance delta from the edge (paper 17353aec)",
   "appears_as": "\\(10^{-6}\\) to \\(10^{-14}\\) in \\(\\log_{10}T\\) (Figure 51).",
   "paper_text": "a distance $\\delta$ from $10^{-6}$ to $10^{-14}$ in $\\log_{10}T$ away",
   "paper_line": 2758,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-019",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "measured lingering time per factor e on the two sides, and the radius 1e-3 (paper 17353aec)",
   "appears_as": "of \\(10^{-3}\\) of the saddle grows by 25.78 and 25.75 steps per factor \\(e\\) in \\(\\delta\\), against the predicted",
   "paper_text": "the last step within $10^{-3}$ of the saddle grows by 25.78 and 25.75 steps per factor $e$ in $\\delta$",
   "paper_line": 2759,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-020",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "largest deviations from the fitted lines, and the predicted slope (paper 17353aec)",
   "appears_as": "25.74, with all points within 4.0 and 2.9 steps of the fitted lines.",
   "paper_text": "(all points within 4.0 and 2.9 steps of the fitted lines)",
   "paper_line": 2760,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-021",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "log-log slopes of the closest approach against delta, against the linear-saddle exponent 0.97 (paper 2b81de3f)",
   "appears_as": "log-log slopes of 0.986 and 0.995, against the predicted 0.97.",
   "paper_text": "the closest approach grows with $\\delta$ with log-log slopes 0.986 and 0.995 (predicted 0.97)",
   "paper_line": 2761,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-022",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "outcome by side of the edge (paper 17353aec)",
   "appears_as": "ends on the strongly contracting orbit \\(S\\), every start above it on \\(W\\).",
   "paper_text": "every start below the edge ends on the strongly contracting orbit and every start above it on the other",
   "paper_line": 2761,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-023",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "range of the confirmed predictions (paper 17353aec)",
   "appears_as": "Both predictions hold over eight decades",
   "paper_text": "Both predictions hold over eight decades",
   "paper_line": 2757,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-024",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "strong numerical evidence that, at this steering strength, the lower edge is where the fixed start crosses the saddle's stable manifold (paper 2b81de3f)",
   "appears_as": "where the fixed start crosses the saddle's stable manifold.",
   "paper_text": "this is strong numerical evidence that, at this steering strength, the lower edge is where the fixed start crosses the saddle's stable manifold",
   "paper_line": 2763,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-025",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "jumps of the outcome bisected along the map columns (paper 17353aec)",
   "appears_as": "Bisecting 676 jumps of the outcome along the map's columns, each to",
   "paper_text": "Bisecting 676 jumps of the outcome along the map's columns (to $2.6\\times10^{-13}$ in $\\log_{10}T$",
   "paper_line": 2764,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-026",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "precision of the bisected edges (paper 17353aec)",
   "appears_as": "\\(2.6\\times10^{-13}\\) in \\(\\log_{10}T\\), traces the hook's other edges (Figure 51a).",
   "paper_text": "(to $2.6\\times10^{-13}$ in $\\log_{10}T$",
   "paper_line": 2765,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-027",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "offset of the upper edge above a spline through the continued fold curve (paper 17353aec)",
   "appears_as": "fold curve, but 0.1 to 1.6 grid rows above a spline through the continued curve's points, and more so toward the",
   "paper_text": "The upper edge follows the kite's fold curve, 0.1 to 1.6 grid rows above a spline through the continued curve's points and more so toward the cusp",
   "paper_line": 2766,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-028",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "upper-edge offset explained: in the map window the loop still lingers at the vanished orbit (alpha above 0.072965 and 0.072967 for half a row and one row beyond the fold) (paper 4e6e2ec6)",
   "appears_as": "0.072965 and 0.072967, respectively, because the loop still lingers at the orbit that vanished there, while over",
   "paper_text": "for $\\alpha$ above 0.072965 and 0.072967, because the loop still lingers at the orbit that vanished there",
   "paper_line": 2770,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-029",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "tip: the tangential contact corresponds to the exponent 1/2, which the boundary points do not resolve (paper 4e6e2ec6)",
   "appears_as": "offset, the exponent \\(1/2\\); these points do not resolve the exponent.",
   "paper_text": "which corresponds to the exponent $1/2$; these points do not resolve the exponent",
   "paper_line": 2810,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-030",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "tip: predicted tangential contact, quadratic growth of the gap along the fold (paper 4e6e2ec6)",
   "appears_as": "The normal form also predicts how the edges meet: tangentially, the gap between them growing quadratically along",
   "paper_text": "The normal form predicts a tangential contact, the gap between the edges growing quadratically along the fold",
   "paper_line": 2809,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-031",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "the basin boundary of two attracting orbits is typically the stable manifold of a saddle orbit (paper 17353aec)",
   "appears_as": "branch and end on the other attractor. That is why the boundary between the basins of two attracting orbits is",
   "paper_text": "the boundary between the basins of two attracting orbits is typically the stable manifold of a saddle orbit between them",
   "paper_line": 2747,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-032",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "lingering time grows by 6/ln mu_u steps per factor e (period 6) (paper 17353aec)",
   "appears_as": "\\(6\\ln(r/\\delta)/\\ln\\mu_u\\) steps. Every factor \\(e\\) by which \\(\\delta\\) shrinks therefore adds \\(6/\\ln\\mu_u\\)",
   "paper_text": "so the time it spends near the saddle grows by $6/\\ln\\mu_u=25.74$ steps for every factor $e$ by which the offset shrinks",
   "paper_line": 2756,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-033",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "closest approach of a passage near a linear saddle: proportional to delta^(chi_s/(chi_s+chi_u)) (paper 2b81de3f)",
   "appears_as": "as for a passage near a linear saddle. Where the attracting directions contract much faster than the repelling one",
   "paper_text": "comes within a distance $\\propto\\delta^{\\chi_s/(\\chi_s+\\chi_u)}$ of the saddle, as for a passage near a linear saddle",
   "paper_line": 2754,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-034",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "bisected brackets: end exponents differ by at least 0.1 (Figure 60 note) (paper 17353aec)",
   "appears_as": "brackets whose end exponents differ by at least 0.1",
   "paper_text": "(cyan; brackets whose end exponents differ by at least 0.1)",
   "paper_line": 2780,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-035",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "steering strength of panels b to d (Figure 60 note) (paper 17353aec)",
   "appears_as": "red star: the steering strength \\(\\alpha = 0.072975\\) of (b) to (d).",
   "paper_text": "red star: the steering strength $\\alpha=0.072975$ of (b)--(d)",
   "paper_line": 2780,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-036",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "arrival along the stable manifold within about 25 steps (Figure 60 note) (paper 17353aec)",
   "appears_as": "it arrives along the stable manifold within about 25 steps, lingers, and leaves along the unstable direction",
   "paper_text": "it arrives along the stable manifold within about 25 steps, lingers, and leaves along the unstable direction",
   "paper_line": 2782,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-037",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "radius of panel c (Figure 60 note) (paper 17353aec)",
   "appears_as": "dotted: the radius \\(10^{-3}\\) of (c)",
   "paper_text": "dotted: the radius $10^{-3}$ of (c)",
   "paper_line": 2783,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-038",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "panel c (Figure 60 note) (paper 17353aec)",
   "appears_as": "(c) The last step within \\(10^{-3}\\) of the saddle against \\(\\ln(1/\\delta)\\)",
   "paper_text": "(c) The last step within $10^{-3}$ of the saddle against $\\ln(1/\\delta)$",
   "paper_line": 2783,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-039",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "eight decades (Figure 60 note) (paper 17353aec)",
   "appears_as": "the points of both sides follow them over eight decades of \\(\\delta\\)",
   "paper_text": "Both predictions hold over eight decades",
   "paper_line": 2757,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-040",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "state dimension (diagram note) (paper 17353aec)",
   "appears_as": "the real state space has 896 dimensions",
   "paper_text": "$d=896$",
   "paper_line": 314,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-041",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "predicted slope and unstable multiplier shown in Figure 60c (alt text) (paper 17353aec)",
   "appears_as": "labeled slope 6/ln mu_u = 25.74, mu_u = 1.2625",
   "paper_text": "$\\mu_u=1.2625$, real",
   "paper_line": 2752,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-042",
   "section": "What was and was not found",
   "claim": "measured lingering time per factor e (found list) (paper 17353aec)",
   "appears_as": "grows by 25.78 and 25.75 steps per factor \\(e\\) in its distance from the edge, against",
   "paper_text": "grows by 25.78 and 25.75 steps per factor $e$ in $\\delta$",
   "paper_line": 2760,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-043",
   "section": "What was and was not found",
   "claim": "predicted lingering time per factor e and the range (found list) (paper 17353aec)",
   "appears_as": "25.74 predicted from the saddle's unstable multiplier, over eight decades",
   "paper_text": "$6/\\ln\\mu_u=25.74$ steps for every factor $e$ by which the offset shrinks. Both predictions hold over eight decades",
   "paper_line": 2757,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-058",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "selected cells and the words they cover (short version) (paper 17353aec)",
   "appears_as": "Float64 Newton solves at 23 selected cells, covering 12 of the words,",
   "paper_text": "23 cells, covering 12 of the 23 words",
   "paper_line": 2869,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-059",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "words not checked (short version) (paper 17353aec)",
   "appears_as": "the other 11 words were not checked. Below the kite",
   "paper_text": "the other 11 words were not checked",
   "paper_line": 2873,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-060",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "majority vote: at least three phases give the winning word (paper 17353aec)",
   "appears_as": "takes the window word W that the most phases give, provided at least three phases give it.",
   "paper_text": "a majority vote over the band phases whose coding is usable (at least three)",
   "paper_line": 2857,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-061",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "the scan's 16 bands (strips of grid rows) (paper 17353aec)",
   "appears_as": "The scan of Figure 57 was computed in 16 strips of grid rows, and the cells were chosen",
   "paper_text": "in the eight of the scan's 16 bands then complete",
   "paper_line": 2909,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-062",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "cells chosen in the half of the scan then complete (eight of the 16 bands), one per label W|X (paper 17353aec)",
   "appears_as": "when eight of the strips, half the scan, were complete: one cell for each label W|X, word and side, with at least",
   "paper_text": "at one cell for each label W|X with at least three coded cells in the half of the scan then complete",
   "paper_line": 2868,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-064",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "checked cells cover 12 of the 23 words (paper 17353aec)",
   "appears_as": "cover 12 of the 23 window words; the other 11 words were not checked.",
   "paper_text": "23 cells, covering 12 of the 23 words",
   "paper_line": 2869,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-065",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "words not checked (paper 17353aec)",
   "appears_as": "cover 12 of the 23 window words; the other 11 words were not checked.",
   "paper_text": "the other 11 words were not checked",
   "paper_line": 2873,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-067",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "words left unchecked by the selected cells (paper 17353aec)",
   "appears_as": "label, at the center of its largest patch, and leave 11 of the 23 words unchecked.",
   "paper_text": "the other 11 words were not checked",
   "paper_line": 2873,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-068",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "checked cells, words covered and words not checked (Table 17 note) (paper 17353aec)",
   "appears_as": "(23 cells covering 12 of the 23 words; the other 11 were not checked).",
   "paper_text": "(23 cells covering 12 of the 23 words; the other 11 were not checked)",
   "paper_line": 2910,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-070",
   "section": "What was and was not found",
   "claim": "selected cells and the words they cover (found list) (paper 17353aec)",
   "appears_as": "all; float64 Newton solves at 23 selected cells, covering 12 of the words, reproduce the",
   "paper_text": "23 cells, covering 12 of the 23 words",
   "paper_line": 2869,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-071",
   "section": "What was and was not found",
   "claim": "words without a float64 check (not-found list) (paper 17353aec)",
   "appears_as": "any float64 check of the 11 window words not selected",
   "paper_text": "the other 11 words were not checked",
   "paper_line": 2873,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "mexc-001",
   "section": "Methods in detail",
   "claim": "figures that color every cell with exponent above 1e-3, also where a period is detected (paper 17353aec)",
   "appears_as": "\\(10^{-3}\\), also where a period is detected, as their notes state: the prompt maps",
   "paper_text": "Two figures color every cell whose exponent exceeds $10^{-3}$, also where a period is detected, as their captions state",
   "paper_line": 4254,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "indep-001",
   "section": "Methods in detail",
   "claim": "protocol of the independent chaos check: the scans' protocol (paper 17353aec)",
   "appears_as": "With the scans' protocol (fixed start, 300 transient steps, twin offset \\(10^{-6}\\)), its",
   "paper_text": "with the scans' protocol (fixed start, 300 transient steps, twin offset $10^{-6}$)",
   "paper_line": 4230,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "indep-002",
   "section": "Methods in detail",
   "claim": "cells of the independent chaos check (paper 17353aec)",
   "appears_as": "300-step exponents at two chaotic cells of Figure 1, \\((0.065201, -0.155998)\\) and",
   "paper_text": "its 300-step exponents at two chaotic cells of Figure~\\ref{fig:cross512}, $(0.065201,-0.155998)$ and $(0.075475,-0.133454)$",
   "paper_line": 4231,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "indep-003",
   "section": "Methods in detail",
   "claim": "300-step exponents of the independent implementation against the scan (paper 17353aec)",
   "appears_as": "\\((0.075475, -0.133454)\\), are 0.098 and 0.354, against 0.113 and 0.359 in the scan",
   "paper_text": "are $0.098$ and $0.354$, against $0.113$ and $0.359$ in the scan",
   "paper_line": 4232,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "indep-004",
   "section": "Methods in detail",
   "claim": "1000-step exponents of the independent implementation (the check reports only its own exponents) (paper 17353aec)",
   "appears_as": "(over 1000 steps it gives 0.106 and 0.332).",
   "paper_text": "($0.106$ and $0.332$ over 1000 steps)",
   "paper_line": 4233,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "indep-005",
   "section": "Methods in detail",
   "claim": "exponent of the independent implementation at the certified period-8 orbit (paper 17353aec)",
   "appears_as": "gives \\(-0.564\\) per step over 1000 steps (\\(-0.579\\) over 300), the value",
   "paper_text": "$-0.564$ per step over 1000 steps ($-0.579$ over 300)",
   "paper_line": 4234,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "indep-006",
   "section": "Methods in detail",
   "claim": "predicted exponent ln(0.0110)/8 from the leading multiplier (paper 17353aec)",
   "appears_as": "\\(\\ln(0.0110)/8\\) that the orbit's leading multiplier predicts:",
   "paper_text": "the value $\\ln(0.0110)/8$ that the orbit's leading multiplier predicts",
   "paper_line": 4234,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-028",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "checked at two neighboring cells across the straight edge (Figure 58 note) (paper 4e6e2ec6)",
   "appears_as": "where we checked it: at two neighboring cells across it both attracting period-6 orbits exist",
   "paper_text": "where we checked it: at two neighboring cells across it both attracting period-6 orbits exist",
   "paper_line": 2715,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "kite-029",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "at one steering strength the start on the edge lies on the stable manifold of a saddle orbit (Figure 58 note) (paper 4e6e2ec6); rebound at paper 13145281",
   "appears_as": "At one steering strength, by strong numerical evidence, the start on the edge lies on the stable manifold of",
   "paper_text": "and at one steering strength, by strong numerical evidence, the start on the edge lies on the stable manifold of a saddle orbit between them",
   "paper_line": 2717,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "tip-001",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "rows beyond the fold where the weaker orbit does not exist (paper 4e6e2ec6)",
   "appears_as": "Half a row and one row beyond the fold, where the weaker orbit \\(W\\), the less contracting of the two, does not exist,",
   "paper_text": "half a row and one row beyond the fold, where the weaker orbit does not exist",
   "paper_line": 2768,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "tip-002",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "map-window exponents beyond the fold (steps 300 to 600) (paper 4e6e2ec6)",
   "appears_as": "the exponent over the map's window (steps 300 to 600) lies between \\(-0.022\\) and \\(+0.012\\) for \\(\\alpha\\) above",
   "paper_text": "the exponent over the map's window (steps 300 to 600) lies between $-0.022$ and $+0.012$ for $\\alpha$ above 0.072965 and 0.072967",
   "paper_line": 2769,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "tip-003",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "long-window exponents of every cell of the strip beyond the fold: the strongly contracting orbit (paper 2b81de3f)",
   "appears_as": "steps 3000 to 3400 every cell of the strip beyond the fold gives the strongly contracting orbit's exponent (\\(-0.18\\) to \\(-0.71\\)).",
   "paper_text": "while over steps 3000 to 3400 every cell of the strip beyond the fold gives the strongly contracting orbit's exponent ($-0.18$ to $-0.71$)",
   "paper_line": 2771,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "tip-004",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "fold points of the continued curve where u0 is negative (slow convergence) (paper 4e6e2ec6)",
   "appears_as": "At seven points of the continued fold curve, \\(u_0\\) is negative at \\(\\alpha = 0.072980\\) to",
   "paper_text": "At seven points of the continued fold curve, $u_0$ is negative at $\\alpha=0.072980$ to $0.073002$",
   "paper_line": 2799,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "tip-005",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "quadratic coefficient fitted to the drift of converging starts (paper 4e6e2ec6)",
   "appears_as": "0.073002, where the start converges slowly onto the orbit (its drift fits \\(u' = u + bu^2\\) with \\(b = 56\\) to 68),",
   "paper_text": "where the start converges slowly onto the orbit (its drift fits $u'=u+bu^2$ with $b=56$ to 68)",
   "paper_line": 2799,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "tip-006",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "fold points where u0 is positive (escape), and the eight located points between them (paper 4e6e2ec6)",
   "appears_as": "and positive at \\(\\alpha = 0.072889\\) to 0.072963, where it escapes. At eight fold points located between them by",
   "paper_text": "and positive at $\\alpha=0.072889$ to $0.072963$, where it escapes",
   "paper_line": 2800,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "tip-007",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Newton residuals of the eight located fold points (paper 4e6e2ec6)",
   "appears_as": "Newton's method at fixed \\(\\alpha\\) (residuals at most \\(5\\times10^{-14}\\)), \\(u_0\\) is nearly linear in \\(\\alpha\\) and",
   "paper_text": "At eight fold points located between them by Newton's method at fixed $\\alpha$ (residuals at most $5\\times10^{-14}$",
   "paper_line": 2801,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "tip-008",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "zero of u0: the predicted tip, to leading order (paper 2b81de3f)",
   "appears_as": "crosses zero at \\(\\alpha = 0.0729655\\) (Figure 52a): that is the predicted tip, to leading order.",
   "paper_text": "crosses zero at $\\alpha=0.0729655$, the predicted tip to leading order",
   "paper_line": 2803,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "tip-009",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "offsets below the fold at which the inside boundary was located (paper 4e6e2ec6)",
   "appears_as": "Inside the fold, the boundary between the two outcomes approaches this point. At offsets of 2, 1, 0.5, 0.25 and",
   "paper_text": "at offsets of 2, 1, 0.5, 0.25 and 0.125 grid rows below the fold",
   "paper_line": 2805,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "tip-010",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "smallest offset below the fold (paper 4e6e2ec6)",
   "appears_as": "0.125 grid rows below the fold, the last cell that ends on the strongly contracting orbit lies at",
   "paper_text": "at offsets of 2, 1, 0.5, 0.25 and 0.125 grid rows below the fold, the last cell that ends on the strongly contracting orbit lies at",
   "paper_line": 2805,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "tip-011",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "boundary positions inside the fold (long window, cells 1e-7 apart) (paper 4e6e2ec6)",
   "appears_as": "\\(\\alpha = 0.0729627\\), 0.0729632, 0.0729637, 0.0729642 and 0.0729645 (long window, cells \\(10^{-7}\\) apart). The",
   "paper_text": "$\\alpha=0.0729627$, 0.0729632, 0.0729637, 0.0729642 and 0.0729645 (long window, cells $10^{-7}$ apart)",
   "paper_line": 2806,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "tip-012",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "extrapolated end of the boundary on the fold, exponents 1/3 to 1/2 (paper 4e6e2ec6)",
   "appears_as": "\\(1/3\\) to \\(1/2\\) put the boundary's end on the fold at \\(\\alpha = 0.0729651\\) to 0.0729657, bracketing the",
   "paper_text": "extrapolations with exponents from $1/3$ to $1/2$ put the boundary's end on the fold at $\\alpha=0.0729651$ to $0.0729657$",
   "paper_line": 2807,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "tip-013",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "map-window boundary displaced from the tip (paper 4e6e2ec6)",
   "appears_as": "to \\(7\\times10^{-7}\\) farther from the tip, as expected: near the fold the saddle's unstable multiplier approaches 1,",
   "paper_text": "In the map's window the boundary appears up to $7\\times10^{-7}$ farther from the tip, as expected where the saddle's unstable multiplier approaches 1 near the fold",
   "paper_line": 2810,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "tip-014",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Figure 61 note: zero of u0, the predicted tip (paper 4e6e2ec6)",
   "appears_as": "where \\(u_0\\) crosses zero at \\(\\alpha = 0.0729655\\) (vertical line, the predicted tip, also in (b) and (c))",
   "paper_text": "where $u_0$ crosses zero at $\\alpha=0.0729655$ (vertical line, the predicted tip, also in (b) and (c))",
   "paper_line": 2820,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "tip-015",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Figure 61 note: the map window (paper 4e6e2ec6)",
   "appears_as": "(b) The largest exponent over the map's window (steps 300 to 600) along rows at fixed offsets from the fold curve",
   "paper_text": "(b) The largest exponent over the map's window (steps 300 to 600) along rows at fixed offsets from the fold curve",
   "paper_line": 2821,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "tip-016",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Figure 61 note: exponents of the two orbits and the threshold (paper 4e6e2ec6)",
   "appears_as": "the strongly contracting orbit has exponents of \\(-0.18\\) to \\(-0.71\\) here, the weaker one exponents near \\(-0.01\\); dotted: the threshold \\(-0.15\\) between them",
   "paper_text": "has exponents of $-0.18$ to $-0.71$ here, the weaker one exponents near $-0.01$; dotted: the threshold $-0.15$ between them",
   "paper_line": 2823,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "tip-017",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Figure 61 note: the long window (paper 4e6e2ec6)",
   "appears_as": "(c) The same cells over steps 3000 to 3400: beyond the fold every cell ends on the strongly contracting orbit.",
   "paper_text": "(c) The same cells over steps 3000 to 3400: beyond the fold every cell ends on the strongly contracting orbit",
   "paper_line": 2824,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "tip-018",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Figure 61 note: exponent 1/2 of a tangential contact (paper 4e6e2ec6)",
   "appears_as": "The straight line in (d) assumes the exponent \\(1/2\\) of a tangential contact",
   "paper_text": "which corresponds to the exponent $1/2$",
   "paper_line": 2810,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "tip-019",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Figure 61 note: extrapolated end for exponents 1/3 to 1/2 (paper 4e6e2ec6)",
   "appears_as": "with exponents from \\(1/3\\) to \\(1/2\\) the extrapolated end lies at \\(\\alpha = 0.0729651\\) to 0.0729657",
   "paper_text": "extrapolations with exponents from $1/3$ to $1/2$ put the boundary's end on the fold at $\\alpha=0.0729651$ to $0.0729657$",
   "paper_line": 2807,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "tip-020",
   "section": "What was and was not found",
   "claim": "found list: zero of u0 at the predicted tip (paper 4e6e2ec6)",
   "appears_as": "the merging orbit changing sign at \\(\\alpha = 0.0729655\\) and the boundary inside the fold",
   "paper_text": "nearly linear in $\\alpha$ and crosses zero at $\\alpha=0.0729655$",
   "paper_line": 2803,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "tip-021",
   "section": "What was and was not found",
   "claim": "found list: extrapolated end of the inside boundary (paper 4e6e2ec6)",
   "appears_as": "extrapolating to 0.0729651 to 0.0729657; and the upper edge's offset from the fold traced",
   "paper_text": "extrapolations with exponents from $1/3$ to $1/2$ put the boundary's end on the fold at $\\alpha=0.0729651$ to $0.0729657$",
   "paper_line": 2807,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "tip-022",
   "section": "What was and was not found",
   "claim": "found list: the upper edge's offset comes from the map's window (paper 4e6e2ec6)",
   "appears_as": "to the map's short measurement window",
   "paper_text": "The offset comes from the map's window",
   "paper_line": 2767,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "expoff-007",
   "section": "Numerics and chaos labels",
   "claim": "agreement of automatic-differentiation tangents with the twin exponents at the 448 checked cells (paper 2b81de3f)",
   "appears_as": "reproduce the twin exponents within 0.0041. The twin starts in a random direction among the state's",
   "paper_text": "automatic-differentiation tangents reproduce the twin exponents within $0.0041$",
   "paper_line": 847,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-041",
   "section": "Changing the prompt",
   "claim": "chaos and periodic windows appear in every prompt tested; the prompt decides where they lie (paper 2b81de3f)",
   "appears_as": "In every prompt we tested, chaos and periodic windows appear, but the prompt decides",
   "paper_text": "In every prompt we tested, chaos and periodic windows appear, but the prompt decides where they lie",
   "paper_line": 5695,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-042",
   "section": "Changing the prompt",
   "claim": "the Gaussian random-vector prompt is scaled to the median embedding norm (paper 2b81de3f)",
   "appears_as": "random direction scaled to the median norm of the token embeddings, the embedding of one",
   "paper_text": "a Gaussian direction at the median embedding norm, the embedding of a random token",
   "paper_line": 5690,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-043",
   "section": "Changing the prompt",
   "claim": "the mixture prompt: Dirichlet(0.1) weights over the embeddings of 64 random tokens (paper 2b81de3f)",
   "appears_as": "random token, and a mixture of the embeddings of 64 random tokens with Dirichlet(0.1)",
   "paper_text": "and a Dirichlet(0.1) mixture of the embeddings of 64 random tokens",
   "paper_line": 5691,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "pv-044",
   "section": "Changing the prompt",
   "claim": "the mixture prompt: weights over 64 tokens (explanation of Dirichlet(0.1)) (paper 2b81de3f)",
   "appears_as": "weights, random weights that sum to one and fall mostly on a few of the 64 tokens.",
   "paper_text": "and a Dirichlet(0.1) mixture of the embeddings of 64 random tokens",
   "paper_line": 5691,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-072",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "at the 16 confirmed cells the full map's leading multiplier has the parity-predicted sign (paper 2b81de3f)",
   "appears_as": "At these 16 cells the full map's leading multiplier also has the sign that the label's parity predicts",
   "paper_text": "At the 16 confirmed cells the full map's leading multiplier also has the sign that the label's parity predicts",
   "paper_line": 2873,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "sd-073",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "the sign rule belongs to the scalar coding; it carries over only while the multiplier stays real and dominant (paper 2b81de3f)",
   "appears_as": "that sign rule belongs to the scalar coding and carries over to the full map only while the leading multiplier stays real and dominant",
   "paper_text": "this sign rule belongs to the scalar coding and carries over to the full map only while that multiplier stays real and dominant",
   "paper_line": 2874,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-044",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "predicted exponent of the closest approach, chi_s/(chi_s+chi_u), with the next modulus as |mu_s| (paper 2b81de3f)",
   "appears_as": "power \\(\\chi_s/(\\chi_s+\\chi_u) = 0.97\\).",
   "paper_text": "(an exponent of 0.97 here)",
   "paper_line": 2755,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-045",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "chi_s from the slowest stable multiplier (the next modulus, 7.8e-4) and chi_u = ln mu_u (paper 2b81de3f)",
   "appears_as": "per factor \\(e\\); with the next modulus as \\(\\lvert\\mu_s\\rvert\\), the closest approach should grow like \\(\\delta\\) to the",
   "paper_text": "with $\\chi_u=\\ln\\mu_u$ and $\\chi_s=-\\ln|\\mu_s|$ from its slowest stable multiplier $\\mu_s$",
   "paper_line": 2755,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-046",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Figure 60 note (d): predicted slope 0.97 from the saddle's multipliers (paper 2b81de3f)",
   "appears_as": "(d) Closest approach to the saddle against \\(\\delta\\); dashed: slope \\(\\chi_s/(\\chi_s+\\chi_u) = 0.97\\) from the saddle's multipliers.",
   "paper_text": "dashed: slope $\\chi_s/(\\chi_s+\\chi_u)=0.97$ from the saddle's multipliers",
   "paper_line": 2786,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-047",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Figure 60 alt text (d): the predicted slope 0.97 (paper 2b81de3f)",
   "appears_as": "labeled slope chi_s/(chi_s + chi_u) = 0.97 (linear saddle)",
   "paper_text": "dashed: slope $\\chi_s/(\\chi_s+\\chi_u)=0.97$ from the saddle's multipliers",
   "paper_line": 2786,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-048",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "closest approach of a passage near a linear saddle (derivation) (paper 2b81de3f)",
   "appears_as": "\\(\\chi_s = -\\ln\\lvert\\mu_s\\rvert\\) and \\(\\chi_u = \\ln\\mu_u\\) the two rates. At that point the repelling part is",
   "paper_text": "with $\\chi_u=\\ln\\mu_u$ and $\\chi_s=-\\ln|\\mu_s|$ from its slowest stable multiplier $\\mu_s$ (an exponent of 0.97 here)",
   "paper_line": 2755,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "hook-049",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "edge prediction for the closest approach: delta^(chi_s/(chi_s+chi_u)) (paper 2b81de3f)",
   "appears_as": "the closest approach should grow like \\(\\delta^{\\chi_s/(\\chi_s+\\chi_u)}\\), and the time near the saddle should grow by",
   "paper_text": "comes within a distance $\\propto\\delta^{\\chi_s/(\\chi_s+\\chi_u)}$ of the saddle",
   "paper_line": 2754,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "tip-023",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "the normal form over one six-step return (paper 2b81de3f)",
   "appears_as": "critical direction. To leading order, one six-step return changes that coordinate as",
   "paper_text": "changes over one six-step return as",
   "paper_line": 2791,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "tip-024",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "the unfolded normal form: eta the distance from the fold, zero on the fold (Kuznetsov) (paper 2b81de3f)",
   "appears_as": "the normal form of the fold ([Kuznetsov, 2023](#ref-kuznetsov-2023)), with \\(\\eta\\) the distance from the fold in the",
   "paper_text": "with $\\eta$ the distance from the fold in the normal form's units and $\\eta=0$ on the fold",
   "paper_line": 2792,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "tip-025",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "the exact tip: landing on the strong-stable set of the saddle-node orbit (paper 2b81de3f)",
   "appears_as": "the fold where \\(u_0\\) changes sign. Exactly, it is where the start lands on the strong-stable set of the",
   "paper_text": "exactly, it is where the start lands on the strong-stable set of the saddle-node orbit, which the zero of $u_0$ approximates near that orbit",
   "paper_line": 2798,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r9-thr-01",
   "section": "Numerics and chaos labels",
   "claim": "chaos threshold raised to 5e-3 (Numerics and chaos labels) (paper 602c70ac)",
   "appears_as": "raising it to \\(5\\times10^{-3}\\) lowers the chaotic",
   "paper_text": "raising it to $5\\times10^{-3}$ lowers the chaotic share of the map of Figure~\\ref{fig:teaser} from 30.1 to 29.8\\,\\%",
   "paper_line": 4249,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r9-thr-02",
   "section": "Numerics and chaos labels",
   "claim": "chaotic share of the map of Figure 1 at the thresholds 1e-3 and 5e-3 (paper 602c70ac)",
   "appears_as": "share of the map of Figure 1, shown below, from 30.1 to 29.8%.",
   "paper_text": "raising it to $5\\times10^{-3}$ lowers the chaotic share of the map of Figure~\\ref{fig:teaser} from 30.1 to 29.8\\,\\%",
   "paper_line": 4249,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r9-thr-03",
   "section": "Methods in detail",
   "claim": "chaos threshold raised to 5e-3: chaotic share of the Figure 1 map 30.1 to 29.8% (methods) (paper 602c70ac)",
   "appears_as": "raising it to \\(5\\times10^{-3}\\) lowers the chaotic share of the map of Figure 1 from 30.1 to 29.8%.",
   "paper_text": "raising it to $5\\times10^{-3}$ lowers the chaotic share of the map of Figure~\\ref{fig:teaser} from 30.1 to 29.8\\,\\%",
   "paper_line": 4249,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r9-fig1-01",
   "section": "Chaos with periodic windows",
   "claim": "Figure 1 note: unresolved cells have neither a detected period nor an exponent above 1e-3 (paper 602c70ac)",
   "appears_as": "have neither a detected period nor an exponent above \\(10^{-3}\\).",
   "paper_text": "have neither a detected period nor an exponent above $10^{-3}$",
   "paper_line": 96,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r9-p6-01",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "chaos behind the text in the followed attractor: no period up to 64 (paper 602c70ac)",
   "appears_as": "period of the state up to 64 is found",
   "paper_text": "an exactly repeating text, no period up to 64 and an exponent of at least 0.005",
   "paper_line": 2525,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r9-p6-02",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "chaos behind the text in the followed attractor: exponent of at least 0.005 (paper 602c70ac)",
   "appears_as": "the exponent is at least 0.005; and slow cells",
   "paper_text": "an exactly repeating text, no period up to 64 and an exponent of at least 0.005",
   "paper_line": 2525,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r9-p6-03",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "slow cells of the followed attractor: exponent below 0.005 (paper 602c70ac)",
   "appears_as": "exponent below 0.005, as for an orbit converging slowly",
   "paper_text": "slow cells in 487 (the same with an exponent below 0.005",
   "paper_line": 2526,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r9-p6-04",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "the maps' chaos threshold 1e-3 as the alternative split (paper 602c70ac)",
   "appears_as": "With the threshold of \\(10^{-3}\\)",
   "paper_text": "with the maps' threshold of $10^{-3}$ the split would be 842 and 456",
   "paper_line": 2526,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r9-p6-05",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "split of the 1298 cells at the threshold 1e-3: 842 chaos behind the text, 456 slow (paper 602c70ac)",
   "appears_as": "the split would be 842 and 456.",
   "paper_text": "with the maps' threshold of $10^{-3}$ the split would be 842 and 456",
   "paper_line": 2526,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r9-p6-06",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Figure 57 note (c): black cells, no period up to 64 and exponent at least 0.005 (paper 602c70ac)",
   "appears_as": "an exactly repeating text with no period up to 64 and an exponent of at least 0.005;",
   "paper_text": "an exactly repeating text with no period up to 64 and an exponent of at least 0.005",
   "paper_line": 2695,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r9-p6-07",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Figure 57 note (c): gray slow cells, exponent below 0.005 (paper 602c70ac)",
   "appears_as": "gray: slow cells, the same with an exponent below 0.005;",
   "paper_text": "gray: slow cells, the same with an exponent below 0.005",
   "paper_line": 2696,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r9-cap-01",
   "section": "Where steering enters",
   "claim": "Figure 15 note: chaotic share criterion (exponent above 1e-3, no period up to 48) (paper 602c70ac)",
   "appears_as": "The share of chaotic cells (finite-horizon exponent above \\(10^{-3}\\), no period up to 48) is given above each",
   "paper_text": "The share of chaotic cells (finite-horizon exponent above $10^{-3}$, no period up to 48) is given above each panel",
   "paper_line": 1494,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r9-cap-02",
   "section": "Why the loop can be chaotic",
   "claim": "Figure 14 note: periods detected up to 24 in the float32 rotation maps (paper 602c70ac)",
   "appears_as": "and periods detected up to 24;",
   "paper_text": "at twin offset $10^{-4}$ and periods up to 24",
   "paper_line": 820,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r9-cap-03",
   "section": "Feigenbaum ratios",
   "claim": "Figure 31 note: orange cells chaotic, with no period up to 48 (paper 1e8e82f4)",
   "appears_as": "(orange: chaotic cells, with no period up to 48)",
   "paper_text": "(orange: chaotic cells, with no period up to 48)",
   "paper_line": 1892,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r9-cap-04",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "Figure 63 note (a): gray cells by exponent above 1e-3 alone (paper 602c70ac)",
   "appears_as": "other cells with an exponent above \\(10^{-3}\\) (gray) and periodic cells (white)",
   "paper_text": "other cells with an exponent above $10^{-3}$ (gray) and periodic cells (white)",
   "paper_line": 2885,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r9-cap-05",
   "section": "Symbolic dynamics of the period-6 shrimp",
   "claim": "Figure 63 alt text (a): gray cells by exponent above 1e-3 (paper 602c70ac)",
   "appears_as": "mostly gray (other cells with an exponent above 1e-3)",
   "paper_text": "other cells with an exponent above $10^{-3}$ (gray) and periodic cells (white)",
   "paper_line": 2885,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r9-deriv-01",
   "section": "Derivative check and Hopfield proof",
   "claim": "Figure 7 alt text (b): best central differences per direction (paper 602c70ac)",
   "appears_as": "cluster between 1.7e-9 and 4.8e-9",
   "paper_text": "(open circles, $1.7\\times10^{-9}$ to $4.8\\times10^{-9}$)",
   "paper_line": 465,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r9-deriv-02",
   "section": "Derivative check and Hopfield proof",
   "claim": "Figure 7 alt text (b): formula (3) per direction (paper 602c70ac)",
   "appears_as": "cluster between 3.8e-14 and 1.35e-13",
   "paper_text": "(filled, $3.8\\times10^{-14}$ to $1.35\\times10^{-13}$)",
   "paper_line": 466,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r9-deriv-03",
   "section": "Derivative check and Hopfield proof",
   "claim": "Figure 7 alt text (b): the gap of four orders of magnitude (paper 602c70ac)",
   "appears_as": "a double arrow labeled times 10 to the 4",
   "paper_text": "more than four orders of magnitude more closely than any finite difference",
   "paper_line": 467,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r9-deriv-04",
   "section": "Derivative check and Hopfield proof",
   "claim": "Figure 7 alt text (a): rounding takes over below h of about 3e-6 (paper 602c70ac)",
   "appears_as": "at h of about 3e-6",
   "paper_text": "below $h\\approx3\\times10^{-6}$ rounding takes over",
   "paper_line": 463,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r9-deriv-05",
   "section": "Derivative check and Hopfield proof",
   "claim": "Figure 7 note (b): the formula agrees more than four orders of magnitude more closely (paper 602c70ac)",
   "appears_as": "more than four orders of magnitude more closely than any finite difference (arrow)",
   "paper_text": "more than four orders of magnitude more closely than any finite difference",
   "paper_line": 467,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r9-mech-01",
   "section": "Why the loop can be chaotic",
   "claim": "Figure 13 note (b): chaotic share under residual steering (paper 602c70ac)",
   "appears_as": "331 of 5353 cells, 6.2%)",
   "paper_text": "331 of 5353 cells, 6.2\\,\\%",
   "paper_line": 681,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r9-mech-02",
   "section": "Why the loop can be chaotic",
   "claim": "Figure 13 note (b): chaotic share under a logit bias alone (paper 602c70ac)",
   "appears_as": "241 of 6837 cells, 3.5%)",
   "paper_text": "241 of 6837 cells, 3.5\\,\\%",
   "paper_line": 682,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r9-mech-03",
   "section": "Why the loop can be chaotic",
   "claim": "Figure 13 note (c): 14 held-out chaotic cells per 0.5B direction (paper 602c70ac)",
   "appears_as": "in the 0.5B model, 14 cells each",
   "paper_text": "a random direction of the philosophy vector's norm in the 0.5B model, 14 cells each",
   "paper_line": 686,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r9-mech-04",
   "section": "Why the loop can be chaotic",
   "claim": "Figure 13 note (c): 10 held-out chaotic cells in the 7B model (paper 602c70ac)",
   "appears_as": "in the 7B model, 10 cells. These are conditional",
   "paper_text": "the philosophy direction in the 7B model, 10 cells",
   "paper_line": 686,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r9-mech-05",
   "section": "Why the loop can be chaotic",
   "claim": "Figure 13 alt text (c): 95% intervals (paper 602c70ac)",
   "appears_as": "Crossover effects with 95% intervals in four rows",
   "paper_text": "means over the held-out chaotic cells with 95\\,\\% bootstrap intervals",
   "paper_line": 684,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r9-cite-01",
   "section": "Why the loop can be chaotic",
   "claim": "Backour's reduction: critical value 2 of the rescaled coupling (paper cda9ca04)",
   "appears_as": "the inverse temperature rescales the coupling, and crossing the critical value 2",
   "paper_text": "the inverse temperature rescales the coupling, and crossing the critical value 2 destabilizes the balanced mixture",
   "paper_line": 475,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-fish-01",
   "section": "Why the loop can be chaotic",
   "claim": "Fisher metric of the tied readout: the covariance between Jacobian and transpose, divided by T^2 (paper 1e8e82f4)",
   "appears_as": "and its transpose and divided by \\(T^2\\), as",
   "paper_text": "placed between a network Jacobian and its transpose and divided by $T^2$, the same covariance is the Fisher information",
   "paper_line": 430,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-blk-01",
   "section": "Why the loop can be chaotic",
   "claim": "block lengths k = 1, 2, 4, ..., 32 at which k times the median overshoot is bounded (paper 1e8e82f4)",
   "appears_as": "for \\(k = 1, 2, 4, \\dots, 32\\)",
   "paper_text": "for $k=1,2,4,\\dots,32$, $k$ times the median overshoot",
   "paper_line": 622,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-blk-02",
   "section": "Why the loop can be chaotic",
   "claim": "k times the median overshoot, chaotic cells: between 1.1 and 3.0 (paper 1e8e82f4)",
   "appears_as": "that product stays between 1.1 and 3.0 over the chaotic cells",
   "paper_text": "the median overshoot stays between 1.1 and 3.0 over the chaotic cells",
   "paper_line": 623,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-blk-03",
   "section": "Why the loop can be chaotic",
   "claim": "k times the median overshoot, periodic cells: between 2.8 and 4.0 (paper 1e8e82f4)",
   "appears_as": "and between 2.8 and 4.0",
   "paper_text": "and between 2.8 and 4.0 over the periodic ones",
   "paper_line": 623,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-lb-01",
   "section": "Why the loop can be chaotic",
   "claim": "logit bias: all but one of the 241 chaotic cells have a nonzero bias (paper 1e8e82f4)",
   "appears_as": "(241 of 6837, all but one with a",
   "paper_text": "(241 of 6837, all but one with a nonzero bias)",
   "paper_line": 720,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-lb-02",
   "section": "Why the loop can be chaotic",
   "claim": "residual-steering grid: 331 of 5353 chaotic; the grids share their temperature rows (paper 1e8e82f4)",
   "appears_as": "on the residual-steering grid (331 of 5353). The two",
   "paper_text": "on the residual-steering grid (331 of 5353; the two grids share their temperature rows",
   "paper_line": 720,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-lb-03",
   "section": "Why the loop can be chaotic",
   "claim": "logit bias: 207 of the 241 chaotic cells at log10 T >= 0.1 (paper 1e8e82f4)",
   "appears_as": "(207 of the 241 cells), where",
   "paper_text": "(207 of the 241 cells), where the network factor itself can expand",
   "paper_line": 723,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-lb-04",
   "section": "Why the loop can be chaotic",
   "claim": "logit bias below log10 T 0.1: 34 of 5676 cells chaotic (paper 1e8e82f4)",
   "appears_as": "34 of the 5676 cells",
   "paper_text": "below, 34 of 5676 cells of the bias grid are chaotic (0.6\\,\\%), against 169 of 4444 (3.8\\,\\%) under residual steering",
   "paper_line": 724,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-lb-05",
   "section": "Why the loop can be chaotic",
   "claim": "logit bias below log10 T 0.1: 0.6% chaotic (paper 1e8e82f4)",
   "appears_as": "of the bias grid are chaotic (0.6%), against",
   "paper_text": "below, 34 of 5676 cells of the bias grid are chaotic (0.6\\,\\%), against 169 of 4444 (3.8\\,\\%) under residual steering",
   "paper_line": 724,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-lb-06",
   "section": "Why the loop can be chaotic",
   "claim": "residual steering below log10 T 0.1: 169 of 4444 cells chaotic (3.8%) (paper 1e8e82f4)",
   "appears_as": "against 169 of 4444 (3.8%) under residual",
   "paper_text": "below, 34 of 5676 cells of the bias grid are chaotic (0.6\\,\\%), against 169 of 4444 (3.8\\,\\%) under residual steering",
   "paper_line": 724,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-ms-01",
   "section": "Why the loop can be chaotic",
   "claim": "Figure 13 note (a): 321 chaotic cells in the 18 rows (paper 1e8e82f4)",
   "appears_as": "The rows hold 321 chaotic and 162 nearly unsteered cells, 6 of them in both groups",
   "paper_text": "(321 chaotic and 162 nearly unsteered cells, 6 of them in both groups)",
   "paper_line": 676,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-ms-02",
   "section": "Why the loop can be chaotic",
   "claim": "Figure 13 note (a): 162 nearly unsteered cells in the 18 rows (paper 1e8e82f4)",
   "appears_as": "321 chaotic and 162 nearly unsteered cells, 6 of them",
   "paper_text": "(321 chaotic and 162 nearly unsteered cells, 6 of them in both groups)",
   "paper_line": 676,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-ms-03",
   "section": "Why the loop can be chaotic",
   "claim": "Figure 13 note (a): 6 cells in both groups (paper 1e8e82f4)",
   "appears_as": "162 nearly unsteered cells, 6 of them in both groups",
   "paper_text": "(321 chaotic and 162 nearly unsteered cells, 6 of them in both groups)",
   "paper_line": 676,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-ms-04",
   "section": "Why the loop can be chaotic",
   "claim": "Figure 13 note (b): chaos rule of the mechanism grids (both twin exponents above 1e-3, no period up to 64) (paper 1e8e82f4)",
   "appears_as": "(both twin exponents above \\(10^{-3}\\) and no period up to 64)",
   "paper_text": "(both twin exponents above $10^{-3}$ and no period up to 64)",
   "paper_line": 679,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-p6-01",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "DSS6 grid: 582 of the 961 cells reached before the time limit (paper 1e8e82f4)",
   "appears_as": "reached 582 of the 961 cells before its time limit",
   "paper_text": "the run reached 582 of the 961 cells before its time limit",
   "paper_line": 2570,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-dt-01",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "DITCH line across the main ditch at log10 T = -0.1530 (paper 1e8e82f4)",
   "appears_as": "\\(\\log_{10}T = -0.1530\\) (21 cells, steps of \\(7\\times10^{-6}\\) in \\(\\alpha\\))",
   "paper_text": "Across the main ditch at $\\log_{10}T=-0.1530$ (21 cells, steps $7\\times10^{-6}$ in $\\alpha$)",
   "paper_line": 2586,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-dt-02",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "DITCH main-ditch line: 21 cells (paper 1e8e82f4)",
   "appears_as": "(21 cells, steps of \\(7\\times10^{-6}\\)",
   "paper_text": "Across the main ditch at $\\log_{10}T=-0.1530$ (21 cells, steps $7\\times10^{-6}$ in $\\alpha$)",
   "paper_line": 2586,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-dt-03",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "DITCH main-ditch line: steps of 7e-6 in alpha (paper 1e8e82f4)",
   "appears_as": "steps of \\(7\\times10^{-6}\\) in \\(\\alpha\\)), the negative leading multiplier",
   "paper_text": "Across the main ditch at $\\log_{10}T=-0.1530$ (21 cells, steps $7\\times10^{-6}$ in $\\alpha$)",
   "paper_line": 2586,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-dt-04",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "main ditch: the negative leading multiplier shrinks from -0.605 to -0.060 (paper 1e8e82f4)",
   "appears_as": "shrinks from \\(-0.605\\) to \\(-0.060\\)",
   "paper_text": "the negative leading multiplier shrinks from $-0.605$ to $-0.060$",
   "paper_line": 2587,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-dt-05",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "main ditch: the lead passes to a complex pair at alpha = 0.072976 (paper 1e8e82f4)",
   "appears_as": "at \\(\\alpha = 0.072976\\) the lead passes to a complex pair,",
   "paper_text": "the lead passes at $\\alpha=0.072976$ to a complex pair, $0.0069\\pm0.0229i$",
   "paper_line": 2587,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-dt-06",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "main ditch: the complex pair 0.0069 +- 0.0229i (paper 1e8e82f4)",
   "appears_as": "\\(0.0069 \\pm 0.0229i\\), and the pair then splits",
   "paper_text": "complex pair, $0.0069\\pm0.0229i$, and the pair splits into two positive multipliers, the lead rising to $+0.71$",
   "paper_line": 2588,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-dt-07",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "main ditch: the lead rises to +0.71 after the pair splits (paper 1e8e82f4)",
   "appears_as": "the lead rising to \\(+0.71\\)",
   "paper_text": "complex pair, $0.0069\\pm0.0229i$, and the pair splits into two positive multipliers, the lead rising to $+0.71$",
   "paper_line": 2588,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-dt-08",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "DITCH line across the dimmer ditch at alpha = 0.07318 (paper 1e8e82f4)",
   "appears_as": "at \\(\\alpha = 0.07318\\) (26 cells, steps of",
   "paper_text": "at $\\alpha=0.07318$ (26 cells, steps $4\\times10^{-5}$ in $\\log_{10}T$), the leading multiplier stays positive",
   "paper_line": 2589,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-dt-09",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "DITCH dimmer-ditch line: 26 cells (paper 1e8e82f4)",
   "appears_as": "(26 cells, steps of",
   "paper_text": "at $\\alpha=0.07318$ (26 cells, steps $4\\times10^{-5}$ in $\\log_{10}T$), the leading multiplier stays positive",
   "paper_line": 2589,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-dt-10",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "DITCH dimmer-ditch line: steps of 4e-5 in log10 T (paper 1e8e82f4)",
   "appears_as": "\\(4\\times10^{-5}\\) in \\(\\log_{10}T\\)), the leading multiplier stays positive",
   "paper_text": "at $\\alpha=0.07318$ (26 cells, steps $4\\times10^{-5}$ in $\\log_{10}T$), the leading multiplier stays positive",
   "paper_line": 2589,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-dt-11",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "dimmer ditch: the leading multiplier falls from 0.122 to a minimum of 0.064 (paper 1e8e82f4)",
   "appears_as": "it falls from 0.122 to a minimum of",
   "paper_text": "it falls from 0.122 to a minimum of 0.064 at $\\log_{10}T=-0.15202$ and rises to 0.171",
   "paper_line": 2590,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-dt-12",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "dimmer ditch: minimum 0.064 at log10 T = -0.15202, then 0.171 (paper 1e8e82f4)",
   "appears_as": "0.064 at \\(\\log_{10}T = -0.15202\\) and rises again to 0.171",
   "paper_text": "it falls from 0.122 to a minimum of 0.064 at $\\log_{10}T=-0.15202$ and rises to 0.171",
   "paper_line": 2590,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-dt-13",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "dimmer ditch: the next multiplier stays negative and below 0.021 in modulus (paper 1e8e82f4)",
   "appears_as": "stays negative and below 0.021",
   "paper_text": "while the next stays negative and below 0.021 in modulus",
   "paper_line": 2591,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-dt-14",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "DITCH2D patch: alpha range (paper 1e8e82f4)",
   "appears_as": "over \\(\\alpha \\in [0.07300, 0.07336]\\) and",
   "paper_text": "A patch of the continued orbit over $\\alpha\\in[0.07300,0.07336]$ and $\\log_{10}T\\in[-0.15294,-0.15170]$",
   "paper_line": 2595,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-dt-15",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "DITCH2D patch: log10 T range (paper 1e8e82f4)",
   "appears_as": "\\(\\log_{10}T \\in [-0.15294, -0.15170]\\)",
   "paper_text": "A patch of the continued orbit over $\\alpha\\in[0.07300,0.07336]$ and $\\log_{10}T\\in[-0.15294,-0.15170]$",
   "paper_line": 2595,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-dt-16",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "DITCH2D patch: 21 x 32 cells, steps 1.8e-5 and 4e-5 (paper 1e8e82f4)",
   "appears_as": "(\\(21\\times32\\) cells, steps of \\(1.8\\times10^{-5}\\) and",
   "paper_text": "($21\\times32$ cells, steps $1.8\\times10^{-5}$ and $4\\times10^{-5}$, four GPU bands",
   "paper_line": 2596,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-dt-17",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "DITCH2D patch: steps of 4e-5 in log10 T, four GPU bands (paper 1e8e82f4)",
   "appears_as": "\\(4\\times10^{-5}\\), computed in four bands on GPUs",
   "paper_text": "($21\\times32$ cells, steps $1.8\\times10^{-5}$ and $4\\times10^{-5}$, four GPU bands",
   "paper_line": 2596,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-dt-18",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "DITCH2D patch: 595 cells solved (paper 1e8e82f4)",
   "appears_as": "595 cells solved, the unsolved ones at the right edge",
   "paper_text": "595 cells solved, the unsolved ones at the right edge, next to the fold",
   "paper_line": 2596,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-dt-19",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "DITCH2D patch: 41 sign changes and 33 complex leading pairs (paper 1e8e82f4)",
   "appears_as": "has 41 sign changes and 33 complex leading pairs",
   "paper_text": "has 41 sign changes and 33 complex leading pairs",
   "paper_line": 2597,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-dt-20",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "DITCH2D patch: peak of the arc of sign changes (paper 1e8e82f4)",
   "appears_as": "with its peak near \\((0.07326, -0.15232)\\)",
   "paper_text": "with its peak near $(0.07326,-0.15232)$",
   "paper_line": 2598,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-dt-21",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "same attracting period-6 orbit on both sides: Newton residuals below 1e-12 (paper 1e8e82f4)",
   "appears_as": "Newton residuals below \\(10^{-12}\\)",
   "paper_text": "with the six-token text of the seed and Newton residuals below $10^{-12}$",
   "paper_line": 2602,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-dt-22",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "fixed start on the coarse grid: the same orbit at 44 of the 45 pairs and 6 of the 9 complex cells (paper 1e8e82f4)",
   "appears_as": "and on the coarse grid at 44 of the 45 pairs",
   "paper_text": "on the coarse grid at 44 of the 45 pairs and 6 of the 9 complex cells",
   "paper_line": 2603,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-dt-23",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "the other cells reach a coexisting attractor of period 8, 16 or 32 (paper 1e8e82f4)",
   "appears_as": "reach a coexisting attractor of period 8, 16 or 32",
   "paper_text": "reach a coexisting attractor of period 8, 16 or 32",
   "paper_line": 2604,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-fig62-01",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Figure 62 note: Gallas's cell turned by 180 degrees (paper 1e8e82f4)",
   "appears_as": "a rotation by \\(180^\\circ\\) that brings it to the orientation of (b)",
   "paper_text": "a rotation by $180^\\circ$ that brings it to the orientation of (b)",
   "paper_line": 2657,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-fig62-02",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Figure 62 note: the 640 x 640 float64 map of the period-6 shrimp (paper 1e8e82f4)",
   "appears_as": "the 640 × 640 float64 map of Figure 48a with the continued fold and flip curves",
   "paper_text": "$640\\times640$ float64 map of Figure~\\ref{fig:p6shrimp}a with the continued fold and flip curves",
   "paper_line": 2660,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-fig62-03",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Figure 63 note: blue dots from the 31 x 31 grid of the continued orbit (paper 7526a62e)",
   "appears_as": "the 31 × 31 grid (blue dots: midpoints of neighboring solved cells whose real leading multipliers have opposite signs",
   "paper_text": "the $31\\times31$ grid (blue dots: midpoints of neighboring solved cells whose real leading multipliers have opposite signs",
   "paper_line": 2675,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-grow-01",
   "section": "Where the network damps",
   "claim": "relative change shrinks by factors of 1.4 and 1.7 by the last block (Qwen2.5-0.5B, Llama-3.1-8B) (paper 1e8e82f4)",
   "appears_as": "only by factors of 1.4 and 1.7",
   "paper_text": "so the change has shrunk relative to the state only by factors of 1.4 and 1.7",
   "paper_line": 3455,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-grow-02",
   "section": "Where the network damps",
   "claim": "relative change shrinks by factors of 12 and 8 by the last block (Qwen2.5-72B, Llama-3.1-70B) (paper 1e8e82f4)",
   "appears_as": "(Llama-3.1-70B), factors of 12",
   "paper_text": "factors of 12 and 8",
   "paper_line": 3457,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-grow-03",
   "section": "Where the network damps",
   "claim": "factor 8 for Llama-3.1-70B (paper 1e8e82f4)",
   "appears_as": "and 8. Their blocks keep writing",
   "paper_text": "factors of 12 and 8",
   "paper_line": 3457,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-grow-04",
   "section": "Where the network damps",
   "claim": "the factors are the exponentials of the log relative changes 0.32 and 0.51 (paper 1e8e82f4)",
   "appears_as": "exponentials of 0.32 and 0.51",
   "paper_text": "is $-0.32$ (Qwen2.5-0.5B) and $-0.51$ (Llama-3.1-8B)",
   "paper_line": 3455,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-grow-05",
   "section": "Where the network damps",
   "claim": "depth profiles compared near 1 nat of entropy (paper 1e8e82f4)",
   "appears_as": "grows too. Near 1 nat, the two grow at",
   "paper_text": "Near 1 nat, the two grow at nearly the same rate in the small models",
   "paper_line": 3454,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-sh-01",
   "section": "Why the two families cross in both orders",
   "claim": "run SH: the four starts discard 600 transient steps and measure over 300 (paper 1e8e82f4)",
   "appears_as": "discard 600 transient steps and measure over the next 300",
   "paper_text": "The four starts discard 600 transient steps and measure over the next 300",
   "paper_line": 3094,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-sh-02",
   "section": "Why the two families cross in both orders",
   "claim": "run SH: the sweeps use 200 and 200 steps, 600 transient steps in their first column or row (paper 1e8e82f4)",
   "appears_as": "sweeps discard 200 and measure over 200, with 600 transient steps in their first",
   "paper_text": "the sweeps use 200 and 200 (600 transient steps in their first column or row)",
   "paper_line": 3095,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-sh3d-01",
   "section": "Why the two families cross in both orders",
   "claim": "Figure 65 note: 90% of the orange points between 0.07 and 0.25 (paper 1e8e82f4)",
   "appears_as": "in (a), 90% of the orange points lie between 0.07 and 0.25",
   "paper_text": "in (a), 90\\,\\% of the orange points lie between 0.07 and 0.25",
   "paper_line": 3164,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-sh3d-02",
   "section": "Why the two families cross in both orders",
   "claim": "Figure 65 note: 99% of the blue points below 0.03 (paper 1e8e82f4)",
   "appears_as": "99% of the blue points below 0.03",
   "paper_text": "99\\,\\% of the blue points below 0.03",
   "paper_line": 3165,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-sh3d-03",
   "section": "Why the two families cross in both orders",
   "claim": "Figure 65 note: (a) thinned to at most 9000 points per map and class (paper 1e8e82f4)",
   "appears_as": "thinned at random to at most 9000 per map and class",
   "paper_text": "thinned at random to at most 9000 per map and class",
   "paper_line": 3167,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r10-sh3d-04",
   "section": "Why the two families cross in both orders",
   "claim": "Figure 65 note: the 192 x 256 grid of the eight maps (paper 1e8e82f4)",
   "appears_as": "one cell of the 192 × 256 grid of Figure 68",
   "paper_text": "on a $192\\times256$ grid as eight maps",
   "paper_line": 3090,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-abs-01",
   "section": "Summary surfaces and abstract",
   "claim": "abstract: reset test on an H100, Qwen2.5-0.5B: 47% of answers changed without the reset against 0.8% with it (paper 318f8980)",
   "appears_as": "fell from 47 to 0.8% in Qwen2.5-0.5B",
   "paper_text": "47 against 0.8\\,\\% of answers changed in Qwen2.5-0.5B",
   "paper_line": 226,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-abs-02",
   "section": "Summary surfaces and abstract",
   "claim": "abstract: reset test on an H100, Qwen2.5-7B: 41% of answers changed without the reset against none with it (paper 318f8980)",
   "appears_as": "from 41% to none in Qwen2.5-7B",
   "paper_text": "and 41\\,\\% against none in Qwen2.5-7B",
   "paper_line": 226,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-abs-03",
   "section": "Summary surfaces and abstract",
   "claim": "abstract: with the reset, accuracy changes by at most 5 points (paper 318f8980)",
   "appears_as": "accuracy changed by at most 5 points",
   "paper_text": "and accuracy changes by at most 5 points",
   "paper_line": 227,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-abs-04",
   "section": "Summary surfaces and abstract",
   "claim": "abstract: the 0.5B pipeline answers 23 of 96 problems correctly at T = 1 (paper 318f8980)",
   "appears_as": "(23 of 96 problems correct in the 0.5B",
   "paper_text": "(23 of 96 problems correct in the 0.5B model at $T=1$)",
   "paper_line": 228,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-abs-05",
   "section": "Summary surfaces and abstract",
   "claim": "abstract: at T = 10^0.4 both models answer 90 to 96 of the 96 correctly and the layout changed no answer (paper 318f8980)",
   "appears_as": "model at \\(T = 1\\)); at \\(T = 10^{0.4}\\), where both models answer 90 to 96",
   "paper_text": "(23 of 96 problems correct in the 0.5B model at $T=1$); at $T=10^{0.4}$, where both models answer 90 to 96 of the 96",
   "paper_line": 228,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-abs-08",
   "section": "Summary surfaces and abstract",
   "claim": "abstract: of the 96 problems, the layout changed no answer at T = 10^0.4 (paper 318f8980)",
   "appears_as": "of the 96 correctly, the layout changed no answer",
   "paper_text": "at $T=10^{0.4}$, where both models answer 90 to 96 of the 96 correctly, the layout changed no answer",
   "paper_line": 228,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-abs-06",
   "section": "Summary surfaces and abstract",
   "claim": "abstract: ordinary greedy chain-of-thought decoding changed 2.3% of its answers, at 89% accuracy (paper 318f8980)",
   "appears_as": "answers 89% of these problems correctly, changed 2.3% of its answers",
   "paper_text": "ordinary greedy chain-of-thought decoding: 2.3\\,\\%, at 89\\,\\% accuracy",
   "paper_line": 1361,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-abs-07",
   "section": "Summary surfaces and abstract",
   "claim": "abstract: feeding back only the most probable token changed 17.6% of the answers (paper 318f8980)",
   "appears_as": "back only the most probable token changed 17.6%",
   "paper_text": "feeding back only the most probable token: 17.6\\,\\%",
   "paper_line": 1363,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-abs-09",
   "section": "Summary surfaces and abstract",
   "claim": "abstract: 190 of 192 chaotic float64 loops separate when only the batch layout changes (paper 318f8980)",
   "appears_as": "the batch layout changed, 190 of 192",
   "paper_text": "190 of 192 chaotic float64 loops of Qwen2.5-0.5B grow past",
   "paper_line": 218,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-ar-00",
   "section": "Reproducibility",
   "claim": "0.5B arithmetic pipeline: accuracy at T = 1 (paper 318f8980)",
   "appears_as": "At \\(T = 1\\) the pipeline",
   "paper_text": "At $T=1$ the pipeline answers 23 of the 96 problems correctly alone and 22 in the batch",
   "paper_line": 1294,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-ar-01",
   "section": "Reproducibility",
   "claim": "0.5B arithmetic pipeline at T = 1: 23 of 96 correct alone, 22 in the batch (paper 318f8980)",
   "appears_as": "23 of the 96 problems correctly alone and 22 in the batch",
   "paper_text": "At $T=1$ the pipeline answers 23 of the 96 problems correctly alone and 22 in the batch",
   "paper_line": 1294,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-ar-02",
   "section": "Reproducibility",
   "claim": "0.5B arithmetic pipeline at T = 10^0.4: 90 of 96 correct in both layouts, no answer changed (paper 318f8980)",
   "appears_as": "at \\(T = 10^{0.4}\\), where it answers 90 of the 96",
   "paper_text": "at $T=10^{0.4}$, where it answers 90 of the 96 correctly in both layouts, no answer changed",
   "paper_line": 1295,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-ar-03",
   "section": "Reproducibility",
   "claim": "7B soft-thinking pipeline answers 51 to 64% of the arithmetic problems (paper 318f8980)",
   "appears_as": "51 to 64% of",
   "paper_text": "whose soft-thinking pipeline answers 51 to 64\\,\\% of these problems",
   "paper_line": 1305,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-ar-03b",
   "section": "Reproducibility",
   "claim": "7B soft-thinking pipeline accuracy at T = 10^0.2: 49 and 61 of 96 (51 to 64%) (paper 318f8980)",
   "appears_as": "these problems at \\(T = 10^{0.2}\\), replicates the result",
   "paper_text": "The pipeline answered 49 of the 96 correctly alone and 61 in the batch",
   "paper_line": 1309,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-ar-04",
   "section": "Reproducibility",
   "claim": "7B at T = 10^0.2: in 24 of the 53 changed answers one layout gave no number (paper 318f8980)",
   "appears_as": "In 24 of these 53 problems",
   "paper_text": "In 24 of these 53 problems one layout gave no number",
   "paper_line": 1307,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-ar-05",
   "section": "Reproducibility",
   "claim": "7B at T = 10^0.2: in 29 problems (30%) both layouts gave different numbers (paper 318f8980)",
   "appears_as": "in the other 29 (30% of the problems)",
   "paper_text": "in the other 29 (30\\,\\% of the problems) both gave numbers",
   "paper_line": 1308,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-ar-06",
   "section": "Reproducibility",
   "claim": "7B at T = 10^0.2: 49 of 96 correct alone and 61 in the batch (paper 318f8980)",
   "appears_as": "The pipeline answered 49 of the 96 correctly alone and 61 in the",
   "paper_text": "The pipeline answered 49 of the 96 correctly alone and 61 in the batch",
   "paper_line": 1309,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-ar-07",
   "section": "Reproducibility",
   "claim": "7B at T = 10^0.4: all 96 correct in both layouts, no answer changed (paper 318f8980)",
   "appears_as": "batch; at \\(T = 10^{0.4}\\) it answered all 96 correctly in both layouts",
   "paper_text": "$T=10^{0.4}$ it answered all 96 correctly in both layouts, and no answer changed",
   "paper_line": 1310,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-ar-08",
   "section": "Reproducibility",
   "claim": "7B excess over greedy decoding at T = 10^0.2 alone: 44.8 points (paper 318f8980)",
   "appears_as": "alone it is 44.8 points (53 against 10 of 96)",
   "paper_text": "at $T=10^{0.2}$ alone it is 44.8 points (53 against 10 of 96)",
   "paper_line": 1313,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-ar-09",
   "section": "Reproducibility",
   "claim": "7B at T = 10^0.2: 53 soft against 10 greedy changes of 96 (paper 318f8980)",
   "appears_as": "points (53 against 10 of 96)",
   "paper_text": "at $T=10^{0.2}$ alone it is 44.8 points (53 against 10 of 96)",
   "paper_line": 1313,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-ar-10",
   "section": "Reproducibility",
   "claim": "the forced greedy baseline answers 1 of the 96 correctly (a computational comparator) (paper 318f8980)",
   "appears_as": "answers 1 of the 96 correctly",
   "paper_text": "it answers 1 of the 96 correctly",
   "paper_line": 1315,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-ar-11",
   "section": "Reproducibility",
   "claim": "0.5B excess of soft over greedy decoding: 95% interval [26.5, 38.1] (paper 318f8980)",
   "appears_as": "(95% interval [26.5, 38.1])",
   "paper_text": "(95\\,\\% interval $[26.5,38.1]$",
   "paper_line": 1298,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-ar-12",
   "section": "Reproducibility",
   "claim": "7B: 53 of 96 changes at T = 10^0.2, the temperature at which the soft trace still matters (paper 318f8980)",
   "appears_as": "problems (55%) at \\(T = 10^{0.2}\\), the",
   "paper_text": "problems (55\\,\\%) at $T=10^{0.2}$, the temperature at which the soft trace still matters",
   "paper_line": 1306,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-ar-13",
   "section": "Reproducibility",
   "claim": "7B excess averaged over the two temperatures of the design, T = 1 and 10^0.2 (paper 318f8980)",
   "appears_as": "two temperatures, \\(T = 1\\) and \\(10^{0.2}\\), as for the 0.5B model",
   "paper_text": "temperatures, $T=1$ and $10^{0.2}$, as for the 0.5B model",
   "paper_line": 1312,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-ar-14",
   "section": "Reproducibility",
   "claim": "7B excess at T = 10^0.2 alone (paper 318f8980)",
   "appears_as": "17.7 points ([9.3, 25.6]); at \\(T = 10^{0.2}\\)",
   "paper_text": "at $T=10^{0.2}$ alone it is 44.8 points",
   "paper_line": 1313,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-ar-15",
   "section": "Reproducibility",
   "claim": "7B at T = 1: the soft pipeline answers none correctly and changed one answer; the excess is negative (paper 318f8980)",
   "appears_as": "and at \\(T = 1\\), where the soft",
   "paper_text": "and at $T=1$, where the soft pipeline answers none correctly and changed one answer, it is negative",
   "paper_line": 1313,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-rs-01",
   "section": "Reproducibility",
   "claim": "reset test: the 0.5B pipeline rerun at T = 1 (paper 318f8980)",
   "appears_as": "reran the 0.5B pipeline at \\(T = 1\\)",
   "paper_text": "we reran the 0.5B pipeline at $T=1$ on 128 newly drawn additions",
   "paper_line": 1322,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-rs-02",
   "section": "Reproducibility",
   "claim": "workstation GPU: the native pipeline changed 74% of its answers with the layout, against 56% on the H100 of the frozen test (paper 318f8980)",
   "appears_as": "with the layout in 74% of the problems, against 56% on the H100 of the",
   "paper_text": "where the native pipeline's answers changed with the layout in 74\\,\\% of the problems, against 56\\,\\% on the H100 of the frozen test",
   "paper_line": 1324,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-rs-03",
   "section": "Reproducibility",
   "claim": "workstation GPU, bfloat16: 88 of 128 answers changed in the free condition (paper 318f8980)",
   "appears_as": "In bfloat16 the answer changed in 88 of the 128 problems",
   "paper_text": "In bfloat16 the answer changed in 88 of the 128 problems (69\\,\\%) in the free arm",
   "paper_line": 1328,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-rs-04",
   "section": "Reproducibility",
   "claim": "workstation GPU: free minus reset, 63 points (95% interval [55, 72]) (paper 318f8980)",
   "appears_as": "of 63 points (95% interval [55, 72])",
   "paper_text": "a difference of 63 points (95\\,\\% interval $[55,72]$",
   "paper_line": 1329,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-rs-05",
   "section": "Reproducibility",
   "claim": "workstation GPU: 82 discordant pairs against 1 (paper 318f8980)",
   "appears_as": "82 changed without the reset and 1 with it",
   "paper_text": "82 discordant pairs against 1",
   "paper_line": 1329,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-rs-06",
   "section": "Reproducibility",
   "claim": "workstation GPU: exact McNemar p = 2e-23 (paper 318f8980)",
   "appears_as": "\\(p = 2\\times10^{-23}\\)",
   "paper_text": "exact McNemar $p=2\\times10^{-23}$",
   "paper_line": 1329,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-rs-07",
   "section": "Reproducibility",
   "claim": "workstation GPU: accuracy between 23 and 25% in every condition (paper 318f8980)",
   "appears_as": "stayed between 23 and 25% in every condition",
   "paper_text": "while accuracy stayed between 23 and 25\\,\\% in every arm",
   "paper_line": 1330,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-rs-08",
   "section": "Reproducibility",
   "claim": "one batched step moves the logits by a median 1.5% of their norm (paper 318f8980)",
   "appears_as": "logits by a median 1.5% of their norm",
   "paper_text": "target's logits by a median $1.5\\,\\%$ of their norm",
   "paper_line": 1331,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-rs-09",
   "section": "Reproducibility",
   "claim": "free condition: the median logit difference grows to 0.79 of the norm by step 32 (paper 318f8980)",
   "appears_as": "grows to 0.79 of that norm by step 32",
   "paper_text": "in the free arm the median difference grows to $0.79$ of it by step 32",
   "paper_line": 1331,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-rs-10",
   "section": "Reproducibility",
   "claim": "reset condition: median per-step logit difference between 1.3 and 3.1% (paper 318f8980)",
   "appears_as": "step stays between 1.3 and 3.1%",
   "paper_text": "the reset arm's median per step stays between $1.3$ and $3.1\\,\\%$",
   "paper_line": 1332,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-rs-11",
   "section": "Reproducibility",
   "claim": "float32: the free drift grows about 140-fold over 32 steps but stays near 1e-4 (paper 318f8980)",
   "appears_as": "140-fold over the 32 steps but stays near \\(10^{-4}\\)",
   "paper_text": "drift grows about 140-fold over the 32 steps but stays near $10^{-4}$",
   "paper_line": 1332,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-rs-12",
   "section": "Reproducibility",
   "claim": "float32 on the workstation: 3 of 128 answers changed, none with the reset (paper 318f8980)",
   "appears_as": "and 3 of the 128 answers",
   "paper_text": "and 3 of the 128 answers changed (none with reset)",
   "paper_line": 1333,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-rs-13",
   "section": "Reproducibility",
   "claim": "H100: exact McNemar p <= 5e-16 for both models (paper 318f8980)",
   "appears_as": "\\(p \\le 5\\times10^{-16}\\)",
   "paper_text": "(exact McNemar $p\\le5\\times10^{-16}$)",
   "paper_line": 1336,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-rs-14",
   "section": "Reproducibility",
   "claim": "H100, Qwen2.5-7B, float32: 33 of 128 answers changed (26%) against none (paper 318f8980)",
   "appears_as": "in 33 of the 128 problems (26%)",
   "paper_text": "even float32 answers changed in 33 (26\\,\\%) against none",
   "paper_line": 1336,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-rs-15",
   "section": "Reproducibility",
   "claim": "H100: the reset condition's median step distance is 0 (paper 318f8980)",
   "appears_as": "median step distance is 0",
   "paper_text": "the reset arm's median step distance is 0",
   "paper_line": 1336,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-rs-16",
   "section": "Reproducibility",
   "claim": "the corrected test compares extracted numbers; until 19 October 2026 it compared decoded answer texts (paper 318f8980)",
   "appears_as": "Until 19 October 2026 the reset test compared the decoded answer texts",
   "paper_text": "Until 19 October 2026 the test compared the decoded answer texts",
   "paper_line": 1341,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-rs-17",
   "section": "Reproducibility",
   "claim": "counts of the text comparison: 102 and 14 (workstation), 85 and 2 and 82 and 2 (H100) (paper 318f8980)",
   "appears_as": "(102 and 14 on the workstation; 85 and 2, and 82 and 2, on the",
   "paper_text": "(102 and 14 on the workstation; 85 and 2, and 82 and 2, on the H100)",
   "paper_line": 1342,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-st-01",
   "section": "Soft Thinking as published",
   "claim": "16 of 256 problems ran in identical batches in both layouts; none changed (paper 318f8980)",
   "appears_as": "16 of the 256 problems ran in identical batches",
   "paper_text": "16 of the 256 problems ran in identical batches in both layouts, and none of them changed",
   "paper_line": 1352,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-st-02",
   "section": "Soft Thinking as published",
   "claim": "among the other 240 problems, 54 changed (22.5%) (paper 318f8980)",
   "appears_as": "the rate is 54 of 240 (22.5%)",
   "paper_text": "among the other 240 the rate is 54 of 240 (22.5\\,\\%)",
   "paper_line": 1353,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-st-03",
   "section": "Soft Thinking as published",
   "claim": "short batches: 11 of the 78 batches of 8 and 26 of the 77 of 16 (paper 318f8980)",
   "appears_as": "11 of the 78 batches of 8 and 26 of the 77 batches of 16",
   "paper_text": "(11 of the 78 batches of 8 and 26 of the 77 of 16",
   "paper_line": 1354,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-bd-01",
   "section": "Reasoning models",
   "claim": "GSM8K: 161 answers changed with soft thinking, 158 of them on problems that reached a budget (paper 318f8980)",
   "appears_as": "161 GSM8K answers that the layout changed with soft thinking, 158 came from",
   "paper_text": "Of the 161 answers that the layout changed with soft thinking, 158 came from problems",
   "paper_line": 1428,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-bd-02",
   "section": "Reasoning models",
   "claim": "budgets: thinking 1536 steps, answer 256 tokens (paper 318f8980)",
   "appears_as": "thinking budget (1536 steps) or the answer budget (256",
   "paper_text": "the thinking budget (1536 steps) or the answer budget (256 tokens)",
   "paper_line": 1429,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-bd-03",
   "section": "Reasoning models",
   "claim": "all 132 changes with sampled thinking on problems that reached a budget (paper 318f8980)",
   "appears_as": "and so did all 132 changes with",
   "paper_text": "and so did all 132 changes with sampled thinking",
   "paper_line": 1430,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-bd-04",
   "section": "Reasoning models",
   "claim": "problems that finished within both budgets: 3 of 480 soft and none of 477 sampled answers changed (paper 318f8980)",
   "appears_as": "the layout changed 3 of 480 soft answers and none of 477 sampled ones",
   "paper_text": "the layout changed 3 of 480 soft answers and none of 477 sampled ones",
   "paper_line": 1431,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-ev-01",
   "section": "Evidence reasoning",
   "claim": "Table 21: answer-level test, 56% and 55% of answers changed, against never and 10% for forced greedy decoding (paper 318f8980)",
   "appears_as": "(56% and 55%, against never and 10% for forced greedy decoding)",
   "paper_text": "56\\,\\% of problems in Qwen2.5-0.5B and 55\\,\\% in Qwen2.5-7B, against never and 10\\,\\% for a forced greedy",
   "paper_line": 224,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-ev-02",
   "section": "Evidence reasoning",
   "claim": "Table 21: greedy chain of thought 2.3%, at 89% accuracy (paper 318f8980)",
   "appears_as": "greedy chain of thought 2.3%, at 89% accuracy",
   "paper_text": "ordinary greedy chain-of-thought decoding: 2.3\\,\\%, at 89\\,\\% accuracy",
   "paper_line": 1361,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-ev-03",
   "section": "Evidence reasoning",
   "claim": "Table 21: 16 problems ran in identical batches (none changed) (paper 318f8980)",
   "appears_as": "16 problems ran in identical batches in both layouts (none changed)",
   "paper_text": "16 of the 256 problems ran in identical batches in both layouts, and none of them changed",
   "paper_line": 1352,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-ev-04",
   "section": "Evidence reasoning",
   "claim": "Table 21: 158 of 161 soft changes on problems that reached a budget (paper 318f8980)",
   "appears_as": "(158 of 161 soft, all 132 sampled)",
   "paper_text": "Of the 161 answers that the layout changed with soft thinking, 158 came from problems",
   "paper_line": 1428,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-ev-05",
   "section": "Evidence reasoning",
   "claim": "Table 21: all 132 sampled changes on problems that reached a budget (paper 318f8980)",
   "appears_as": "(158 of 161 soft, all 132 sampled)",
   "paper_text": "and so did all 132 changes with sampled thinking",
   "paper_line": 1430,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-wp-01",
   "section": "Reproducibility",
   "claim": "within-prompt test: the first 1000 prompts steered slightly at block 14 (paper 318f8980)",
   "appears_as": "The first 1000 of these",
   "paper_text": "We steered the first 1000 of these prompts slightly, at block 14",
   "paper_line": 4574,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-wp-02",
   "section": "Reproducibility",
   "claim": "within-prompt test: steering at block 14 (paper 318f8980)",
   "appears_as": "steered slightly, at block 14, along philosophy,",
   "paper_text": "We steered the first 1000 of these prompts slightly, at block 14",
   "paper_line": 4574,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-wp-03",
   "section": "Reproducibility",
   "claim": "within-prompt test: strength 1% of the residual norm (paper 318f8980)",
   "appears_as": "1% of the norm of",
   "paper_text": "The strength, 1\\,\\% of the residual norm",
   "paper_line": 4575,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-wp-04",
   "section": "Reproducibility",
   "claim": "within-prompt test: calibration kept greedy accuracy within 5 points (paper 318f8980)",
   "appears_as": "stayed within 5",
   "paper_text": "greedy accuracy stayed within 5 points of the unsteered model on the first 200 of these prompts",
   "paper_line": 4576,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-wp-05",
   "section": "Reproducibility",
   "claim": "within-prompt test: calibration on the first 200 prompts (paper 318f8980)",
   "appears_as": "first 200 of these prompts",
   "paper_text": "greedy accuracy stayed within 5 points of the unsteered model on the first 200 of these prompts",
   "paper_line": 4576,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-wp-06",
   "section": "Reproducibility",
   "claim": "within-prompt test: greedy accuracy 0.87 to 0.89 under the pushes (paper 318f8980)",
   "appears_as": "on the 1000 prompts greedy accuracy is 0.87",
   "paper_text": "on the 1000 prompts it is 0.87 to 0.89, against 0.89 unsteered",
   "paper_line": 4577,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-wp-07",
   "section": "Reproducibility",
   "claim": "within-prompt test: 0.89 unsteered (paper 318f8980)",
   "appears_as": "to 0.89 under the pushes, against 0.89 unsteered",
   "paper_text": "on the 1000 prompts it is 0.87 to 0.89, against 0.89 unsteered",
   "paper_line": 4577,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-wp-08",
   "section": "Reproducibility",
   "claim": "within-prompt test: the loop's label differs between conditions for 508 of 1000 prompts (paper 318f8980)",
   "appears_as": "for 508 of the 1000 prompts",
   "paper_text": "differs between conditions for 508 of the 1000 prompts",
   "paper_line": 4578,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-wp-09",
   "section": "Reproducibility",
   "claim": "within-prompt test: 3992 prompt-condition rows (paper 318f8980)",
   "appears_as": "over 3992 prompt-condition",
   "paper_text": "(3992 prompt-condition rows)",
   "paper_line": 4579,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-wp-10",
   "section": "Reproducibility",
   "claim": "within-prompt test: a chaotic label is associated with +0.36 points of accuracy (paper 318f8980)",
   "appears_as": "a change of +0.36 points",
   "paper_text": "associated with a change of $+0.36$ points",
   "paper_line": 4579,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-wp-11",
   "section": "Reproducibility",
   "claim": "within-prompt test: 95% interval [-0.36, 1.08] (paper 318f8980)",
   "appears_as": "(95% interval [−0.36, 1.08];",
   "paper_text": "(95\\,\\% interval $[-0.36,1.08]$; permutation within prompts, $p=0.34$)",
   "paper_line": 4580,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-wp-12",
   "section": "Reproducibility",
   "claim": "within-prompt test: permutation p = 0.34 (paper 318f8980)",
   "appears_as": "permutation test within prompts, \\(p = 0.34\\)",
   "paper_text": "(95\\,\\% interval $[-0.36,1.08]$; permutation within prompts, $p=0.34$)",
   "paper_line": 4580,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-1d-01",
   "section": "Saddle-node bottleneck",
   "claim": "stripe orbits: leading multiplier 0.0025 to 0.086, more than three orders of magnitude above the next (paper 318f8980)",
   "appears_as": "the leading multiplier, 0.0025 to 0.086, exceeds the next by more than",
   "paper_text": "the leading multiplier, $0.0025$ to $0.086$, exceeds the next by more than three orders of magnitude",
   "paper_line": 1535,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-1d-02",
   "section": "Saddle-node bottleneck",
   "claim": "stripe orbits: the next multiplier modulus 3e-6 at period 6 (paper 318f8980)",
   "appears_as": "the next falls from \\(3\\times10^{-6}\\) at period 6 to",
   "paper_text": "the next falls from $3\\times10^{-6}$ at period 6 to $2\\times10^{-14}$ at period 20",
   "paper_line": 1536,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-1d-03",
   "section": "Saddle-node bottleneck",
   "claim": "stripe orbits: the next multiplier modulus 2e-14 at period 20 (paper 318f8980)",
   "appears_as": "\\(2\\times10^{-14}\\) at period 20",
   "paper_text": "the next falls from $3\\times10^{-6}$ at period 6 to $2\\times10^{-14}$ at period 20",
   "paper_line": 1536,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-1d-04",
   "section": "Saddle-node bottleneck",
   "claim": "the 2-cycle's two leading multipliers, -0.271 and -0.058 (paper 318f8980)",
   "appears_as": "−0.271 and −0.058, differ by a",
   "paper_text": "The two leading multipliers of the 2-cycle, $-0.271$ and $-0.058$, differ by a factor of only about 5",
   "paper_line": 1539,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-1d-05",
   "section": "Saddle-node bottleneck",
   "claim": "the 2-cycle's two leading multipliers differ by a factor of only about 5 (paper 318f8980)",
   "appears_as": "factor of only about 5",
   "paper_text": "The two leading multipliers of the 2-cycle, $-0.271$ and $-0.058$, differ by a factor of only about 5",
   "paper_line": 1539,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-wl-00",
   "section": "Saddle-node bottleneck",
   "claim": "natural reinjection: entry points v from -3e-4 to -7e-4, slightly upstream of the middle (paper 318f8980)",
   "appears_as": "\\(v \\approx -3\\times10^{-4}\\) to \\(-7\\times10^{-4}\\) at the four distances",
   "paper_text": "($v\\approx-3\\times10^{-4}$ to $-7\\times10^{-4}$, in the same",
   "paper_line": 1679,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-wl-0a",
   "section": "Saddle-node bottleneck",
   "claim": "natural reinjection: entry points down to v = -7e-4 (paper 318f8980)",
   "appears_as": "to \\(-7\\times10^{-4}\\) at the four distances",
   "paper_text": "($v\\approx-3\\times10^{-4}$ to $-7\\times10^{-4}$, in the same",
   "paper_line": 1679,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-rl-01",
   "section": "Reasoning models",
   "claim": "R1-Llama accuracy difference: interval excludes zero although McNemar p = 0.096 (paper 318f8980)",
   "appears_as": "although its McNemar \\(p\\) is 0.096",
   "paper_text": "often ($[-8.6,-0.8]$; McNemar $p=0.096$).",
   "paper_line": 1417,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-wl-01",
   "section": "Saddle-node bottleneck",
   "claim": "a window of period p spends N = (p - 6)/2 iterates of G in the bottleneck (paper 318f8980)",
   "appears_as": "spends \\(N = (p - 6)/2\\) iterates of \\(G\\) in the bottleneck",
   "paper_text": "A window of period $p$ spends $N=(p-6)/2$ iterates of $G$ in the bottleneck",
   "paper_line": 1684,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-wl-02",
   "section": "Saddle-node bottleneck",
   "claim": "full-passage prefactor pi^2/(ab) = 0.0803 (paper 318f8980)",
   "appears_as": "full-passage prefactor \\(\\pi^2/(ab) = 0.0803\\)",
   "paper_text": "full-passage prefactor $\\pi^2/(ab)=0.0803$",
   "paper_line": 1691,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-dg-01",
   "section": "Saddle-node bottleneck",
   "claim": "bottleneck diagram: the network's fold coefficients a = -4.834 and b = -25.4285 (paper 318f8980)",
   "appears_as": "coefficients \\(a = -4.834\\) and \\(b = -25.4285\\), in the oriented",
   "paper_text": "here $a=-4.834$ per unit $\\alpha$ and $b=-25.4285$",
   "paper_line": 1615,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-dg-02",
   "section": "Saddle-node bottleneck",
   "claim": "bottleneck diagram: the channel half-width U = 0.1/|b| (paper 318f8980)",
   "appears_as": "with \\(U = 0.1/\\lvert b\\rvert\\). It is a picture",
   "paper_text": "($U=0.1/|b|$)",
   "paper_line": 1642,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-dg-03",
   "section": "Saddle-node bottleneck",
   "claim": "bottleneck diagram: a full passage at eps = 1e-5 takes 71 iterates, as on the network (paper 318f8980)",
   "appears_as": "The 71 iterates of a full passage at \\(\\varepsilon = 10^{-5}\\), from",
   "paper_text": "$1\\times10^{-5}$ & 71 / 71 & 36 / 37 & 70 / 71",
   "paper_line": 1653,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-dg-04",
   "section": "Saddle-node bottleneck",
   "claim": "bottleneck diagram: the network takes 71 iterates as well (paper 318f8980)",
   "appears_as": "the network takes 71 iterates as well (Table 5)",
   "paper_text": "$1\\times10^{-5}$ & 71 / 71 & 36 / 37 & 70 / 71",
   "paper_line": 1653,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-dg-05",
   "section": "Saddle-node bottleneck",
   "claim": "bottleneck diagram: the measured entry points, v about -7e-4 to -3e-4 (paper 7526a62e)",
   "appears_as": "The orange bar marks the range of the median entry points (\\(v \\approx -7\\times10^{-4}\\) to \\(-3\\times10^{-4}\\))",
   "paper_text": "($v\\approx-3\\times10^{-4}$ to $-7\\times10^{-4}$, in the same",
   "paper_line": 1679,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-dg-06",
   "section": "Saddle-node bottleneck",
   "claim": "bottleneck diagram: a natural passage lasts on average 0.60 to 0.67 of the normal form's passage (paper cda9ca04)",
   "appears_as": "on average 0.60 to 0.67 of the normal form's passage through the same channel. The orange bar",
   "paper_text": "on average a natural passage lasts 0.60 to 0.67 of the normal form's passage through the same channel from end to end",
   "paper_line": 1683,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-448-01",
   "section": "Reproducibility",
   "claim": "Figure 23 note: 448 cells, 192 chaotic, 192 periodic and 64 with neither label (paper 318f8980)",
   "appears_as": "the 448 cells, 192 chaotic, 192 periodic and 64 with neither label, grouped",
   "paper_text": "The 448 cells (192 chaotic, 192 periodic, 64 with neither label) of Qwen2.5-0.5B-Instruct",
   "paper_line": 1460,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r11-448-02",
   "section": "Reproducibility",
   "claim": "Figure 24 note: 448 cells, 192 chaotic, 192 periodic and 64 with neither label (paper 318f8980)",
   "appears_as": "the 448 cells of two float64 maps, 192 chaotic, 192 periodic and 64 with neither label; 1500 lockstep steps",
   "paper_text": "the 448 cells of two float64 maps, 192 chaotic, 192 periodic and 64 with neither label, 1500",
   "paper_line": 1220,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-frac-01",
   "section": "Saddle-node bottleneck",
   "claim": "passage fraction from free trajectories (Table 7) (paper 7526a62e)",
   "appears_as": "| Free trajectories, four distances from the fold | mean laminar phase | passage through the whole channel | 0.60 to 0.67 |",
   "paper_text": "free trajectories, four distances & mean laminar phase & passage through the whole channel & 0.60--0.67",
   "paper_line": 1708,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-frac-02",
   "section": "Saddle-node bottleneck",
   "claim": "passage fraction from window centers (Table 7) (paper 7526a62e)",
   "appears_as": "| Window centers, \\(N = 4\\) to 7 | \\(d_N N^2 = 0.0263\\) to 0.0265 | \\(\\pi^2/(ab) = 0.0803\\) | 0.57 |",
   "paper_text": "window centers, $N=4$--7 & $d_NN^2=0.0263$--$0.0265$ & $\\pi^2/(ab)=0.0803$ & 0.57",
   "paper_line": 1709,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-frac-03",
   "section": "Saddle-node bottleneck",
   "claim": "passage fraction from fold edges (Table 7) (paper 7526a62e)",
   "appears_as": "| Fold edges, periods 16 to 20 | slope 6.13 | \\(\\sqrt{ab}/\\pi = 3.53\\) (ratio 1.74) | 0.58 |",
   "paper_text": "fold edges, periods 16--20 & slope $6.13$ & $\\sqrt{ab}/\\pi=3.53$ (ratio 1.74) & 0.58",
   "paper_line": 1710,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-frac-04",
   "section": "Saddle-node bottleneck",
   "claim": "half-passage value in the Table 7 note (paper 7526a62e)",
   "appears_as": "A half passage would give \\(f = 1/2\\) and \\(d_N N^2 = \\pi^2/(4ab) = 0.0201\\).",
   "paper_text": "A half passage would give $f=1/2$ and $d_NN^2=\\pi^2/(4ab)=0.0201$.",
   "paper_line": 1717,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-frac-05",
   "section": "Saddle-node bottleneck",
   "claim": "range of the three passage fractions, 0.57 to 0.67, from the rows of the paper's passage-fraction table (0.60-0.67, 0.57, 0.58) (paper 7526a62e)",
   "appears_as": "give similar values, 0.57 to 0.67, but they are not three independent confirmations,",
   "paper_text": "0.60--0.67",
   "paper_line": 1708,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-fold-01",
   "section": "Saddle-node bottleneck",
   "claim": "laps read from the texts, not identified geometrically (paper 7526a62e)",
   "appears_as": "identified geometrically in the state space.",
   "paper_text": "the laps were not identified geometrically",
   "paper_line": 1685,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-fold-02",
   "section": "Saddle-node bottleneck",
   "claim": "bottleneck scale at the fold edges of periods 16 to 32 (paper 7526a62e)",
   "appears_as": "compared with the counting window: at the fold edges of periods 16 to 32 its scale",
   "paper_text": "at the fold edges of periods 16 to 32 its scale $\\sqrt{|a|\\eps/|b|}$ is 1.35 to 3.51 times $U$",
   "paper_line": 1753,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-fold-03",
   "section": "Saddle-node bottleneck",
   "claim": "displaced start: one random direction, other directions and sizes not tested (paper 7526a62e)",
   "appears_as": "most one; other directions and sizes were not tested.",
   "paper_text": "(other directions and sizes were not tested)",
   "paper_line": 1645,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-fold-04",
   "section": "Saddle-node bottleneck",
   "claim": "42 of 48 summed over both tests, first secondary then primary (paper 7526a62e)",
   "appears_as": "Summed over both tests, in which it was first the secondary and then the primary",
   "paper_text": "Summed over both frozen tests, in which it was first the secondary and then the primary predictor",
   "paper_line": 1820,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-fold-05",
   "section": "Saddle-node bottleneck",
   "claim": "laminar phases lengthen as eps^(-1/2) (paper 7526a62e)",
   "appears_as": "laminar phases lengthen as \\(\\varepsilon^{-1/2}\\) toward the fold",
   "paper_text": "whose laminar phases lengthen as $\\eps^{-1/2}$ toward the fold",
   "paper_line": 1676,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-casc-01",
   "section": "Feigenbaum ratios",
   "claim": "rounding level of next moduli below about 1e-12 (paper 7526a62e)",
   "appears_as": "From the fifth flip on it is below about \\(10^{-12}\\),",
   "paper_text": "Next moduli below about $10^{-12}$ lie at the rounding level of products of",
   "paper_line": 2017,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-casc-02",
   "section": "Feigenbaum ratios",
   "claim": "Table 12 note: rounding level of next moduli (paper 7526a62e)",
   "appears_as": "Next moduli below about \\(10^{-12}\\) lie at the rounding level of products of dozens to hundreds of \\(896\\times896\\) Jacobians (48 to 768 here)",
   "paper_text": "Next moduli below about $10^{-12}$ lie at the rounding level of products of hundreds of $896\\times896$ Jacobians",
   "paper_line": 2017,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-casc-03",
   "section": "Feigenbaum ratios",
   "claim": "deviation of delta_3 from delta (Table 12) (paper 7526a62e)",
   "appears_as": "| 3.124 | \\(-1.55\\) |",
   "paper_text": "deviations from $\\delta=4.6692$ are $-1.55$, $-0.17$, $-0.048$, $-0.0074$, $-0.0019$ and $-0.00036$",
   "paper_line": 1934,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-casc-04",
   "section": "Feigenbaum ratios",
   "claim": "deviation of delta_4 from delta (Table 12) (paper 7526a62e)",
   "appears_as": "| 4.4988 | \\(-0.17\\) |",
   "paper_text": "deviations from $\\delta=4.6692$ are $-1.55$, $-0.17$, $-0.048$, $-0.0074$, $-0.0019$ and $-0.00036$",
   "paper_line": 1934,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-casc-05",
   "section": "Feigenbaum ratios",
   "claim": "deviation of delta_5 from delta (Table 12) (paper 7526a62e)",
   "appears_as": "| 4.6208 | \\(-0.048\\) |",
   "paper_text": "deviations from $\\delta=4.6692$ are $-1.55$, $-0.17$, $-0.048$, $-0.0074$, $-0.0019$ and $-0.00036$",
   "paper_line": 1934,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-casc-06",
   "section": "Feigenbaum ratios",
   "claim": "deviation of delta_6 from delta (Table 12) (paper 7526a62e)",
   "appears_as": "| 4.6618 | \\(-0.0074\\) |",
   "paper_text": "deviations from $\\delta=4.6692$ are $-1.55$, $-0.17$, $-0.048$, $-0.0074$, $-0.0019$ and $-0.00036$",
   "paper_line": 1934,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-casc-07",
   "section": "Feigenbaum ratios",
   "claim": "deviation of delta_7 from delta (Table 12) (paper 7526a62e)",
   "appears_as": "| 4.6673 | \\(-0.0019\\) |",
   "paper_text": "deviations from $\\delta=4.6692$ are $-1.55$, $-0.17$, $-0.048$, $-0.0074$, $-0.0019$ and $-0.00036$",
   "paper_line": 1934,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-casc-08",
   "section": "Feigenbaum ratios",
   "claim": "deviation of delta_8 from delta (Table 12) (paper 7526a62e)",
   "appears_as": "| 4.6688 | \\(-0.00036\\) |",
   "paper_text": "deviations from $\\delta=4.6692$ are $-1.55$, $-0.17$, $-0.048$, $-0.0074$, $-0.0019$ and $-0.00036$",
   "paper_line": 1934,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-p6-01",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "A and B: other multipliers at the nearest fold points (paper 7526a62e)",
   "appears_as": "point. A and B are not. At the continued fold points nearest them, the orbit's other multipliers are at most 0.0022",
   "paper_text": "nearest them the orbit's other multipliers are at most 0.0022 in modulus, none near $-1$",
   "paper_line": 2560,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-p6-02",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "A and B: other multipliers at the nearest flip points (paper 7526a62e)",
   "appears_as": "in modulus, none near \\(-1\\); at the flip points nearest them, the others are at most 0.0042, none near \\(+1\\).",
   "paper_text": "them the others are at most 0.0042, none near $+1$",
   "paper_line": 2561,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-p6-03",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "finer patch around line A's minimum: cells and steps (paper 7526a62e)",
   "appears_as": "**Ten times finer at line A.** On 225 cells around line A's minimum, with steps of \\(1.8\\times10^{-6}\\) in \\(\\alpha\\)",
   "paper_text": "Ten times finer, on 225 cells around that minimum (steps $1.8\\times10^{-6}$ in $\\alpha$ and $4\\times10^{-6}$ in $\\log_{10}T$",
   "paper_line": 2591,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-p6-04",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "finer patch: range of the leading multiplier (paper 7526a62e)",
   "appears_as": "multiplier is again real and positive everywhere, between 0.056 and 0.075, with the same minimum at",
   "paper_text": "real and positive everywhere (0.056 to 0.075)",
   "paper_line": 2593,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-p6-05",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "finer patch: minimum at alpha = 0.07318 (paper 7526a62e)",
   "appears_as": "\\(\\alpha = 0.07318\\) (0.0638). It falls toward smaller \\(\\alpha\\)",
   "paper_text": "at $\\alpha=0.07318$ (0.0638)",
   "paper_line": 2594,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-d2-01",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "DELTA2D grid size and steps (paper 7526a62e)",
   "appears_as": "(Figure 55). On a grid of \\(27\\times37\\) cells (steps of \\(10^{-5}\\) in \\(\\alpha\\) and \\(2.5\\times10^{-5}\\) in",
   "paper_text": "A $27\\times37$ grid over the top of the body (steps $10^{-5}$ in $\\alpha$ and $2.5\\times10^{-5}$ in $\\log_{10}T$) gave 852 continued orbits",
   "paper_line": 2606,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-d2-02",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "DELTA2D: 852 orbits, residuals (paper 7526a62e)",
   "appears_as": "text and residuals at most \\(1.0\\times10^{-12}\\), and the three leading eigenvectors of the monodromy matrix were",
   "paper_text": "Newton residuals at most $1.0\\times10^{-12}$ and the three leading Ritz vectors stored at every cell; the 147 unsolved",
   "paper_line": 2608,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-d2-03",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "DELTA2D: unsolved cells beyond the fold (paper 7526a62e); rebound at paper 13145281",
   "appears_as": "the 147 unsolved cells have no converged orbit on the followed branch and lie in the corner",
   "paper_text": "the 147 unsolved cells have no converged orbit on the followed branch and lie in the corner beyond the located fold",
   "paper_line": 2608,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-d2-04",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "sign of tau matches the leading multiplier (paper 7526a62e); rebound at paper 13145281",
   "appears_as": "The sign of \\(\\tau\\) matches the sign of the leading multiplier in 849",
   "paper_text": "The sign of $\\tau$ matches that of the leading multiplier in 849 of the 852 cells",
   "paper_line": 2613,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-d2-05",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "all 42 measured sign changes within one cell of a tau sign change (paper 7526a62e)",
   "appears_as": "42 measured sign changes of a real leading multiplier lies within one cell of a sign change of \\(\\tau\\); and 60 of the",
   "paper_text": "the 42 measured sign changes of a real leading multiplier lies within one cell of a sign change of $\\tau$; and 60 of the 64 sign changes of $\\tau$",
   "paper_line": 2615,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-d2-06",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "saddle of tau: position and value (paper 7526a62e); rebound at paper 13145281",
   "appears_as": "\\((\\alpha, \\log_{10}T) = (0.073188, -0.152083)\\), where \\(\\tau = 0.045\\).",
   "paper_text": "at $(0.073188,-0.152083)$ with the value 0.045",
   "paper_line": 2619,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-d2-07",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Hessian eigenvalues of tau at its saddle (paper 7526a62e); rebound at paper 13145281",
   "appears_as": "derivatives (the Hessian), are \\(-8.0\\times10^{-4}\\) and \\(3.5\\times10^{-3}\\) per squared cell, one negative and one",
   "paper_text": "(Hessian eigenvalues $-8.0\\times10^{-4}$ and $3.5\\times10^{-3}$ per squared cell, from a fit over $5\\times5$ cells with residual $3.9\\times10^{-4}$)",
   "paper_line": 2619,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-d2-08",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "fit residual at the tau saddle (paper 7526a62e)",
   "appears_as": "positive, as a saddle requires (fit residual \\(3.9\\times10^{-4}\\)).",
   "paper_text": "with residual $3.9\\times10^{-4}$",
   "paper_line": 2620,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-d2-09",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "saddle of the leading multiplier (paper 7526a62e); rebound at paper 13145281",
   "appears_as": "one-dimensional shrimp. A fit to the leading multiplier itself finds a saddle of the same kind nearby, 0.067 at",
   "paper_text": "The leading multiplier has a fitted saddle nearby, 0.067 at $(0.073195,-0.152138)$",
   "paper_line": 2622,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-d2-10",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Hessian eigenvalues of the leading multiplier at its saddle (paper 7526a62e)",
   "appears_as": "\\((0.073195, -0.152138)\\) (Hessian eigenvalues \\(-5.6\\times10^{-4}\\) and \\(2.8\\times10^{-3}\\)): along the valley",
   "paper_text": "(Hessian eigenvalues $-5.6\\times10^{-4}$ and $2.8\\times10^{-3}$)",
   "paper_line": 2622,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-d2-11",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "drift of the second multiplier across the delta saddle region (paper 7526a62e)",
   "appears_as": "the steady drift of the second multiplier (from \\(-0.010\\) to \\(-0.034\\) across seven columns at the saddle), and its",
   "paper_text": "the steady drift of the second multiplier (from $-0.010$ to $-0.034$ across seven columns at the saddle)",
   "paper_line": 2626,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-d2-12",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "delta's zero set misses the arc: 11 of 32 (paper 7526a62e)",
   "appears_as": "zero set misses the arc: only 11 of its 32 sign changes lie within one cell of a measured sign change.",
   "paper_text": "11 of its 32 sign changes lie within one cell of a measured sign change",
   "paper_line": 2627,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-d2-13",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "38 of the 852 cells with tracking overlap below 0.9 (paper 13145281)",
   "appears_as": "In 38 of the 852 cells the tracking overlap falls below 0.9, a sign that the",
   "paper_text": "In 38 of the 852 cells the tracking overlap falls below 0.9, indicating possible mixing with a third direction",
   "paper_line": 2628,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-d2-14",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Figure 64 note: colors clipped at +-0.2 and saddle value (paper 7526a62e)",
   "appears_as": "(colors clipped at \\(\\pm0.2\\)), its zero curves (black), the measured sign changes of the real leading multiplier (white dots)",
   "paper_text": "(colors clipped at $\\pm0.2$), its zero curves",
   "paper_line": 2638,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-d2-15",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Figure 64 note: saddle of tau (paper 7526a62e); rebound at paper 13145281",
   "appears_as": "the numerically fitted saddle of \\(\\tau\\) (gold cross, \\(\\tau = 0.045\\)) with the level curve through it (dashed)",
   "paper_text": "the numerically fitted saddle of $\\tau$ (gold cross, $\\tau=0.045$) with the level curve through it (dashed)",
   "paper_line": 2640,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-d2-16",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Figure 64 note: 852 continued orbits and steps (paper 7526a62e)",
   "appears_as": "A two-dimensional block of the monodromy, initialized from its leading directions, was tracked from cell to cell by subspace overlap over 852 continued orbits (steps of \\(10^{-5}\\) in \\(\\alpha\\) and \\(2.5\\times10^{-5}\\) in \\(\\log_{10}T\\)",
   "paper_text": "over 852 continued orbits (float64; steps $10^{-5}$ in $\\alpha$ and $2.5\\times10^{-5}$ in $\\log_{10}T$",
   "paper_line": 2637,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-f63-01",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Figure 63 note: patch steps (paper 7526a62e)",
   "appears_as": "a patch across the top of the lighter, lens-shaped region with steps of \\(1.8\\times10^{-5}\\) in \\(\\alpha\\) and \\(4\\times10^{-5}\\) in \\(\\log_{10}T\\)",
   "paper_text": "a patch across the top of the lens 1.8\\,$\\times10^{-5}$ by $4\\times10^{-5}$ in its steps",
   "paper_line": 2676,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-f63-02",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Figure 63 note: line A minimum and next modulus (paper 7526a62e)",
   "appears_as": "(b) Along line A the leading multiplier (solid) dips to 0.064 at \\(\\log_{10}T = -0.15202\\) but stays positive, and the next modulus (dashed) stays at most 0.021",
   "paper_text": "(b) Along line A the leading multiplier (solid) dips to $0.064$ at $\\log_{10}T=-0.15202$ but stays positive, and the next modulus (dashed) stays at most $0.021$",
   "paper_line": 2679,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-f63-03",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Figure 63 note: line B sign change (paper 7526a62e)",
   "appears_as": "changes sign through a complex leading pair (open marker), from \\(-0.605\\) to \\(+0.710\\).",
   "paper_text": "changes sign through a complex leading pair (open marker), from $-0.605$ to $+0.710$",
   "paper_line": 2682,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-f63-04",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Figure 63 note: line positions (paper 7526a62e)",
   "appears_as": "line A across the dim top ditch at \\(\\alpha = 0.07318\\), with its lowest leading multiplier circled, and line B across the main ditch at \\(\\log_{10}T = -0.153\\)",
   "paper_text": "line A across the dim top ditch at $\\alpha=0.07318$, with its lowest leading multiplier circled, and line B across the main ditch at $\\log_{10}T=-0.153$",
   "paper_line": 2678,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-sig-01",
   "section": "What the evidence supports",
   "claim": "Feigenbaum ratio row of the signature table (paper 7526a62e)",
   "appears_as": "| **Feigenbaum ratio** | ratios approach the constant of a universality class | ratios reach 4.6688, against \\(\\delta = 4.6692\\) | consistent |",
   "paper_text": "ratios reach 4.6688, against $\\delta=4.6692$",
   "paper_line": 3906,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-sync-01",
   "section": "Synchronization of coupled loops",
   "claim": "sync: start after a 1000-step transient, copy B at 1e-3 (paper 7526a62e)",
   "appears_as": "program mixes them as in the equation above. Copy A started on the attractor after a",
   "paper_text": "Copy~A started on the attractor after a 1000-step transient and copy~B at a relative distance $10^{-3}$ from it in a random direction",
   "paper_line": 3748,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-sync-02",
   "section": "Synchronization of coupled loops",
   "claim": "sync: copy B at relative distance 1e-3 (paper 7526a62e)",
   "appears_as": "1000-step transient, and copy B at a relative distance of \\(10^{-3}\\) from it in a",
   "paper_text": "copy~B at a relative distance $10^{-3}$ from it in a random direction",
   "paper_line": 3749,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-sync-03",
   "section": "Synchronization of coupled loops",
   "claim": "sync: run lengths and coupling grid (paper 7526a62e)",
   "appears_as": "random direction. Pairs ran for 3000 steps at couplings from 0 to 0.30 in steps of",
   "paper_text": "Pairs ran 3000 steps at couplings from 0 to 0.30 in steps of 0.01 and 10,000 steps at eight couplings near each threshold",
   "paper_line": 3749,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-sync-04",
   "section": "Synchronization of coupled loops",
   "claim": "sync: long runs near each threshold (paper 7526a62e)",
   "appears_as": "0.01, and for 10,000 steps at eight couplings near each threshold. A pair counted as",
   "paper_text": "10,000 steps at eight couplings near each threshold",
   "paper_line": 3750,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-sync-05",
   "section": "Synchronization of coupled loops",
   "claim": "sync: criterion (paper 7526a62e)",
   "appears_as": "stayed below \\(10^{-8}\\) over its last 500 steps. To measure the transverse",
   "paper_text": "stayed below $10^{-8}$ over its last 500 steps",
   "paper_line": 3751,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-sync-06",
   "section": "Synchronization of coupled loops",
   "claim": "sync: transverse exponent measurement (paper 7526a62e)",
   "appears_as": "exponent directly, copy B was started at a relative distance of \\(10^{-7}\\) from",
   "paper_text": "copy~B started at relative distance $10^{-7}$ from copy~A and was reset to that distance after every step for 2000 steps",
   "paper_line": 3751,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-sync-07",
   "section": "Synchronization of coupled loops",
   "claim": "sync takeaway: threshold range (paper 7526a62e)",
   "appears_as": "state rises with the chaos, from 0.046 in the weakest chaos to 0.177 in the",
   "paper_text": "The predicted threshold for a stable synchronized state rises with the chaos, from 0.046 in the weakest to 0.177 in the strongest",
   "paper_line": 3803,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12-sync-08",
   "section": "Synchronization of coupled loops",
   "claim": "sync takeaway: measured growth rate within 0.051 per step of the prediction (paper fcf2d462)",
   "appears_as": "coupling, within 0.051 per step. The predicted threshold for a stable synchronized",
   "paper_text": "the measured growth rate approximately followed the prediction at every coupling, within 0.051 per step",
   "paper_line": 3802,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12b-sync-01",
   "section": "Synchronization of coupled loops",
   "claim": "far starts: copy B 500 steps further along the attractor, 2000 steps, couplings in steps of 0.02 (paper fcf2d462)",
   "appears_as": "protocol, far starts, copy B started 500 steps further along the attractor than copy",
   "paper_text": "Far starts put copy~B 500 steps further along the attractor (2000 steps, couplings in steps of 0.02)",
   "paper_line": 3752,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12b-sync-02",
   "section": "Synchronization of coupled loops",
   "claim": "far starts: run length and coupling step (paper fcf2d462)",
   "appears_as": "A, and pairs ran for 2000 steps at couplings in steps of 0.02. Other prefixes, models",
   "paper_text": "(2000 steps, couplings in steps of 0.02)",
   "paper_line": 3752,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12b-sync-03",
   "section": "Synchronization of coupled loops",
   "claim": "predicted transverse exponents at c = 0.105 to 0.115 (paper fcf2d462)",
   "appears_as": "on average (the predicted transverse exponents are \\(-0.040\\) to \\(-0.065\\)), it",
   "paper_text": "(predicted transverse exponents $-0.040$ to $-0.065$)",
   "paper_line": 3766,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12b-sync-04",
   "section": "Synchronization of coupled loops",
   "claim": "cell 1: far-start pairs on joint periodic orbits above c* (paper fcf2d462)",
   "appears_as": "2-cycle `\"it is\"`, and two far-start pairs at \\(c = 0.14\\) and 0.20, above that",
   "paper_text": "two far-start pairs at $c=0.14$ and 0.20, above that cell's $c^*$",
   "paper_line": 3774,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12b-sync-05",
   "section": "Synchronization of coupled loops",
   "claim": "Table 22: lambda_1 row (paper fcf2d462)",
   "appears_as": "| \\(\\lambda_1\\) (per step) | 0.098 | 0.437 | 0.196 |",
   "paper_text": "$\\lambda_1$ (per step) & 0.098 & 0.437 & 0.196",
   "paper_line": 3789,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12b-sync-06",
   "section": "Synchronization of coupled loops",
   "claim": "Table 22: predicted c* row (paper fcf2d462)",
   "appears_as": "| Predicted \\(c^*\\) | 0.046 | 0.177 | 0.089 |",
   "paper_text": "predicted $c^*$ & 0.046 & 0.177 & 0.089",
   "paper_line": 3790,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12b-sync-07",
   "section": "Synchronization of coupled loops",
   "claim": "Table 22: near starts, 3000 steps, 1e-8 (paper fcf2d462)",
   "appears_as": "| Near, 3000, \\(10^{-8}\\) | \\((0.04, 0.05]\\) | \\((0.22, 0.23]^{*}\\) | \\((0.15, 0.16]^{*}\\) |",
   "paper_text": "near, 3000, $10^{-8}$ & $(0.04,0.05]$ & $(0.22,0.23]^{*}$ & $(0.15,0.16]^{*}$",
   "paper_line": 3791,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12b-sync-08",
   "section": "Synchronization of coupled loops",
   "claim": "Table 22: near starts, 3000 steps, 1e-6 (paper fcf2d462)",
   "appears_as": "| Near, 3000, \\(10^{-6}\\) | \\((0.04, 0.05]\\) | \\((0.19, 0.20]\\) | \\((0.13, 0.14]\\) |",
   "paper_text": "near, 3000, $10^{-6}$ & $(0.04,0.05]$ & $(0.19,0.20]$ & $(0.13,0.14]$",
   "paper_line": 3792,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12b-sync-09",
   "section": "Synchronization of coupled loops",
   "claim": "Table 22: near starts, 10,000 steps, 1e-8 (paper fcf2d462)",
   "appears_as": "| Near, 10,000, \\(10^{-8}\\) | \\((0.045, 0.05]\\) | none up to 0.19 | \\((0.12, 0.15]\\) |",
   "paper_text": "near, 10,000, $10^{-8}$ & $(0.045,0.05]$ & none up to 0.19 & $(0.12,0.15]$",
   "paper_line": 3793,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12b-sync-10",
   "section": "Synchronization of coupled loops",
   "claim": "Table 22: near starts, 10,000 steps, 1e-6 (paper fcf2d462)",
   "appears_as": "| Near, 10,000, \\(10^{-6}\\) | \\((0.045, 0.05]\\) | \\((0.18, 0.19]\\) | \\((0.12, 0.15]^{*}\\) |",
   "paper_text": "near, 10,000, $10^{-6}$ & $(0.045,0.05]$ & $(0.18,0.19]$ & $(0.12,0.15]^{*}$",
   "paper_line": 3794,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12b-sync-11",
   "section": "Synchronization of coupled loops",
   "claim": "Table 22: far starts, 2000 steps, 1e-8 (paper fcf2d462)",
   "appears_as": "| Far, 2000, \\(10^{-8}\\) | \\((0.20, 0.22]^{*\\dagger}\\) | \\((0.18, 0.20]\\) | \\((0.14, 0.16]\\) |",
   "paper_text": "far, 2000, $10^{-8}$ & $(0.20,0.22]^{*\\dagger}$ & $(0.18,0.20]$ & $(0.14,0.16]$",
   "paper_line": 3795,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12b-sync-12",
   "section": "Synchronization of coupled loops",
   "claim": "Table 22: far starts, 2000 steps, 1e-6 (paper fcf2d462)",
   "appears_as": "| Far, 2000, \\(10^{-6}\\) | \\((0.20, 0.22]^{*\\dagger}\\) | \\((0.18, 0.20]\\) | \\((0.10, 0.12]\\) |",
   "paper_text": "far, 2000, $10^{-6}$ & $(0.20,0.22]^{*\\dagger}$ & $(0.18,0.20]$ & $(0.10,0.12]$",
   "paper_line": 3796,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12b-sync-13",
   "section": "Synchronization of coupled loops",
   "claim": "Table 22 note: near and far starts (paper fcf2d462)",
   "appears_as": "Near starts: copy B at relative distance \\(10^{-3}\\) from copy A; far starts: copy B 500 steps further along the attractor.",
   "paper_text": "Near starts: copy~B at relative distance $10^{-3}$ from copy~A; far starts: copy~B 500 steps further along the attractor.",
   "paper_line": 3781,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12b-sync-14",
   "section": "Synchronization of coupled loops",
   "claim": "Table 22 note: criteria (paper fcf2d462)",
   "appears_as": "Criterion: the relative difference stays below \\(10^{-8}\\) or \\(10^{-6}\\) throughout the last 500 steps.",
   "paper_text": "Criterion: the relative difference stays below $10^{-8}$ or $10^{-6}$ throughout the last 500 steps.",
   "paper_line": 3782,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r12b-disc-01",
   "section": "Discussion",
   "claim": "conclusion: three periodic orbits proved with interval arithmetic (paper fcf2d462); corrected after arxiv-v1 at paper 1b718635",
   "appears_as": "transformer in float64, and four of its periodic orbits are proved to exist with",
   "paper_text": "computer-assisted proofs for only four orbits at three parameter points",
   "paper_line": 6509,
   "paper_file": "paper/llm/main.tex",
   "paper_commit": "1b71863581386048c50d41b1f8137a6ba6adec25"
  },
  {
   "id": "r12b-disc-02",
   "section": "Discussion",
   "claim": "conclusion: chaos with embedded windows in all three model families scanned (paper fcf2d462); rebound at paper 13145281",
   "appears_as": "periodic windows appears in all three model families we scanned, so these feedback",
   "paper_text": "Chaos with embedded periodic windows appears in all three model families we scanned",
   "paper_line": 4083,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r13-abs-01",
   "section": "Summary surfaces and abstract",
   "claim": "42 of 48 by stage, abstract (paper cda9ca04)",
   "appears_as": "came within one iterate of the return map in 42 of 48 measured passages (24 and 18 of 24); both tests' all-row",
   "paper_text": "over two frozen stages (24 and 18 of 24)",
   "paper_line": 77,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r13-abs-02",
   "section": "Summary surfaces and abstract",
   "claim": "42 of 48 by stage, key result (paper cda9ca04)",
   "appears_as": "(24 and 18 of 24 in the two stages);",
   "paper_text": "over two frozen stages (24 and 18 of 24)",
   "paper_line": 77,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r13-abs-03",
   "section": "What the evidence supports",
   "claim": "42 of 48 by stage, claims table (paper cda9ca04)",
   "appears_as": "42 of 48 within one iterate (24 and 18 of 24 in the two stages)",
   "paper_text": "over two frozen stages (24 and 18 of 24)",
   "paper_line": 77,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r13-nat-01",
   "section": "Saddle-node bottleneck",
   "claim": "median signed forecast error of complete natural phases, -7.7 to -4.1 percent (paper cda9ca04)",
   "appears_as": "four distances up to \\(\\varepsilon = 10^{-4}\\) lies between \\(-7.7\\)% and",
   "paper_text": "the median signed forecast error at the four offsets up to $\\eps=10^{-4}$ lies between $-7.7\\%$ and $-4.1\\%$",
   "paper_line": 1681,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r13-nat-02",
   "section": "Saddle-node bottleneck",
   "claim": "signed errors at the four offsets (paper cda9ca04)",
   "appears_as": "\\(-4.1\\)% (signed errors of \\(-4.88\\), \\(-4.08\\), \\(-7.41\\) and \\(-7.69\\)%),",
   "paper_text": "(signed errors $-4.88$, $-4.08$, $-7.41$ and $-7.69\\%$)",
   "paper_line": 1682,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r13-nat-03",
   "section": "Saddle-node bottleneck",
   "claim": "single phases differ by up to 71 percent (paper cda9ca04)",
   "appears_as": "although single phases differ by up to 71%. On average a natural passage",
   "paper_text": "although single phases differ by up to 71\\%",
   "paper_line": 1683,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r13-nat-04",
   "section": "Saddle-node bottleneck",
   "claim": "complete phases: within 3U and within 0.05 of the channel (paper cda9ca04)",
   "appears_as": "lasts. For complete phases, those that stay within \\(\\lvert u\\rvert < 3U\\) and within",
   "paper_text": "for complete phases, which stay within $|u|<3U$ and within 0.05 of the channel in the other directions",
   "paper_line": 1680,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r13-loc-01",
   "section": "Saddle-node bottleneck",
   "claim": "estimated localization scales of the fold edges (paper cda9ca04)",
   "appears_as": "localization scales of the fold edges are about \\(2\\times10^{-5}\\) to \\(2\\times10^{-4}\\)",
   "paper_text": "The estimated localization scales of the edges are about $2\\times10^{-5}$ to $2\\times10^{-4}$ of their distances",
   "paper_line": 1749,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r13-loc-02",
   "section": "Saddle-node bottleneck",
   "claim": "error models of the localization scales (paper cda9ca04)",
   "appears_as": "of their distances (from the extrapolated locations for periods 16 to 20, and from an",
   "paper_text": "(extrapolated locations for periods 16 to 20, and a uniform-within-cell error model for the grid boundaries of periods 22 to 32)",
   "paper_line": 1750,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r13-p6-01",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "fixed-start scans at nearby parameters: all but two unresolved cells (paper cda9ca04)",
   "appears_as": "of the seed and Newton residuals below \\(10^{-12}\\). Fixed-start scans at the nearest parameters find period six at",
   "paper_text": "fixed-start scans at the nearest parameters find period six at all patch and line cells but two at the patch's edge",
   "paper_line": 2602,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r13-p6-02",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "coarse grid: 6 of the 9 complex cells (paper cda9ca04)",
   "appears_as": "and at 6 of the 9 complex cells; the others, at the upper left, reach a coexisting attractor of period 8, 16 or 32.",
   "paper_text": "on the coarse grid at 44 of the 45 pairs and 6 of the 9 complex cells",
   "paper_line": 2603,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r13-samp-01",
   "section": "Sampling and the bottleneck",
   "claim": "single samples: 11 percent of steps in the channel (paper cda9ca04)",
   "appears_as": "one to three per offset (11% of steps in the",
   "paper_text": "(11\\% of steps in the channel)",
   "paper_line": 5169,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-abs-01",
   "section": "Summary surfaces and abstract",
   "claim": "abstract opening: expected-embedding feedback turns the model into a discrete-time dynamical system (paper 13145281)",
   "appears_as": "feeding a pretrained language model the expected embedding of",
   "paper_text": "Feeding a pretrained language model the expected embedding of its own next-token distribution turns it into a discrete-time dynamical system with continuous states",
   "paper_line": 42,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-abs-02",
   "section": "Summary surfaces and abstract",
   "claim": "abstract close: quantitative predictions, with rigorous guarantees for selected periodic orbits (paper 13145281)",
   "appears_as": "rigorous guarantees for selected periodic orbits of the full transformer.",
   "paper_text": "with rigorous guarantees for selected periodic orbits of the full transformer",
   "paper_line": 82,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-abs-03",
   "section": "Summary surfaces and abstract",
   "claim": "summary: changes consistent with rounding carried through long feedback (paper 13145281)",
   "appears_as": "in some, the changes are consistent with rounding carried through long feedback",
   "paper_text": "consistent with bfloat16 rounding being carried through long feedback",
   "paper_line": 66,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-abs-04",
   "section": "Summary surfaces and abstract",
   "claim": "abstract: injected float64 perturbations mostly shrink in the Qwen2.5-7B and R1-Distill-Qwen-7B pipelines (paper 13145281)",
   "appears_as": "the Qwen2.5-7B and DeepSeek-R1-Distill-Qwen-7B pipelines mostly shrink over the",
   "paper_text": "injected perturbations in the Qwen2.5-7B and DeepSeek-R1-Distill-Qwen-7B pipelines mostly shrink over the observed runs",
   "paper_line": 65,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-abs-05",
   "section": "Summary surfaces and abstract",
   "claim": "abstract: the reset test replaces the cache and logits by those of a reference run (paper 13145281)",
   "appears_as": "replacing the target problem's cache (the attention keys and values stored for the",
   "paper_text": "replacing the target's cache and logits by those of a batch-1 reference run before every soft step",
   "paper_line": 122,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-status-01",
   "section": "Study status",
   "claim": "the full report is supplementary material to the article of the same title (paper 13145281)",
   "appears_as": "supplementary material to the article of the same title",
   "paper_text": "Supplementary material to the article of the same title",
   "paper_line": 28,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-num-01",
   "section": "Numerics and chaos labels",
   "claim": "only one positive exponent estimate at the sampled chaotic cells (paper 13145281)",
   "appears_as": "chaotic cells whose spectra we estimated, only one direction expands over the",
   "paper_text": "none has two positive estimates",
   "paper_line": 4532,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-rep-01",
   "section": "What the chaos does to reproducibility",
   "claim": "Soft Thinking as published: injected float64 perturbations mostly shrink (paper 13145281)",
   "appears_as": "pipeline mostly shrink over its observed runs: on",
   "paper_text": "In float64, injected perturbations mostly shrink over the same pipeline's observed runs.",
   "paper_line": 1371,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-rep-02",
   "section": "What the chaos does to reproducibility",
   "claim": "Soft Thinking as published: the flips do not require the float64 map's chaos (paper 13145281)",
   "appears_as": "and none changed an answer. These changes therefore do not require the float64",
   "paper_text": "These flips therefore do not require the float64 map's chaos",
   "paper_line": 1373,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-rep-03",
   "section": "What the chaos does to reproducibility",
   "claim": "reasoning models: consistent with rounding carried through feedback, no global contraction (paper 13145281)",
   "appears_as": "show that the loop contracts everywhere.",
   "paper_text": "they do not establish global contraction",
   "paper_line": 1448,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-rep-04",
   "section": "What the chaos does to reproducibility",
   "claim": "reasoning models: 216 of 256 copies ended below the initial displacement (table row) (paper 13145281)",
   "appears_as": "| Reasoning model in which float64 perturbations mostly shrink (DeepSeek-R1-Distill-Qwen-7B, bfloat16) |",
   "paper_text": "216 of 256 copies ended the thinking at a distance from their base row below the initial displacement",
   "paper_line": 1446,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-casc-01",
   "section": "Feigenbaum ratios",
   "claim": "level n of the ratio figure carries delta_(n+1) (paper 13145281)",
   "appears_as": "Level \\(n\\) carries the ratio of the \\(n\\)th band to the \\((n+1)\\)th, which is \\(\\delta_{n+1}\\)",
   "paper_text": "level $n$ carries the ratio of the $n$th to the $(n+1)$th band, $\\delta_{n+1}$ in the notation of the text",
   "paper_line": 1876,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-d2-01",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "local quadratic fit to the trace gives the saddle (paper 13145281)",
   "appears_as": "a local quadratic fit to the",
   "paper_text": "a local quadratic fit to $\\tau$ gives a saddle",
   "paper_line": 2618,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-d2-02",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "the fitted saddle and the zero curves support a local trace-based explanation (paper 13145281)",
   "appears_as": "The fitted saddle and the measured zero curves thus support a local explanation, from",
   "paper_text": "The fitted saddle and the measured zero curves support a local trace-based explanation",
   "paper_line": 2621,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-d2-03",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "the pre-specified determinant saddle was not found under the specified procedure (paper 13145281)",
   "appears_as": "no saddle of",
   "paper_text": "none was found on the sampled patch under the specified fitting and filtering procedure",
   "paper_line": 2625,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-d2-04",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "no exact two-dimensional reduction of the full map is established (paper 13145281)",
   "appears_as": "This local evidence does not establish that the full map reduces",
   "paper_text": "This local evidence does not establish an exact two-dimensional reduction of the full map",
   "paper_line": 2629,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-d2-05",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "three cells with low tracking overlap (paper 13145281)",
   "appears_as": "(the other three have low tracking overlap, a sign of possible mixing with a third direction)",
   "paper_text": "the other three have low tracking overlap, indicating possible mixing with a third direction",
   "paper_line": 2614,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-d2-06",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "the zero curves resemble the trace-zero skeleton of two-dimensional maps (paper 13145281)",
   "appears_as": "resembles the trace-zero skeleton that Façanha, Oldeman and Glass use for shrimps in two-dimensional maps",
   "paper_text": "This resembles the trace-zero skeleton that Fa\\c{c}anha, Oldeman and Glass use for shrimps in two-dimensional maps",
   "paper_line": 2616,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-d2-07",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Figure 64 title: trace geometry associated with the separation (paper 13145281)",
   "appears_as": "Figure 55: trace geometry associated with the separation of the two pseudo-superstable lines",
   "paper_text": "Trace geometry associated with the separation of the two pseudo-superstable lines",
   "paper_line": 2635,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-d2-08",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Figure 64: gray cells have no converged orbit on the followed branch (paper 13145281)",
   "appears_as": "gray: no converged orbit on the followed branch, beyond the fold",
   "paper_text": "gray: no converged orbit on the followed branch",
   "paper_line": 2637,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-d2-09",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Figure 64: the rectangle is refined ten times in each parameter relative to the orange patch (paper 13145281)",
   "appears_as": "refined by a factor of ten in each parameter relative to the orange patch of Figure 54a",
   "paper_text": "refined by a factor of ten in each parameter relative to the orange patch",
   "paper_line": 2643,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-d2-10",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Figure 64: small crosses mark tracking overlap below 0.9 (paper 13145281)",
   "appears_as": "small crosses mark cells where the tracking overlap falls below 0.9, a sign of possible mixing",
   "paper_text": "small crosses mark cells where the tracking overlap falls below 0.9",
   "paper_line": 2641,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-d2-11",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Figure 64: the determinant saddle asked for in advance was not found (paper 13145281)",
   "appears_as": "the saddle of \\(\\delta\\) asked for in advance was not found.",
   "paper_text": "none was found on the sampled patch under the specified fitting and filtering procedure",
   "paper_line": 2625,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-d2-12",
   "section": "What was and was not found",
   "claim": "determinant saddle not found on the sampled patch (paper 13145281)",
   "appears_as": "at the top of the period-6 body: none was found on the sampled patch with the fitting",
   "paper_text": "none was found on the sampled patch under the specified fitting and filtering procedure",
   "paper_line": 2625,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-d2-13",
   "section": "What was and was not found",
   "claim": "no exact two-dimensional reduction at the top of the period-6 body (paper 13145281)",
   "appears_as": "- an exact two-dimensional reduction of the full map at the top of the period-6 body:",
   "paper_text": "This local evidence does not establish an exact two-dimensional reduction of the full map",
   "paper_line": 2629,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-d2-14",
   "section": "Cusps and shrimp-like windows",
   "claim": "the ditches resemble the trace-zero skeleton (section summary) (paper 13145281)",
   "appears_as": "leading multipliers, tracked as a pair, sum to zero, which resembles the trace-zero",
   "paper_text": "This resembles the trace-zero skeleton",
   "paper_line": 2616,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-d2-15",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "short version: the determinant pass was not found (paper 13145281)",
   "appears_as": "different pass, of the product of the two multipliers, which we had predicted there before the computation, was not",
   "paper_text": "none was found on the sampled patch under the specified fitting and filtering procedure",
   "paper_line": 2625,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-kite-01",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "kite caption: basin boundary on a saddle stable manifold by strong numerical evidence (paper 13145281)",
   "appears_as": "At one steering strength, by strong numerical evidence, the start on the edge lies",
   "paper_text": "by strong numerical evidence, the start on the edge lies on the stable manifold of a saddle orbit between them",
   "paper_line": 2717,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-1d-01",
   "section": "Evidence for low-dimensional dynamics",
   "claim": "one exponent per direction, 896 directions (paper 13145281)",
   "appears_as": "The map has one exponent for each of its 896 directions,",
   "paper_text": "The map has one exponent for each of its 896 directions",
   "paper_line": 3189,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-1d-02",
   "section": "Evidence for low-dimensional dynamics",
   "claim": "four perturbations followed at once with the exact derivative (paper 13145281)",
   "appears_as": "To find the next few, we followed four small perturbations at once with the",
   "paper_text": "we followed four small perturbations at once with the network's exact derivative",
   "paper_line": 3190,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-1d-03",
   "section": "Evidence for low-dimensional dynamics",
   "claim": "the spectra at three representative chaotic cells only (paper 13145281)",
   "appears_as": "their logarithmic growth rates. We did this only at three representative chaotic",
   "paper_text": "We did this only at three representative chaotic cells",
   "paper_line": 3193,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-1d-04",
   "section": "Evidence for low-dimensional dynamics",
   "claim": "low-dimensional dynamics with one expanding direction at three sampled cells (paper 13145281)",
   "appears_as": "at the three sampled cells, with one expanding direction.",
   "paper_text": "These estimates suggest low-dimensional dynamics at the three sampled cells, with one expanding direction.",
   "paper_line": 3197,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-1d-05",
   "section": "Evidence for low-dimensional dynamics",
   "claim": "Kaplan-Yorke estimate as one plus the largest exponent over the magnitude of the next (paper 13145281)",
   "appears_as": "gives one plus the largest exponent divided by the magnitude of the next.",
   "paper_text": "one plus the largest exponent divided by the magnitude of the next",
   "paper_line": 3196,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-1d-06",
   "section": "Evidence for low-dimensional dynamics",
   "claim": "the leading singular value becomes more dominant over a cycle (paper 13145281)",
   "appears_as": "cycle, however, the leading singular value becomes far more dominant.",
   "paper_text": "Composed over a cycle, however, the leading singular value becomes more dominant.",
   "paper_line": 3185,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-1d-07",
   "section": "Evidence for low-dimensional dynamics",
   "claim": "the two-token model agrees qualitatively and does not reproduce the cascade (paper 13145281)",
   "appears_as": "The agreement is qualitative: the model does not reproduce the cascade.",
   "paper_text": "The agreement is qualitative: it does not reproduce the cascade.",
   "paper_line": 3205,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-pic-01",
   "section": "One picture",
   "claim": "one expanding direction at the three sampled chaotic cells (paper 13145281)",
   "appears_as": "At the three sampled chaotic cells, the finite-time spectra suggest one expanding",
   "paper_text": "At the three sampled chaotic cells, the finite-time spectra suggest one expanding direction.",
   "paper_line": 3235,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-evi-01",
   "section": "What the evidence supports",
   "claim": "claims table: the reset test replaced cache and logits by those of a reference run (paper 13145281)",
   "appears_as": "an exploratory test that replaced the target's cache and logits by those of a reference run computed alone",
   "paper_text": "replacing the target's cache and logits by those of a batch-1 reference run before every soft step",
   "paper_line": 122,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-evi-02",
   "section": "What the evidence supports",
   "claim": "claims table: Soft Thinking as published, injected float64 perturbations mostly shrink (paper 13145281)",
   "appears_as": "(none changed); in float64, injected perturbations mostly shrink over the observed runs |",
   "paper_text": "In float64, injected perturbations mostly shrink over the same pipeline's observed runs.",
   "paper_line": 1371,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-evi-03",
   "section": "What the evidence supports",
   "claim": "claims table: R1-Distill-Qwen-7B consistent with rounding carried through feedback (paper 13145281)",
   "appears_as": "consistent with rounding carried through the feedback in DeepSeek-R1-Distill-Qwen-7B",
   "paper_text": "These observations are consistent with its layout flips arising mainly from bfloat16 rounding carried through feedback",
   "paper_line": 1447,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-sig-01",
   "section": "What the evidence supports",
   "claim": "signature table, cusp row: the three conditions at C and five more located cusps (paper 13145281)",
   "appears_as": "the three conditions hold at the kite's cusp C and at five more located cusps",
   "paper_text": "the three conditions hold at the kite's cusp C and at five more located cusps",
   "paper_line": 3902,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-sig-02",
   "section": "What the evidence supports",
   "claim": "signature table, pseudo-superstable row: local explanation, supported numerically (paper 13145281)",
   "appears_as": "the trace-zero curves and fitted saddle of a tracked two-dimensional block support a local explanation",
   "paper_text": "the tracked two-dimensional block's trace-zero curves and fitted saddle support a local explanation of the ditches' separation on the sampled patch",
   "paper_line": 3903,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-sig-03",
   "section": "What the evidence supports",
   "claim": "signature table, pseudo-superstable status (paper 13145281)",
   "appears_as": "| supported numerically on the patch |",
   "paper_text": "supported numerically on the patch",
   "paper_line": 3903,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-sig-04",
   "section": "What the evidence supports",
   "claim": "signature table, basin-boundary requirements (paper 13145281)",
   "appears_as": "changes with the initial state; both attractors exist on both sides of it; the start lies on a saddle",
   "paper_text": "changes with the initial state; both attractors exist on both sides of it; the start lies on a saddle",
   "paper_line": 3907,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-sig-05",
   "section": "What the evidence supports",
   "claim": "signature table, basin-boundary evidence (paper 13145281)",
   "appears_as": "absent with random-token starts; both period-6 orbits exist on both sides; from it the loop nears a",
   "paper_text": "absent with random-token starts; both period-6 orbits exist on both sides; from it the loop nears a",
   "paper_line": 3908,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-lim-01",
   "section": "Limitations",
   "claim": "the first arithmetic tests use two Qwen2.5 models (0.5B and 7B) (paper 13145281)",
   "appears_as": "Qwen2.5 models (0.5B and 7B) and a soft-thinking pipeline without the top-\\(k\\)",
   "paper_text": "The initial arithmetic reproducibility tests use two Qwen2.5 models (0.5B and 7B)",
   "paper_line": 3917,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-lim-02",
   "section": "Limitations",
   "claim": "later GSM8K tests: published settings and three reasoning models (paper 13145281)",
   "appears_as": "GSM8K tests include one at Soft Thinking's published settings and separate tests",
   "paper_text": "The later GSM8K tests include one at the published Soft Thinking settings and separate tests of three reasoning models",
   "paper_line": 3921,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-lim-03",
   "section": "Limitations",
   "claim": "the rate for reasoning that completes is not established (paper 13145281)",
   "appears_as": "layout, so these measurements do not establish the rate for reasoning that",
   "paper_text": "These measurements do not establish the rate for reasoning that completes",
   "paper_line": 3923,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-disc-01",
   "section": "Discussion",
   "claim": "a complete mechanistic account of one forward pass would not predict a long trajectory (paper 13145281)",
   "appears_as": "mechanistic account of what a single forward pass does would then not predict a long",
   "paper_text": "Even a complete mechanistic account of what a single forward pass does would then not predict a long trajectory",
   "paper_line": 3972,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-conc-01",
   "section": "Discussion",
   "claim": "conclusion: a smooth discrete-time dynamical system (paper 13145281)",
   "appears_as": "discrete-time dynamical system, a smooth map iterated step by step, and it behaves",
   "paper_text": "a smooth discrete-time dynamical system, a smooth map iterated step by step",
   "paper_line": 4073,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-conc-02",
   "section": "Discussion",
   "claim": "conclusion: scope of the derivative factorization (paper 13145281)",
   "appears_as": "network whose last layer is a linear output head followed by a softmax. Its factors",
   "paper_text": "the derivative factorization applies to smooth networks with a linear output head followed by softmax",
   "paper_line": 4081,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-conc-03",
   "section": "Discussion",
   "claim": "conclusion: feedback dynamics not confined to one family of models (paper 13145281)",
   "appears_as": "dynamics are not confined to one family of models.",
   "paper_text": "these feedback dynamics are not confined to one family of models",
   "paper_line": 4084,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-data-01",
   "section": "Reproducibility and artifact ledger",
   "claim": "interval-arithmetic certificates are in the repository (paper 13145281)",
   "appears_as": "The interval-arithmetic certificates are in the repository, with the verification",
   "paper_text": "The interval-arithmetic certificates are in the repository, with the verification code, the exact map and input specifications",
   "paper_line": 4089,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-data-02",
   "section": "Reproducibility and artifact ledger",
   "claim": "the period-8 record lists the 37 prefix token IDs (paper 13145281)",
   "appears_as": "and the steering vector, and the 37 prefix token IDs; the record of the coexisting",
   "paper_text": "and lists the 37 prefix token IDs",
   "paper_line": 5845,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-data-03",
   "section": "Reproducibility and artifact ledger",
   "claim": "the coexistence release record (paper 13145281)",
   "appears_as": "the record of the coexisting period-2 and period-3 orbits |",
   "paper_text": "The record is \\path{codex/coexistence-task33/pair-certificate-release.json}",
   "paper_line": 5869,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-data-04",
   "section": "Appendix B",
   "claim": "bulky raw data outside the repository, checksums inside (paper 13145281)",
   "appears_as": "In the repository; CC BY 4.0. Bulky raw trajectories and model states are kept outside the repository, which holds their checksums",
   "paper_text": "Bulky raw trajectories and model states are kept outside the repository, which holds their checksums.",
   "paper_line": 4091,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-ai-01",
   "section": "Appendix C",
   "claim": "designs, run cards, failed attempts, audits and records are kept in the repository (paper 13145281)",
   "appears_as": "results and the manuscript. The test designs fixed in advance, run cards, failed",
   "paper_text": "Frozen designs, run cards, failed attempts, audits and hash-bound records of every run are kept in the project repository",
   "paper_line": 4113,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-ack-01",
   "section": "Acknowledgments",
   "claim": "acknowledgment as in the report (paper 13145281)",
   "appears_as": "The author thanks Jennifer Hoffman and Emin Arakelian for stimulating discussions",
   "paper_text": "The author thanks Jennifer Hoffman and Emin Arakelian for stimulating discussions about large language models",
   "paper_line": 4094,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-contr-01",
   "section": "This note's contribution",
   "claim": "contribution: injected float64 perturbations mostly shrink in two pipelines (paper 13145281)",
   "appears_as": "Qwen2.5-7B and DeepSeek-R1-Distill-Qwen-7B pipelines mostly shrink over the",
   "paper_text": "injected perturbations in the Qwen2.5-7B and DeepSeek-R1-Distill-Qwen-7B pipelines mostly shrink over the observed runs",
   "paper_line": 65,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-cov-01",
   "section": "Stretch, squeeze and fold",
   "claim": "range of the three leading exponents, 0.109 to 0.424 (paper 13145281)",
   "appears_as": "exponents of 0.109 to 0.424 ([Evidence for low-dimensional dynamics]",
   "paper_text": "$0.109$, $0.424$ and $0.239$ per step",
   "paper_line": 3194,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-cov-02",
   "section": "What the chaos does to reproducibility",
   "claim": "R1-Distill-Qwen-7B: 14.5 percent of GSM8K answers changed (table row) (paper 13145281)",
   "appears_as": "the batch layout changed 14.5% of its GSM8K answers, nearly all on problems",
   "paper_text": "DeepSeek-R1-Distill-Qwen-7B for 14.5\\,\\% of the problems",
   "paper_line": 1410,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-cov-03",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "sign of the trace matches in 849 of the 852 cells (paper 13145281)",
   "appears_as": "of the 852 cells (the other three have low tracking overlap",
   "paper_text": "849 of the 852 cells (the other three have low tracking overlap",
   "paper_line": 2614,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-cov-04",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "saddle fit over 5 by 5 cells (paper 13145281)",
   "appears_as": "landscape over \\(5\\times5\\) cells finds a saddle point",
   "paper_text": "from a fit over $5\\times5$ cells with residual",
   "paper_line": 2620,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-cov-05",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "the same 5 by 5 fit in the procedure description (paper 13145281)",
   "appears_as": "(The procedure fits a quadratic over \\(5\\times5\\) cells and keeps a",
   "paper_text": "from a fit over $5\\times5$ cells with residual",
   "paper_line": 2620,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-cov-06",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Figure 64 caption: 11 of the 32 sign changes of the determinant near measured ones (paper 13145281)",
   "appears_as": "(11 of its 32 sign changes lie within one cell of a measured one)",
   "paper_text": "11 of its 32 sign changes lie within one cell of a measured sign change",
   "paper_line": 2627,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-cov-07",
   "section": "A second shrimp, in the plane of Figure 1",
   "claim": "Figure 64 alt text: tracking overlap below 0.9 (paper 13145281)",
   "appears_as": "mark cells where the tracking overlap falls below 0.9; the same rectangle.",
   "paper_text": "small crosses mark cells where the tracking overlap falls below 0.9",
   "paper_line": 2641,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-cov-08",
   "section": "What the evidence supports",
   "claim": "claims table: 190 of 192 chaotic loops separate (paper 13145281)",
   "appears_as": "| 190 of 192 chaotic loops separate under a batch-layout change",
   "paper_text": "190 of 192 chaotic float64 loops of Qwen2.5-0.5B grow past",
   "paper_line": 218,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-cov-09",
   "section": "What the evidence supports",
   "claim": "claims table: median ratio 0.91 (paper 13145281)",
   "appears_as": "(median ratio 0.91 to the exponent's schedule) |",
   "paper_text": "(median ratio 0.91)",
   "paper_line": 219,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r14-cov-10",
   "section": "What the evidence supports",
   "claim": "claims table: 10 of 192 periodic loops separate (paper 13145281)",
   "appears_as": "| 10 of 192 periodic loops; replicated at 7B, 8B and 70B |",
   "paper_text": "& periodic & 10 / 192 &",
   "paper_line": 1253,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r15-001",
   "section": "What the chaos does to reproducibility",
   "claim": "window of the 173-cell token-difference count (last 500 of 1500 steps)",
   "appears_as": "differs between the runs at some step of the last 500",
   "paper_text": "differs between the runs at some step of the last 500",
   "paper_line": 1190,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r17-lead-01",
   "section": "Lead caption",
   "claim": "the lead image is the 640 x 640 HR10 map of the period-6 shrimp",
   "appears_as": "in a 640 by 640 map, about seven times finer than",
   "paper_text": "$640\\times640$ fixed-start map centered on the body",
   "paper_line": 2535,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "r17-lead-02",
   "section": "Lead caption",
   "claim": "HR10 cells are about seven times finer than Figure 1's",
   "appears_as": "about seven times finer than",
   "paper_text": "about seven times finer than Figure~\\ref{fig:cross512}",
   "paper_line": 2536,
   "paper_file": "paper/llm/main.tex"
  },
  {
   "id": "memory-primitive-period",
   "section": "A third knob changes the child's trace saddle",
   "claim": "primitive period",
   "appears_as": "18 steps",
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   "appears_as": "seven new accepted saddles",
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   "section": "Reproducibility and artifact ledger",
   "claim": "where the native evidence of the third proof is kept (added 26 October 2026 at paper 1b718635)",
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     "id": "memory-root-determinant",
     "section": "A third knob changes the child's trace saddle",
     "claim": "root determinant",
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     "id": "memory-root-positive-multiplier",
     "section": "A third knob changes the child's trace saddle",
     "claim": "root positive multiplier",
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     "id": "memory-closure-upper-rounded",
     "section": "A third knob changes the child's trace saddle",
     "claim": "closure upper rounded",
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     "id": "memory-neighbor-change-upper-rounded",
     "section": "A third knob changes the child's trace saddle",
     "claim": "neighbor change upper rounded",
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     "id": "memory-sensitivity-upper-rounded",
     "section": "A third knob changes the child's trace saddle",
     "claim": "sensitivity upper rounded",
     "appears_as": "8.773\\times10^{-12}",
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     "field": "validation.maximum_empirical_height_sensitivity",
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    {
     "id": "memory-token-period",
     "section": "A third knob changes the child's trace saddle",
     "claim": "token-period",
     "appears_as": "six-token text",
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     "style": "word",
     "operation": "primitive-token-period"
    },
    {
     "id": "memory-token-repetitions",
     "section": "A third knob changes the child's trace saddle",
     "claim": "token-repetitions",
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     "receipt": "memory-anchor-crossing-receipt.json",
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     "style": "word",
     "operation": "token-repetitions"
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    {
     "id": "memory-percent-bracket-2",
     "section": "A third knob changes the child's trace saddle",
     "claim": "memory sign-bracket percentage",
     "appears_as": "0.6%",
     "receipt": "memory-local-extension-receipt.json",
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     "source_commit": "d2a15964bdae9358ad2dbc363980a10294b2cb2e",
     "field": "accepted_centers.2.parameter",
     "style": "format",
     "format": ".1f",
     "operation": "times-100"
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    {
     "id": "memory-percent-bracket-3",
     "section": "A third knob changes the child's trace saddle",
     "claim": "memory sign-bracket percentage",
     "appears_as": "0.7%",
     "receipt": "memory-local-extension-receipt.json",
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     "operation": "times-100"
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     "id": "memory-root-rounded-percent",
     "section": "Summary surfaces and memory continuation",
     "claim": "rounded memory connection estimate",
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     "receipt": "memory-local-extension-receipt.json",
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     "field": "height_root.memory_percent",
     "style": "format",
     "format": ".3f"
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    {
     "id": "memory-scan-original-alpha",
     "section": "A third knob changes the child's trace saddle",
     "claim": "original panel steering center",
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     "id": "memory-scan-original-temperature",
     "section": "A third knob changes the child's trace saddle",
     "claim": "original panel log-temperature center",
     "appears_as": "-0.15440238178",
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     "id": "memory-scan-candidate-alpha",
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     "section": "A third knob changes the child's trace saddle",
     "claim": "translated panel log-temperature center",
     "appears_as": "-0.15804614858",
     "receipt": "memory-junction-scan-receipt.json",
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     "id": "memory-scan-original-beta",
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     "claim": "residual-qualified memory parameter",
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     "style": "format",
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    },
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     "id": "memory-scan-alpha-span",
     "section": "A third knob changes the child's trace saddle",
     "claim": "physical steering span",
     "appears_as": "3\\times10^{-6}",
     "receipt": "memory-junction-scan-receipt.json",
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     "id": "memory-scan-temperature-span",
     "section": "A third knob changes the child's trace saddle",
     "claim": "physical log-temperature span",
     "appears_as": "9\\times10^{-6}",
     "receipt": "memory-junction-scan-receipt.json",
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     "id": "memory-scan-horizontal-nodes",
     "section": "A third knob changes the child's trace saddle",
     "claim": "horizontal grid nodes",
     "appears_as": "128\\times128",
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     "source_commit": "b87a9e74ab364801ce8bb3ee86cc585c2bc2e338",
     "field": "scan_settings.resolution.1",
     "style": "integer"
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    {
     "id": "memory-scan-vertical-nodes",
     "section": "A third knob changes the child's trace saddle",
     "claim": "vertical grid nodes",
     "appears_as": "128\\times128",
     "receipt": "memory-junction-scan-receipt.json",
     "receipt_sha256": "b9867638bf6dfac461e5f42dee3f75ef01a156ff918d9356296cf6bb49f72d3a",
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    {
     "id": "memory-scan-settling",
     "section": "A third knob changes the child's trace saddle",
     "claim": "settling horizon",
     "appears_as": "300 settling steps",
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    {
     "id": "memory-scan-measurement",
     "section": "A third knob changes the child's trace saddle",
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     "appears_as": "300 measurement steps",
     "receipt": "memory-junction-scan-receipt.json",
     "receipt_sha256": "b9867638bf6dfac461e5f42dee3f75ef01a156ff918d9356296cf6bb49f72d3a",
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     "field": "scan_settings.samples",
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    {
     "id": "memory-scan-cells",
     "section": "A third knob changes the child's trace saddle",
     "claim": "new measured cells",
     "appears_as": "16,384 new cells",
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     "field": "totals.cells",
     "style": "format",
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    {
     "id": "memory-scan-recurrence",
     "section": "A third knob changes the child's trace saddle",
     "claim": "detected recurrence candidate period",
     "appears_as": "period 18",
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     "field": "map_equivalence.period",
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    {
     "id": "memory-scan-token-period",
     "section": "A third knob changes the child's trace saddle",
     "claim": "canonical token readout period",
     "appears_as": "six-token cycle",
     "receipt": "memory-junction-scan-receipt.json",
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     "source_commit": "b87a9e74ab364801ce8bb3ee86cc585c2bc2e338",
     "field": "readout_comparison.token_period",
     "style": "word"
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    {
     "id": "memory-scan-growth-min",
     "section": "A third knob changes the child's trace saddle",
     "claim": "minimum new finite-time growth estimate",
     "appears_as": "−0.526492",
     "receipt": "memory-junction-scan-receipt.json",
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     "style": "format",
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     "id": "memory-scan-growth-max",
     "section": "A third knob changes the child's trace saddle",
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     "receipt": "memory-junction-scan-receipt.json",
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     "field": "totals.lyapunov_range.1",
     "style": "format",
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    },
    {
     "id": "memory-return-point-count",
     "section": "A third knob changes the child's trace saddle",
     "claim": "full-state return points per phase for the primitive state cycle",
     "appears_as": "three return points",
     "receipt": "memory-anchor-crossing-receipt.json",
     "receipt_sha256": "557a53931f8824d4f92dfb91135ed8eff747ba3b0cab91c5efe72b295947ebab",
     "source_commit": "d2a15964bdae9358ad2dbc363980a10294b2cb2e",
     "field": "summary.endpoint.tokens",
     "style": "word",
     "operation": "token-repetitions"
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   ],
   "reference_verification": {
    "Plantinga": {
     "title": "Certified Algorithms for Implicit Surfaces",
     "author": "Simon Plantinga",
     "locator": "Appendix B, Proposition 16, printed page 93",
     "url": "https://cs.nyu.edu/~exact/pap/mesh/vegter/plantingaThesis.pdf",
     "checked_date": "2026-10-22",
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   },
   "verifier_sha256": "e17512052d512c4edb590e4ff3850c4fabb98d3baaff10de12539b7240b706b6",
   "mobile_verification": "python make_memory_mobile.py --verify; byte identity plus source receipt SHA guard"
  },
  {
   "id": "memory-direct-20261022",
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   "figure_receipts": {
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   "verifier": "verify_memory_update.py",
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     "id": "memory-direct-beta-before",
     "section": "A third knob changes the child's trace saddle",
     "claim": "fresh before probe memory",
     "appears_as": "\\beta=0.006",
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     "id": "memory-direct-roots",
     "section": "A third knob changes the child's trace saddle",
     "claim": "completed trace-zero candidates",
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     "id": "memory-direct-slices",
     "section": "A third knob changes the child's trace saddle",
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     "section": "A third knob changes the child's trace saddle",
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     "id": "memory-direct-root-residual",
     "section": "A third knob changes the child's trace saddle",
     "claim": "upper bound on phase-zero root trace residuals",
     "appears_as": "1.94\\times10^{-11}",
     "receipt": "memory-connection-probe-receipt.json",
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     "section": "A third knob changes the child's trace saddle",
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    },
    {
     "id": "memory-direct-normal-step",
     "section": "A third knob changes the child's trace saddle",
     "claim": "positive magnitude of measured normal offset",
     "appears_as": "\\pm0.003",
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