{
  "figures": {
    "fig-toy-cobwebs.png": "629ddc63b419df5291a0ed2b98e37c000162d85f5fe3b533146da1f605af35da",
    "fig-toy-route.png": "aaa34dbc7dd3b127cf0ec67868d71a777f5a14c4545b04e52b1037c283b3025d"
  },
  "model": "u_{t+1} = 1 / (1 + exp(-g(u_t) / T)); f'(u) = p1 p2 g'(u) / T; toy, no language model",
  "panels": {
    "rising": {
      "g": "g(u) = 6u - 2.5",
      "inv_t": 1.0,
      "start": 0.04,
      "attractor": [
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      ],
      "period": 1,
      "lyapunov": -1.565
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    "falling": {
      "g": "g(u) = 3 - 6u",
      "inv_t": 1.0,
      "start": 0.56,
      "attractor": [
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      ],
      "period": 2,
      "lyapunov": -0.931
    },
    "folding": {
      "g": "g(u) = 10u(1 - u) - 1",
      "inv_t": 3.6,
      "start": 0.3,
      "attractor": null,
      "period": null,
      "lyapunov": 0.347
    }
  },
  "fold_scan": {
    "g": "10u(1 - u) - 1",
    "inv_t_range": [
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      7.0
    ],
    "points": 3000,
    "transient": 4000,
    "recorded": 300,
    "start": 0.5,
    "first_flip_inv_t": 1.088,
    "first_chaos_inv_t": 1.99,
    "last_chaos_inv_t": 4.824,
    "contraction_bound_inv_t": 0.4,
    "max_lyapunov": 0.569,
    "chaotic_share_of_scan": 0.28,
    "greedy_state_at_max_inv_t": 0.000975
  },
  "generator": "make_toy_loop_figures.py",
  "matplotlib": "3.11.2",
  "numpy": "2.4.6"
}