{
  "meta": {
    "simulated": true,
    "label": "Simulated",
    "seed": 0,
    "seedRule": "First seed in 0, 1, 2, ... whose latent sequence has between 2 and 4 disengaged epochs of at least 8 trials; the rule reads only the latent sequence, before any choice is simulated or any posterior is computed.",
    "rng": "mulberry32; latent sequence and blocks from deriveSeed(seed, 0); replicate k choices and rewards from deriveSeed(seed, 1, k); replicate 0 is the plotted session.",
    "trials": 300,
    "replicates": 200,
    "interval": 0.9,
    "filtered": true,
    "params": {
      "alpha": 0.3,
      "qInitial": 0.5,
      "betaEngaged": 3,
      "betaDisengaged": 0.2,
      "pStayEngaged": 0.988,
      "pStayDisengaged": 0.98,
      "pStartEngaged": 1,
      "rewardGood": 0.8,
      "rewardBad": 0.2,
      "blockMin": 30,
      "blockMax": 50
    },
    "encoding": {
      "t": "trial, 1-based",
      "p": "filtered posterior P(engaged | choices and rewards up to t) of replicate 0, true parameters",
      "lo": "5th percentile of the filtered posterior across replicates",
      "hi": "95th percentile of the filtered posterior across replicates",
      "z": "true latent state: 1 engaged, 0 disengaged",
      "c": "chosen option, 0 or 1",
      "r": "reward: 1 rewarded, 0 not",
      "good": "option rewarded with probability rewardGood on this trial",
      "reversals": "first trial after each reversal",
      "trialsToDetect": "trials from epoch onset to the first trial within the epoch with p < 0.5; detection metrics count only disengaged epochs of at least 8 trials"
    },
    "generator": "scripts/simulate-hero.ts",
    "note": "Simulated session generated from the model with its true parameters; these are not experimental data.",
    "reference": "Engagement-state durations are geometric with means matched to the reversal agent of Katahira (2025, bioRxiv v1), whose durations were uniform; inverse temperatures follow that agent; the learning rule is simplified (no forgetting, Q initialised at 0.5)."
  },
  "trials": [
    { "t": 1, "p": 1, "lo": 1, "hi": 1, "z": 1, "c": 0, "r": 0, "good": 1 },
    { "t": 2, "p": 0.985, "lo": 0.985, "hi": 0.99, "z": 1, "c": 0, "r": 0, "good": 1 },
    { "t": 3, "p": 0.98, "lo": 0.96, "hi": 0.984, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 4, "p": 0.979, "lo": 0.937, "hi": 0.981, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 5, "p": 0.979, "lo": 0.901, "hi": 0.979, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 6, "p": 0.98, "lo": 0.872, "hi": 0.98, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 7, "p": 0.98, "lo": 0.831, "hi": 0.978, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 8, "p": 0.981, "lo": 0.801, "hi": 0.978, "z": 1, "c": 1, "r": 0, "good": 1 },
    { "t": 9, "p": 0.979, "lo": 0.81, "hi": 0.978, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 10, "p": 0.979, "lo": 0.808, "hi": 0.979, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 11, "p": 0.98, "lo": 0.711, "hi": 0.979, "z": 1, "c": 1, "r": 0, "good": 1 },
    { "t": 12, "p": 0.977, "lo": 0.74, "hi": 0.979, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 13, "p": 0.978, "lo": 0.742, "hi": 0.98, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 14, "p": 0.979, "lo": 0.723, "hi": 0.98, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 15, "p": 0.98, "lo": 0.699, "hi": 0.98, "z": 1, "c": 1, "r": 0, "good": 1 },
    { "t": 16, "p": 0.978, "lo": 0.719, "hi": 0.98, "z": 1, "c": 1, "r": 0, "good": 1 },
    { "t": 17, "p": 0.973, "lo": 0.691, "hi": 0.98, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 18, "p": 0.973, "lo": 0.667, "hi": 0.98, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 19, "p": 0.975, "lo": 0.672, "hi": 0.981, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 20, "p": 0.977, "lo": 0.659, "hi": 0.981, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 21, "p": 0.979, "lo": 0.622, "hi": 0.98, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 22, "p": 0.98, "lo": 0.644, "hi": 0.981, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 23, "p": 0.882, "lo": 0.689, "hi": 0.981, "z": 1, "c": 0, "r": 1, "good": 1 },
    { "t": 24, "p": 0.913, "lo": 0.486, "hi": 0.981, "z": 0, "c": 1, "r": 0, "good": 1 },
    { "t": 25, "p": 0.921, "lo": 0.354, "hi": 0.98, "z": 0, "c": 1, "r": 1, "good": 1 },
    { "t": 26, "p": 0.864, "lo": 0.199, "hi": 0.973, "z": 0, "c": 0, "r": 0, "good": 1 },
    { "t": 27, "p": 0.9, "lo": 0.072, "hi": 0.956, "z": 0, "c": 1, "r": 1, "good": 1 },
    { "t": 28, "p": 0.758, "lo": 0.088, "hi": 0.956, "z": 0, "c": 0, "r": 0, "good": 1 },
    { "t": 29, "p": 0.481, "lo": 0.051, "hi": 0.947, "z": 0, "c": 0, "r": 0, "good": 1 },
    { "t": 30, "p": 0.61, "lo": 0.075, "hi": 0.958, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 31, "p": 0.724, "lo": 0.102, "hi": 0.966, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 32, "p": 0.813, "lo": 0.124, "hi": 0.972, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 33, "p": 0.876, "lo": 0.195, "hi": 0.976, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 34, "p": 0.918, "lo": 0.182, "hi": 0.979, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 35, "p": 0.944, "lo": 0.202, "hi": 0.978, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 36, "p": 0.96, "lo": 0.234, "hi": 0.98, "z": 1, "c": 1, "r": 0, "good": 1 },
    { "t": 37, "p": 0.967, "lo": 0.255, "hi": 0.981, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 38, "p": 0.973, "lo": 0.321, "hi": 0.982, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 39, "p": 0.976, "lo": 0.408, "hi": 0.982, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 40, "p": 0.979, "lo": 0.405, "hi": 0.982, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 41, "p": 0.981, "lo": 0.421, "hi": 0.982, "z": 1, "c": 1, "r": 0, "good": 1 },
    { "t": 42, "p": 0.98, "lo": 0.443, "hi": 0.982, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 43, "p": 0.98, "lo": 0.53, "hi": 0.982, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 44, "p": 0.889, "lo": 0.52, "hi": 0.982, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 45, "p": 0.916, "lo": 0.568, "hi": 0.981, "z": 1, "c": 1, "r": 0, "good": 0 },
    { "t": 46, "p": 0.923, "lo": 0.624, "hi": 0.979, "z": 1, "c": 1, "r": 0, "good": 0 },
    { "t": 47, "p": 0.914, "lo": 0.55, "hi": 0.977, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 48, "p": 0.922, "lo": 0.549, "hi": 0.976, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 49, "p": 0.935, "lo": 0.611, "hi": 0.973, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 50, "p": 0.859, "lo": 0.585, "hi": 0.969, "z": 1, "c": 1, "r": 0, "good": 0 },
    { "t": 51, "p": 0.9, "lo": 0.61, "hi": 0.965, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 52, "p": 0.929, "lo": 0.561, "hi": 0.967, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 53, "p": 0.949, "lo": 0.58, "hi": 0.969, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 54, "p": 0.962, "lo": 0.585, "hi": 0.973, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 55, "p": 0.97, "lo": 0.585, "hi": 0.974, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 56, "p": 0.975, "lo": 0.539, "hi": 0.976, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 57, "p": 0.978, "lo": 0.559, "hi": 0.978, "z": 1, "c": 0, "r": 0, "good": 0 },
    { "t": 58, "p": 0.977, "lo": 0.658, "hi": 0.978, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 59, "p": 0.978, "lo": 0.523, "hi": 0.979, "z": 1, "c": 0, "r": 0, "good": 0 },
    { "t": 60, "p": 0.975, "lo": 0.565, "hi": 0.98, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 61, "p": 0.975, "lo": 0.558, "hi": 0.981, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 62, "p": 0.976, "lo": 0.515, "hi": 0.981, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 63, "p": 0.978, "lo": 0.551, "hi": 0.981, "z": 1, "c": 0, "r": 0, "good": 0 },
    { "t": 64, "p": 0.976, "lo": 0.61, "hi": 0.981, "z": 1, "c": 0, "r": 0, "good": 0 },
    { "t": 65, "p": 0.957, "lo": 0.613, "hi": 0.981, "z": 1, "c": 1, "r": 1, "good": 0 },
    { "t": 66, "p": 0.939, "lo": 0.647, "hi": 0.982, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 67, "p": 0.937, "lo": 0.665, "hi": 0.982, "z": 1, "c": 0, "r": 1, "good": 0 },
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    { "t": 71, "p": 0.954, "lo": 0.658, "hi": 0.983, "z": 1, "c": 0, "r": 0, "good": 0 },
    { "t": 72, "p": 0.957, "lo": 0.638, "hi": 0.983, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 73, "p": 0.962, "lo": 0.645, "hi": 0.983, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 74, "p": 0.968, "lo": 0.66, "hi": 0.983, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 75, "p": 0.972, "lo": 0.645, "hi": 0.983, "z": 1, "c": 0, "r": 0, "good": 0 },
    { "t": 76, "p": 0.941, "lo": 0.661, "hi": 0.983, "z": 1, "c": 1, "r": 0, "good": 0 },
    { "t": 77, "p": 0.951, "lo": 0.678, "hi": 0.983, "z": 1, "c": 0, "r": 0, "good": 0 },
    { "t": 78, "p": 0.952, "lo": 0.655, "hi": 0.983, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 79, "p": 0.958, "lo": 0.668, "hi": 0.983, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 80, "p": 0.965, "lo": 0.734, "hi": 0.983, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 81, "p": 0.971, "lo": 0.726, "hi": 0.983, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 82, "p": 0.975, "lo": 0.751, "hi": 0.983, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 83, "p": 0.874, "lo": 0.504, "hi": 0.983, "z": 0, "c": 1, "r": 0, "good": 0 },
    { "t": 84, "p": 0.582, "lo": 0.265, "hi": 0.981, "z": 0, "c": 1, "r": 0, "good": 0 },
    { "t": 85, "p": 0.209, "lo": 0.144, "hi": 0.974, "z": 0, "c": 1, "r": 0, "good": 0 },
    { "t": 86, "p": 0.328, "lo": 0.085, "hi": 0.96, "z": 0, "c": 0, "r": 1, "good": 0 },
    { "t": 87, "p": 0.465, "lo": 0.152, "hi": 0.962, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 88, "p": 0.604, "lo": 0.184, "hi": 0.968, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 89, "p": 0.724, "lo": 0.261, "hi": 0.971, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 90, "p": 0.816, "lo": 0.293, "hi": 0.975, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 91, "p": 0.88, "lo": 0.284, "hi": 0.977, "z": 1, "c": 0, "r": 1, "good": 0 },
    { "t": 92, "p": 0.481, "lo": 0.297, "hi": 0.979, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 93, "p": 0.607, "lo": 0.342, "hi": 0.978, "z": 1, "c": 0, "r": 0, "good": 1 },
    { "t": 94, "p": 0.687, "lo": 0.395, "hi": 0.976, "z": 1, "c": 0, "r": 0, "good": 1 },
    { "t": 95, "p": 0.718, "lo": 0.381, "hi": 0.972, "z": 1, "c": 0, "r": 1, "good": 1 },
    { "t": 96, "p": 0.773, "lo": 0.422, "hi": 0.971, "z": 1, "c": 0, "r": 0, "good": 1 },
    { "t": 97, "p": 0.788, "lo": 0.456, "hi": 0.967, "z": 1, "c": 0, "r": 0, "good": 1 },
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    { "t": 101, "p": 0.55, "lo": 0.471, "hi": 0.966, "z": 1, "c": 0, "r": 0, "good": 1 },
    { "t": 102, "p": 0.627, "lo": 0.413, "hi": 0.969, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 103, "p": 0.721, "lo": 0.484, "hi": 0.97, "z": 1, "c": 1, "r": 0, "good": 1 },
    { "t": 104, "p": 0.78, "lo": 0.412, "hi": 0.969, "z": 1, "c": 1, "r": 0, "good": 1 },
    { "t": 105, "p": 0.813, "lo": 0.426, "hi": 0.973, "z": 1, "c": 1, "r": 0, "good": 1 },
    { "t": 106, "p": 0.828, "lo": 0.416, "hi": 0.975, "z": 1, "c": 1, "r": 1, "good": 1 },
    { "t": 107, "p": 0.869, "lo": 0.513, "hi": 0.978, "z": 1, "c": 1, "r": 0, "good": 1 },
    { "t": 108, "p": 0.89, "lo": 0.532, "hi": 0.979, "z": 1, "c": 1, "r": 1, "good": 1 },
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    { "t": 118, "p": 0.94, "lo": 0.657, "hi": 0.982, "z": 1, "c": 1, "r": 1, "good": 1 },
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    { "t": 123, "p": 0.638, "lo": 0.536, "hi": 0.982, "z": 0, "c": 0, "r": 0, "good": 1 },
    { "t": 124, "p": 0.751, "lo": 0.33, "hi": 0.982, "z": 0, "c": 1, "r": 1, "good": 1 },
    { "t": 125, "p": 0.284, "lo": 0.159, "hi": 0.981, "z": 0, "c": 0, "r": 0, "good": 1 },
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    { "t": 127, "p": 0.116, "lo": 0.046, "hi": 0.964, "z": 0, "c": 1, "r": 1, "good": 1 },
    { "t": 128, "p": 0.209, "lo": 0.027, "hi": 0.962, "z": 0, "c": 1, "r": 1, "good": 1 },
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    "medianTrialsToDetect": 2.5,
    "bandWidthMedian": 0.541,
    "text": "Simulated session of 300 trials in which a Q-learning agent switches between two latent states that differ only in inverse temperature (β = 3.0 engaged, β = 0.2 disengaged). The filtered posterior probability of the engaged state averages 0.80 on engaged trials and 0.27 on disengaged trials, and falls below 0.5 in 2 of 2 disengaged epochs of at least 8 trials, a median of 2.5 trials after onset. Across 200 replicates that share the latent sequence, the 90% interval has a median width of 0.54."
  }
}