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  "parameters": {
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    "p": 0.02,
    "w0": 3.0,
    "dt": 0.002,
    "horizon": 80.0
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      "rate_predicted": 7.0,
      "rate_observed": 7.0024511439339205,
      "rate_relative_error": 0.00035016341913150583
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      "rate_observed": 3.500612642954197,
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      "rate_observed": 1.7501531428669415,
      "rate_relative_error": 8.751020968083318e-05
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      "predicted_T_bound": 1.3795182106578003,
      "observed_T": 1.1882000000000001,
      "exact_T": 1.1882523095313346,
      "rate_predicted": 1.1666666666666665,
      "rate_observed": 1.1667347275159077,
      "rate_relative_error": 5.833787077813569e-05
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      "max_x": 0.10636961687321454,
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      "predicted_regime": "bounded"
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      "predicted_regime": "bounded"
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      "max_x": 1.7063696168743616,
      "final_w": 0.4,
      "unbounded_by_80": false,
      "predicted_regime": "unbounded (marginal at equality)"
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      "final_x": 1827965.8278582732,
      "max_x": 1827965.8278582732,
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      "unbounded_by_80": true,
      "predicted_regime": "unbounded (marginal at equality)"
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      "final_w": 0.8,
      "unbounded_by_80": true,
      "predicted_regime": "unbounded (marginal at equality)"
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    "max_x": 1.4438561056544417,
    "final_w": 0.3636363636048379,
    "unbounded_by_80": false,
    "predicted_regime": "unbounded (marginal at equality)"
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  "quantitative_checks": {
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      "predicted": "a*V",
      "max_relative_error": 0.00035016341913150583
    },
    "PITO_threshold_prediction": {
      "predicted": "V*epsilon=2*b/a",
      "observed_values": [
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        1.0769230769230766,
        1.0769230769230766,
        1.076923076923077
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      "target": 1.0769230769230769
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    "crossing_bound": {
      "predicted": "observed_T <= predicted_T_bound",
      "maximum_observed_minus_predicted": -0.0049853402374507305
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    "plant_boundary": {
      "predicted": "gamma=d=0.4; gamma<d bounded, gamma>=d unbounded",
      "observed": {
        "0.2": false,
        "0.39": false,
        "0.4": false,
        "0.6": true,
        "0.8": true
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    },
    "regulated_boundedness": {
      "predicted": "feedback reduces gain and bounds x",
      "observed_max_x": 1.4438561056544417,
      "observed_final_w": 0.3636363636048379
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  }
}