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  "track": "dynamics",
  "model": "rnn_small",
  "metric_direction": "lower is better",
  "n_seeds": 8,
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    "idea_wins": 8,
    "n_pairs": 8,
    "per_seed_diffs": [
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      -0.00046224328252719715,
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      -0.0006978852907195687
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    "p_value": 0.0081,
    "mde": 9.642354488901526e-05,
    "mde_rel_pct": 15.722895764378306,
    "verdict": "idea better (significant)",
    "system_worked": true
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  "mechanism_signature": {
    "math_sanity": {
      "max_ratio": 0.7304509862882015,
      "bound": 0.88,
      "passed": true
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    "selected_cfg": {
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      "radius": 0.88
    },
    "candidate_results": [
      {
        "cfg": {
          "lr": 0.001,
          "radius": 0.88
        },
        "mean": 0.0023357835689239437
      },
      {
        "cfg": {
          "lr": 0.003,
          "radius": 0.88
        },
        "mean": 0.0002383494229434291
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      {
        "cfg": {
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          "radius": 0.88
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    "predicted_contraction_bound": 0.8710182309150696,
    "observed_input_sensitivity": 0.007450580131262541,
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    "within_bound": true,
    "confirmed": true,
    "interpretation": "trained-model perturbation sensitivity versus certified recurrent operator bound"
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  "protocol_notes": {
    "matched_track": "dynamics: controlled pendulum rollout is a stability/control task",
    "baseline": "vanilla rnn_small with Adam via bench.train_model",
    "intervention": "post-step recurrent spectral projection implementing a conservative quadratic Lyapunov certificate",
    "epochs": 20,
    "batch": 128,
    "paired_seeds": [
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      3,
      4,
      5,
      6,
      7
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    "baseline_grid": [
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    "idea_grid": [
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}