{
  "bench_version": 1,
  "track": "dynamics",
  "model": "rnn_small",
  "metric_direction": "lower is better",
  "n_seeds": 8,
  "baseline": {
    "best_cfg": {
      "lr": 0.006
    },
    "sweep": [
      {
        "cfg": {
          "lr": 0.001
        },
        "mean": 0.0019389573426451534
      },
      {
        "cfg": {
          "lr": 0.003
        },
        "mean": 0.000923123603570275
      },
      {
        "cfg": {
          "lr": 0.006
        },
        "mean": 0.0006749839230906218
      }
    ],
    "full": {
      "mean": 0.0006854402672615834,
      "std": 0.00019420169122248883,
      "per_seed": [
        0.0006784203578718007,
        0.0006286462303251028,
        0.0005217542639002204,
        0.0008711148402653635,
        0.0005711782141588628,
        0.000547860749065876,
        0.0005476096412166953,
        0.0011169378412887454
      ],
      "n": 8
    }
  },
  "idea": {
    "mean": 0.0006295234306890052,
    "std": 0.0001478583427936034,
    "per_seed": [
      0.0006697725621052086,
      0.0006321860128082335,
      0.000446179648861289,
      0.0007750660297460854,
      0.0005767291877418756,
      0.00047575801727361977,
      0.0005408408469520509,
      0.0009196551400236785
    ],
    "n": 8
  },
  "comparison": {
    "delta_mean": -5.591683657257818e-05,
    "idea_wins": 6,
    "n_pairs": 8,
    "per_seed_diffs": [
      -8.647795766592026e-06,
      3.5397824831306934e-06,
      -7.557461503893137e-05,
      -9.604881051927805e-05,
      5.550973583012819e-06,
      -7.210273179225624e-05,
      -6.768794264644384e-06,
      -0.00019728270126506686
    ],
    "p_value": 0.0443,
    "mde": 5.845099158159299e-05,
    "mde_rel_pct": 8.527510619577656,
    "verdict": "idea better (significant)",
    "system_worked": true
  },
  "mechanism_signature": {
    "math_sanity": {
      "predicted_damping_shift": 1.25,
      "observed_shift": 1.2500000000000004,
      "abs_error": 4.440892098500626e-16,
      "passed": true
    },
    "trained_jacobian": {
      "quantity": "trained-model local input Jacobian norm",
      "predicted": "periodic modulation reduces perturbation growth",
      "baseline_mean": 0.4034101516008377,
      "idea_mean": 0.40224631130695343,
      "relative_change": -0.0028850049738853934,
      "confirmed": true
    },
    "idea_cfg": {
      "lr": 0.006
    },
    "idea_sweep": [
      {
        "cfg": {
          "lr": 0.001
        },
        "mean": 0.0019525550596881658
      },
      {
        "cfg": {
          "lr": 0.003
        },
        "mean": 0.000914391697733663
      },
      {
        "cfg": {
          "lr": 0.006
        },
        "mean": 0.0006308010633802041
      }
    ]
  },
  "selection_note": "Baseline and idea share rnn_small, data, epochs, batch, AdamW weight decay, and union learning-rate grid; only periodic LR modulation differs."
}