1{
  2  "bench_version": 1,
  3  "track": "dynamics",
  4  "model": "rnn_small",
  5  "metric_direction": "lower is better",
  6  "n_seeds": 8,
  7  "baseline": {
  8    "best_cfg": {
  9      "lr": 0.006
 10    },
 11    "sweep": [
 12      {
 13        "cfg": {
 14          "lr": 0.001
 15        },
 16        "mean": 0.0014035784406587481
 17      },
 18      {
 19        "cfg": {
 20          "lr": 0.003
 21        },
 22        "mean": 0.000857145045301877
 23      },
 24      {
 25        "cfg": {
 26          "lr": 0.006
 27        },
 28        "mean": 0.0005846045824000612
 29      }
 30    ],
 31    "full": {
 32      "mean": 0.0006132683593023103,
 33      "std": 0.00012424553172221234,
 34      "per_seed": [
 35        0.0005031590699218214,
 36        0.0007117226487025619,
 37        0.0004876864841207862,
 38        0.0006358501268550754,
 39        0.0004713028611149639,
 40        0.0005687447264790535,
 41        0.0006691908929497004,
 42        0.0008584900642745197
 43      ],
 44      "n": 8
 45    }
 46  },
 47  "idea": {
 48    "mean": 0.0001349421136183082,
 49    "std": 2.309535756281096e-05,
 50    "per_seed": [
 51      0.00011737410386558622,
 52      0.00014533710782416165,
 53      0.0001241672143805772,
 54      0.0001715633989078924,
 55      0.0001070009166141972,
 56      0.00010650144395185634,
 57      0.00014698794984724373,
 58      0.00016060477355495095
 59    ],
 60    "n": 8
 61  },
 62  "comparison": {
 63    "delta_mean": -0.00047832624568400206,
 64    "idea_wins": 8,
 65    "n_pairs": 8,
 66    "per_seed_diffs": [
 67      -0.00038578496605623513,
 68      -0.0005663855408784002,
 69      -0.000363519269740209,
 70      -0.00046428672794718295,
 71      -0.0003643019445007667,
 72      -0.00046224328252719715,
 73      -0.0005222029431024566,
 74      -0.0006978852907195687
 75    ],
 76    "p_value": 0.0081,
 77    "mde": 9.642354488901526e-05,
 78    "mde_rel_pct": 15.722895764378306,
 79    "verdict": "idea better (significant)",
 80    "system_worked": true
 81  },
 82  "mechanism_signature": {
 83    "math_sanity": {
 84      "max_ratio": 0.7304509862882015,
 85      "bound": 0.88,
 86      "passed": true
 87    },
 88    "selected_cfg": {
 89      "lr": 0.006,
 90      "radius": 0.88
 91    },
 92    "candidate_results": [
 93      {
 94        "cfg": {
 95          "lr": 0.001,
 96          "radius": 0.88
 97        },
 98        "mean": 0.0023357835689239437
 99      },
100      {
101        "cfg": {
102          "lr": 0.003,
103          "radius": 0.88
104        },
105        "mean": 0.0002383494229434291
106      },
107      {
108        "cfg": {
109          "lr": 0.006,
110          "radius": 0.88
111        },
112        "mean": 0.0001349421136183082
113      }
114    ],
115    "predicted_contraction_bound": 0.8710182309150696,
116    "observed_input_sensitivity": 0.007450580131262541,
117    "trained_recurrent_norm": 0.8710182309150696,
118    "within_bound": true,
119    "confirmed": true,
120    "interpretation": "trained-model perturbation sensitivity versus certified recurrent operator bound"
121  },
122  "protocol_notes": {
123    "matched_track": "dynamics: controlled pendulum rollout is a stability/control task",
124    "baseline": "vanilla rnn_small with Adam via bench.train_model",
125    "intervention": "post-step recurrent spectral projection implementing a conservative quadratic Lyapunov certificate",
126    "epochs": 20,
127    "batch": 128,
128    "paired_seeds": [
129      0,
130      1,
131      2,
132      3,
133      4,
134      5,
135      6,
136      7
137    ],
138    "baseline_grid": [
139      0.001,
140      0.003,
141      0.006
142    ],
143    "idea_grid": [
144      0.001,
145      0.003,
146      0.006
147    ]
148  }
149}