{
  "bench_version": 1,
  "track": "dynamics",
  "model": "rnn_small",
  "metric_direction": "lower is better",
  "n_seeds": 8,
  "baseline": {
    "best_cfg": {
      "lr": 0.002
    },
    "sweep": [
      {
        "cfg": {
          "lr": 0.001
        },
        "mean": 0.00028059784381184727
      },
      {
        "cfg": {
          "lr": 0.002
        },
        "mean": 0.0001786892862583045
      },
      {
        "cfg": {
          "lr": 0.003
        },
        "mean": 0.00018342551447858568
      }
    ],
    "full": {
      "mean": 0.000164712047080684,
      "std": 4.489169459326852e-05,
      "per_seed": [
        0.00020323635544627905,
        0.00021873260266147554,
        0.00013271479110699147,
        0.0001600733958184719,
        0.0001428304531145841,
        0.00023414976021740586,
        0.00011625964543782175,
        0.00010969937284244224
      ],
      "n": 8
    }
  },
  "idea": {
    "mean": 0.000707463565049693,
    "std": 5.862115619486818e-05,
    "per_seed": [
      0.000648840912617743,
      0.0008204824407584965,
      0.0006285406416282058,
      0.0007532027084380388,
      0.0007002238417044282,
      0.0007392585976049304,
      0.0007051959400996566,
      0.0006639634375460446
    ],
    "n": 8
  },
  "comparison": {
    "delta_mean": 0.000542751517969009,
    "idea_wins": 0,
    "n_pairs": 8,
    "per_seed_diffs": [
      0.00044560455717146397,
      0.000601749838097021,
      0.0004958258505212143,
      0.0005931293126195669,
      0.0005573933885898441,
      0.0005051088373875245,
      0.0005889362946618348,
      0.0005542640647036023
    ],
    "p_value": 0.0081,
    "mde": 4.639948748729596e-05,
    "mde_rel_pct": 28.17006303404585,
    "verdict": "idea worse (significant)",
    "system_worked": false
  },
  "mechanism_signature": {
    "idea_sweep": [
      {
        "cfg": {
          "lr": 0.001
        },
        "mean": 0.0013710275816265494
      },
      {
        "cfg": {
          "lr": 0.002
        },
        "mean": 0.0008818475471343845
      },
      {
        "cfg": {
          "lr": 0.003
        },
        "mean": 0.000712766675860621
      }
    ],
    "predicted": "energy should not increase under sufficiently small Euler steps",
    "observed_energy_nonincreasing_fraction": 1.0,
    "observed_energy_first_last": [
      -2.293245553970337,
      -3.0686049461364746
    ],
    "observed_grad_norm_first_last": [
      1.0507688522338867,
      0.8547213077545166
    ],
    "predicted_boundary_eta_L": 2.0,
    "observed_local_energy_boundary": "not estimated (learned Hessian unavailable in budget)",
    "confirmed": true
  },
  "protocol_notes": {
    "track_choice": "dynamics matches stability/control/Lyapunov structure",
    "shared_lr_union": [
      0.001,
      0.002,
      0.003
    ],
    "epochs": 18,
    "batch": 128,
    "baseline_architecture": "matched VectorCell recurrent scaffold (vector field)",
    "idea_architecture": "matched recurrent hidden width with scalar energy gradient"
  }
}