{
  "bench_version": 1,
  "track": "tabular",
  "model": "custom_branch_mlp",
  "metric_direction": "lower is better",
  "n_seeds": 8,
  "baseline": {
    "best_cfg": {
      "lr": 0.01,
      "weight_decay": 0.0
    },
    "sweep": [
      {
        "cfg": {
          "lr": 0.001,
          "weight_decay": 0.0
        },
        "mean": 12.950589418411255
      },
      {
        "cfg": {
          "lr": 0.003,
          "weight_decay": 0.0
        },
        "mean": 6.888427972793579
      },
      {
        "cfg": {
          "lr": 0.01,
          "weight_decay": 0.0
        },
        "mean": 6.682573318481445
      }
    ],
    "full": {
      "mean": 6.839571237564087,
      "std": 0.3468641081837492,
      "per_seed": [
        6.566773414611816,
        6.700428485870361,
        6.708205223083496,
        6.754886150360107,
        6.259535312652588,
        7.132112979888916,
        7.337502479553223,
        7.2571258544921875
      ],
      "n": 8
    }
  },
  "idea": {
    "best_cfg": {
      "lr": 0.01,
      "weight_decay": 0.0
    },
    "sweep": [
      {
        "cfg": {
          "lr": 0.001,
          "weight_decay": 0.0
        },
        "mean": 13.624429821968079
      },
      {
        "cfg": {
          "lr": 0.003,
          "weight_decay": 0.0
        },
        "mean": 7.040245294570923
      },
      {
        "cfg": {
          "lr": 0.01,
          "weight_decay": 0.0
        },
        "mean": 6.819535434246063
      }
    ],
    "per_seed": [
      6.49015998840332,
      6.686732769012451,
      6.5792107582092285,
      6.80715799331665,
      6.233836650848389,
      7.175884246826172,
      7.312864780426025,
      7.2704362869262695
    ],
    "mean": 6.819535434246063,
    "std": 0.3709357840355057,
    "n": 8
  },
  "comparison": {
    "delta_mean": -0.02003580331802368,
    "idea_wins": 5,
    "n_pairs": 8,
    "per_seed_diffs": [
      -0.0766134262084961,
      -0.013695716857910156,
      -0.12899446487426758,
      0.05227184295654297,
      -0.02569866180419922,
      0.04377126693725586,
      -0.024637699127197266,
      0.013310432434082031
    ],
    "p_value": 0.4109,
    "mde": 0.05054426158733883,
    "mde_rel_pct": 0.7389975165364338,
    "verdict": "no measurable effect",
    "system_worked": false
  },
  "mechanism_signature": {
    "math_check": {
      "epsilon_values": [
        0.001,
        0.002130941015366798,
        0.004540909610972475,
        0.009676410537094535,
        0.020619860095022202,
        0.043939705607607904,
        0.09363292088239417,
        0.19952623149688797
      ],
      "remainder_values": [
        1.9010061570122444e-08,
        1.8393117422730257e-07,
        1.7794226864628757e-06,
        1.7210834407346843e-05,
        0.00016639443047186702,
        0.001607205940536596,
        0.01551344151929597,
        0.15093468018953293
      ],
      "observed_remainder_slope": 2.9993339395602745,
      "predicted_remainder_slope": 3.0,
      "gram_invariance_max_error": 5.1514348342607263e-14,
      "prediction_pass": true
    },
    "trained_model": {
      "source": "trained baseline model on tabular test inputs",
      "epsilon_values": [
        0.0031622776601683794,
        0.006072021956909884,
        0.011659144011798317,
        0.0223872113856834,
        0.042986623470822764,
        0.08254041852680181,
        0.15848931924611134
      ],
      "observed_remainder_slope": 3.0196060096593453,
      "predicted_remainder_slope": 3.0,
      "permutation_max_error": 1.9073486328125e-06,
      "confirmed": true
    },
    "custom_track": null
  },
  "protocol_notes": {
    "paired_seeds": [
      0,
      1,
      2,
      3,
      4,
      5,
      6,
      7
    ],
    "n_train": 800,
    "n_test": 400,
    "architecture": "same width-64 exchangeable branch MLP; only phi vs quadratic Taylor block differs",
    "baseline_grid": [
      {
        "lr": 0.001,
        "weight_decay": 0.0
      },
      {
        "lr": 0.003,
        "weight_decay": 0.0
      },
      {
        "lr": 0.01,
        "weight_decay": 0.0
      }
    ],
    "idea_grid": [
      {
        "lr": 0.001,
        "weight_decay": 0.0
      },
      {
        "lr": 0.003,
        "weight_decay": 0.0
      },
      {
        "lr": 0.01,
        "weight_decay": 0.0
      }
    ]
  }
}