{
  "bench_version": 1,
  "track": "sequence",
  "model": "transformer_tiny",
  "metric_direction": "lower is better",
  "n_seeds": 8,
  "baseline": {
    "best_cfg": {
      "lr": 0.003,
      "m": 8
    },
    "sweep": [
      {
        "cfg": {
          "lr": 0.001,
          "m": 4
        },
        "mean": 0.8542857021093369
      },
      {
        "cfg": {
          "lr": 0.003,
          "m": 8
        },
        "mean": 0.6984880715608597
      },
      {
        "cfg": {
          "lr": 0.006,
          "m": 8
        },
        "mean": 0.8044749051332474
      }
    ],
    "full": {
      "mean": 0.7327230274677277,
      "std": 0.08377880235319037,
      "per_seed": [
        0.6893054246902466,
        0.6570264101028442,
        0.6207273006439209,
        0.826893150806427,
        0.7129261493682861,
        0.7505295276641846,
        0.8937446475028992,
        0.7106316089630127
      ],
      "n": 8
    },
    "idea_union_grid": [
      {
        "lr": 0.001,
        "m": 4
      },
      {
        "lr": 0.003,
        "m": 8
      },
      {
        "lr": 0.006,
        "m": 8
      }
    ]
  },
  "idea": {
    "mean": 0.8882134854793549,
    "std": 0.053050946493547683,
    "per_seed": [
      0.9650673866271973,
      0.8446772694587708,
      0.9014532566070557,
      0.8312016725540161,
      0.9647780656814575,
      0.8639494776725769,
      0.9117944836616516,
      0.822786271572113
    ],
    "n": 8
  },
  "comparison": {
    "delta_mean": 0.1554904580116272,
    "idea_wins": 0,
    "n_pairs": 8,
    "per_seed_diffs": [
      0.2757619619369507,
      0.1876508593559265,
      0.28072595596313477,
      0.004308521747589111,
      0.2518519163131714,
      0.11341995000839233,
      0.01804983615875244,
      0.11215466260910034
    ],
    "p_value": 0.0081,
    "mde": 0.09260611707336146,
    "mde_rel_pct": 12.638625183298233,
    "verdict": "idea worse (significant)",
    "system_worked": false
  },
  "mechanism_signature": {
    "math_sanity": {
      "tail_decreases_with_degree": true,
      "equal_variation_error_decreases_with_m": true,
      "tail_values": [
        [
          0.1487212707001282,
          0.023721270700128194,
          0.002887937366794935,
          0.00028377070012819416,
          2.33540334615423e-05
        ],
        [
          0.7182818284590451,
          0.2182818284590451,
          0.05161516179237857,
          0.009948495125712054,
          0.0016151617923787498
        ],
        [
          4.38905609893065,
          2.3890560989306504,
          1.0557227655973174,
          0.3890560989306504,
          0.1223894322639838
        ]
      ],
      "equal_m_values": [
        378.4287934927351,
        23.171073846375336,
        3.426756281352258,
        0.6860001329013983,
        0.15486263389122001
      ],
      "lie_dims_d2": [
        2,
        1,
        2,
        3,
        6
      ],
      "cost_examples": [
        5,
        6,
        12,
        16
      ]
    },
    "idea_trials": [
      {
        "cfg": {
          "lr": 0.001,
          "m": 4
        },
        "mean": 0.88559989631176
      },
      {
        "cfg": {
          "lr": 0.003,
          "m": 8
        },
        "mean": 0.8925289064645767
      },
      {
        "cfg": {
          "lr": 0.006,
          "m": 8
        },
        "mean": 0.9592751115560532
      }
    ],
    "selected_cfg": {
      "lr": 0.001,
      "m": 4
    },
    "mechanism_signature": {
      "prediction": "larger local Taylor tail should proxy larger CDE approximation error",
      "predicted_tail_mean": 572838.6955113218,
      "observed_test_mse_mean": 0.9075925201177597,
      "seed_level_correlation": 0.32441424694383164,
      "confirmed": false,
      "note": "Both quantities are measured on trained benchmark systems; eight seed points do not establish the claimed quantitative relation."
    }
  }
}