outputs/calibration_limit_summary.json

{
  "destructive_controls": {
    "fixed_beta_8": {
      "all_finite": true,
      "graphs_changed_beyond_1e-6": 50,
      "maximum_absolute_error": 1.8368553314178566,
      "mean_absolute_error": 0.613734691169597
    },
    "removed_violation_penalty": {
      "all_finite": true,
      "graphs_changed_beyond_1e-6": 13,
      "maximum_absolute_error": 10.0,
      "mean_absolute_error": 1.21
    }
  },
  "execution_scope": {
    "alpha_grid": [
      0.01,
      0.02,
      0.03,
      0.04,
      0.05,
      0.06,
      0.07,
      0.08,
      0.09,
      0.1,
      0.11,
      0.12,
      0.13,
      0.14,
      0.15
    ],
    "claim_nodes": 503,
    "dataset": "released MATH_open_subclaims_with_scores_and_semantic_eval.json",
    "dependency_edges": 496,
    "graph_temperature_evaluations": 450,
    "graphs": 50,
    "graphs_with_false_nodes": 13,
    "quantile_evaluations": 135,
    "temperature_schedule": [
      0.5,
      0.2,
      0.1,
      0.05,
      0.02,
      0.01,
      0.005,
      0.002,
      0.001
    ]
  },
  "final_temperature_result": {
    "beta": 1000.0,
    "graphs_within_1e-10": 50,
    "graphs_within_1e-6": 50,
    "maximum_absolute_error": 4.32542890393961e-13,
    "mean_absolute_error": 8.92619311798626e-15,
    "tau_s": 0.03162277660168379,
    "temperature": 0.001
  },
  "gates": {
    "all_15_final_quantiles_within_1e-10": true,
    "all_reported_values_finite": true,
    "final_all_50_within_1e-10": true,
    "final_max_error_below_1e-10": true,
    "fixed_beta_destructive_control_fails": true,
    "lambda_grid_span_exactly_one_half": true,
    "mean_error_contracts_by_1e8": true,
    "official_dataset_sha256_exact": true,
    "official_release_scale_50_graphs_503_nodes": true,
    "quantile_order_statistic_stability_bound": true,
    "removed_violation_destructive_control_fails": true,
    "theorem_source_markers_exact": true
  },
  "no_paper_scale_rerun_invented": true,
  "official_commit": "0b4d5487a9868a18c4f9aa5b3d96cdccc705ca97",
  "paper_id": "XfndtVLIub",
  "quantile_recovery": {
    "alphas": 15,
    "final_maximum_absolute_error": 0.0,
    "order_statistic_stability_bound_holds_all_cells": true,
    "scope_note": "Quantile recovery is certified as an order-statistic corollary of uniform score convergence; it is not attributed to the theorem text alone."
  },
  "registered_claim": "Theorem 3.1 calibration convergence and conformal quantile recovery",
  "source_checks": {
    "lambda_grid_span": true,
    "score_conclusion": true,
    "single_limit_schedule": true,
    "sqrt_margin": true
  },
  "status": "pass",
  "temperature_results": [
    {
      "beta": 2.0,
      "graphs_within_1e-10": 0,
      "graphs_within_1e-6": 0,
      "maximum_absolute_error": 5.023173588989156,
      "mean_absolute_error": 1.5931000670957345,
      "tau_s": 0.7071067811865476,
      "temperature": 0.5
    },
    {
      "beta": 5.0,
      "graphs_within_1e-10": 0,
      "graphs_within_1e-6": 0,
      "maximum_absolute_error": 5.358487725428276,
      "mean_absolute_error": 1.1243537537855317,
      "tau_s": 0.4472135954999579,
      "temperature": 0.2
    },
    {
      "beta": 10.0,
      "graphs_within_1e-10": 0,
      "graphs_within_1e-6": 0,
      "maximum_absolute_error": 4.13099223342072,
      "mean_absolute_error": 0.6374636678771154,
      "tau_s": 0.31622776601683794,
      "temperature": 0.1
    },
    {
      "beta": 20.0,
      "graphs_within_1e-10": 0,
      "graphs_within_1e-6": 0,
      "maximum_absolute_error": 1.9926415571154799,
      "mean_absolute_error": 0.1997130122709958,
      "tau_s": 0.22360679774997896,
      "temperature": 0.05
    },
    {
      "beta": 50.0,
      "graphs_within_1e-10": 1,
      "graphs_within_1e-6": 2,
      "maximum_absolute_error": 1.4585052946539498,
      "mean_absolute_error": 0.043990007453380324,
      "tau_s": 0.1414213562373095,
      "temperature": 0.02
    },
    {
      "beta": 100.0,
      "graphs_within_1e-10": 9,
      "graphs_within_1e-6": 23,
      "maximum_absolute_error": 0.02927062476515907,
      "mean_absolute_error": 0.0016116510764306513,
      "tau_s": 0.1,
      "temperature": 0.01
    },
    {
      "beta": 200.0,
      "graphs_within_1e-10": 29,
      "graphs_within_1e-6": 43,
      "maximum_absolute_error": 0.001925516180114606,
      "mean_absolute_error": 6.329592270834183e-05,
      "tau_s": 0.07071067811865475,
      "temperature": 0.005
    },
    {
      "beta": 500.0,
      "graphs_within_1e-10": 47,
      "graphs_within_1e-6": 50,
      "maximum_absolute_error": 4.6462416758430436e-07,
      "mean_absolute_error": 1.0947915756176485e-08,
      "tau_s": 0.044721359549995794,
      "temperature": 0.002
    },
    {
      "beta": 1000.0,
      "graphs_within_1e-10": 50,
      "graphs_within_1e-6": 50,
      "maximum_absolute_error": 4.32542890393961e-13,
      "mean_absolute_error": 8.92619311798626e-15,
      "tau_s": 0.03162277660168379,
      "temperature": 0.001
    }
  ],
  "theorem_contract": {
    "beta": "T^-1",
    "hard_oracle": "largest threshold whose selected ancestor-coherent subgraph contains no false node",
    "lambda_grid_span": 0.5,
    "required_upper_bound": 1.0,
    "soft_keep": "sigmoid((tau-risk+sqrt(T))/T)",
    "soft_sort_shim_used_in_reported_path": false,
    "tau_s": "T^0.5"
  }
}