{ "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" } }