{ "scope": "Actual retained OWNER1 data only; 24 small-vector consistency audits and one preselected retained full-basis mathematical reconstruction. No population-quality aggregation, ranking, new experiment, synthetic fixture, solver, native/model call, or candidate-code import.", "limits": [ "Other owners not accessed; no inference about their results.", "23 cases lack full basis: their gradients/residuals and optimization are not independently reconstructed.", "Stored solver success/status are reports, not independently rerun solver validation.", "Floating-point comparisons report exact equality and differences, without arbitrary tolerance. Different reductions/BLAS may change final bits. Declared acceptance is exact feasibility and computed gap in [0,1e-6], not an interval/formal certificate.", "Active masks are checked for shape/domain only, not independently validated as solver internals; zero-column identities can be verified from basis only for preselected case." ], "numpy_version_for_audit": "2.3.5", "cases": [ { "case": "librispeech_2094-142345-0032", "checks": { "retained_arrays_finite": true, "numeric_diagnostics_finite": true, "gains_exact_box_feasible": true, "gains32_exact_box_feasible": true, "rounded_gain_conversion_exact": true, "projected_gradient_exact": true, "shapes_correct": true, "float_dtypes_correct": true, "active_mask_values_valid": true, "zero_columns_indices_valid": true, "reported_positive_solver_success": true, "stored_vector_gap_accepted": true, "reported_acceptance_consistent": true, "solver_parameters_match_frozen_source": true, "declared_dimensions_clock_valid": true }, "diagnostic_recalculations": { "frank_wolfe_gap": { "recomputed": 4.143004220992099e-08, "reported": 4.143004220992099e-08, "exact_equal": true, "absolute_difference": 0.0 }, "frank_wolfe_gap_direct_formula": { "recomputed": 4.143004220594215e-08, "reported": 4.143004220594215e-08, "exact_equal": true, "absolute_difference": 0.0 }, "projected_gradient_inf_norm": { "recomputed": 3.2454908970636076e-05, "reported": 3.2454908970636076e-05, "exact_equal": true, "absolute_difference": 0.0 }, "max_box_violation": { "recomputed": 0.0, "reported": 0.0, "exact_equal": true, "absolute_difference": 0.0 }, "zero_observed_column_count": { "recomputed": 0, "reported": 0, "exact_equal": true, "absolute_difference": 0 } }, "active_mask_counts": { "-1": 1, "0": 364, "1": 284 }, "zero_columns": [], "gain_range": [ 1.4541311353244422e-10, 0.9999999999999999 ] }, { "case": "librispeech_2094-142345-0039", "checks": { "retained_arrays_finite": true, "numeric_diagnostics_finite": true, "gains_exact_box_feasible": true, "gains32_exact_box_feasible": true, "rounded_gain_conversion_exact": true, "projected_gradient_exact": true, "shapes_correct": true, "float_dtypes_correct": true, "active_mask_values_valid": true, "zero_columns_indices_valid": true, "reported_positive_solver_success": true, "stored_vector_gap_accepted": true, "reported_acceptance_consistent": true, "solver_parameters_match_frozen_source": true, "declared_dimensions_clock_valid": true }, "diagnostic_recalculations": { "frank_wolfe_gap": { "recomputed": 2.0458599837403513e-07, "reported": 2.0458599837403513e-07, "exact_equal": true, "absolute_difference": 0.0 }, "frank_wolfe_gap_direct_formula": { "recomputed": 2.0458599837153146e-07, "reported": 2.0458599837153146e-07, "exact_equal": true, "absolute_difference": 0.0 }, "projected_gradient_inf_norm": { "recomputed": 2.777526067765379e-05, "reported": 2.777526067765379e-05, "exact_equal": true, "absolute_difference": 0.0 }, "max_box_violation": { "recomputed": 0.0, "reported": 0.0, "exact_equal": true, "absolute_difference": 0.0 }, "zero_observed_column_count": { "recomputed": 0, "reported": 0, "exact_equal": true, "absolute_difference": 0 } }, "active_mask_counts": { "-1": 4, "0": 901, "1": 296 }, "zero_columns": [], "gain_range": [ 1.3413020926990882e-12, 0.9999999999999999 ] }, { "case": "librispeech_2094-142345-0040", "checks": { "retained_arrays_finite": true, "numeric_diagnostics_finite": true, "gains_exact_box_feasible": true, "gains32_exact_box_feasible": true, "rounded_gain_conversion_exact": true, "projected_gradient_exact": true, "shapes_correct": true, "float_dtypes_correct": true, "active_mask_values_valid": true, "zero_columns_indices_valid": true, "reported_positive_solver_success": true, "stored_vector_gap_accepted": true, "reported_acceptance_consistent": true, "solver_parameters_match_frozen_source": true, "declared_dimensions_clock_valid": true }, "diagnostic_recalculations": { "frank_wolfe_gap": { "recomputed": 3.5142336341867374e-08, "reported": 3.5142336341867374e-08, "exact_equal": true, "absolute_difference": 0.0 }, "frank_wolfe_gap_direct_formula": { "recomputed": 3.514233634302477e-08, "reported": 3.514233634302477e-08, "exact_equal": true, "absolute_difference": 0.0 }, "projected_gradient_inf_norm": { "recomputed": 3.5570619651204005e-05, "reported": 3.5570619651204005e-05, "exact_equal": true, "absolute_difference": 0.0 }, "max_box_violation": { "recomputed": 0.0, "reported": 0.0, "exact_equal": true, "absolute_difference": 0.0 }, "zero_observed_column_count": { "recomputed": 0, "reported": 0, "exact_equal": true, "absolute_difference": 0 } }, "active_mask_counts": { "-1": 9, "0": 215, "1": 254 }, "zero_columns": [], "gain_range": [ 4.319806709359953e-14, 0.9999999999999999 ] }, { "case": "librispeech_2300-131720-0022", "checks": { "retained_arrays_finite": true, "numeric_diagnostics_finite": true, "gains_exact_box_feasible": true, "gains32_exact_box_feasible": true, "rounded_gain_conversion_exact": true, "projected_gradient_exact": true, "shapes_correct": true, "float_dtypes_correct": true, "active_mask_values_valid": true, "zero_columns_indices_valid": true, "reported_positive_solver_success": true, "stored_vector_gap_accepted": true, "reported_acceptance_consistent": true, "solver_parameters_match_frozen_source": true, "declared_dimensions_clock_valid": true }, "diagnostic_recalculations": { "frank_wolfe_gap": { "recomputed": 1.7116485691538674e-08, "reported": 1.7116485691538674e-08, "exact_equal": true, "absolute_difference": 0.0 }, "frank_wolfe_gap_direct_formula": { "recomputed": 1.7116485694079753e-08, "reported": 1.7116485694079753e-08, "exact_equal": true, "absolute_difference": 0.0 }, "projected_gradient_inf_norm": { "recomputed": 2.041448977596616e-05, "reported": 2.041448977596616e-05, "exact_equal": true, "absolute_difference": 0.0 }, "max_box_violation": { "recomputed": 0.0, "reported": 0.0, "exact_equal": true, "absolute_difference": 0.0 }, "zero_observed_column_count": { "recomputed": 0, "reported": 0, "exact_equal": true, "absolute_difference": 0 } }, "active_mask_counts": { "-1": 14, "0": 797, "1": 390 }, "zero_columns": [], "gain_range": [ 5.2634753378676616e-20, 0.9999999999999999 ] }, { "case": "librispeech_2300-131720-0028", "checks": { "retained_arrays_finite": true, "numeric_diagnostics_finite": true, "gains_exact_box_feasible": true, "gains32_exact_box_feasible": true, "rounded_gain_conversion_exact": true, "projected_gradient_exact": true, "shapes_correct": true, "float_dtypes_correct": true, "active_mask_values_valid": true, "zero_columns_indices_valid": true, "reported_positive_solver_success": true, "stored_vector_gap_accepted": true, "reported_acceptance_consistent": true, "solver_parameters_match_frozen_source": true, "declared_dimensions_clock_valid": true }, "diagnostic_recalculations": { "frank_wolfe_gap": { "recomputed": 3.444545534688966e-08, "reported": 3.444545534688966e-08, "exact_equal": true, "absolute_difference": 0.0 }, "frank_wolfe_gap_direct_formula": { "recomputed": 3.444545533526355e-08, "reported": 3.444545533526355e-08, "exact_equal": true, "absolute_difference": 0.0 }, "projected_gradient_inf_norm": { "recomputed": 2.8954971945660546e-05, "reported": 2.8954971945660546e-05, "exact_equal": true, "absolute_difference": 0.0 }, "max_box_violation": { "recomputed": 0.0, "reported": 0.0, "exact_equal": true, "absolute_difference": 0.0 }, "zero_observed_column_count": { "recomputed": 0, "reported": 0, "exact_equal": true, "absolute_difference": 0 } }, "active_mask_counts": { "-1": 6, "0": 760, "1": 435 }, "zero_columns": [], "gain_range": [ 6.861267092620925e-14, 0.9999999999999999 ] }, { "case": "librispeech_2300-131720-0041", "checks": { "retained_arrays_finite": true, "numeric_diagnostics_finite": true, "gains_exact_box_feasible": true, "gains32_exact_box_feasible": true, "rounded_gain_conversion_exact": true, "projected_gradient_exact": true, "shapes_correct": true, "float_dtypes_correct": true, "active_mask_values_valid": true, "zero_columns_indices_valid": true, "reported_positive_solver_success": true, "stored_vector_gap_accepted": true, "reported_acceptance_consistent": true, "solver_parameters_match_frozen_source": true, "declared_dimensions_clock_valid": true }, "diagnostic_recalculations": { "frank_wolfe_gap": { "recomputed": 2.2196289321580165e-07, "reported": 2.2196289321580165e-07, "exact_equal": true, "absolute_difference": 0.0 }, "frank_wolfe_gap_direct_formula": { "recomputed": 2.2196289321818607e-07, "reported": 2.2196289321818607e-07, "exact_equal": true, "absolute_difference": 0.0 }, "projected_gradient_inf_norm": { "recomputed": 6.0398999763178196e-05, "reported": 6.0398999763178196e-05, "exact_equal": true, "absolute_difference": 0.0 }, "max_box_violation": { "recomputed": 0.0, "reported": 0.0, "exact_equal": true, "absolute_difference": 0.0 }, "zero_observed_column_count": { "recomputed": 0, "reported": 0, "exact_equal": true, "absolute_difference": 0 } }, "active_mask_counts": { "-1": 0, "0": 743, "1": 8 }, "zero_columns": [], "gain_range": [ 2.3048507239156132e-07, 0.9999999999999999 ] }, { "case": "librispeech_237-126133-0003", "checks": { "retained_arrays_finite": true, "numeric_diagnostics_finite": true, "gains_exact_box_feasible": true, "gains32_exact_box_feasible": true, "rounded_gain_conversion_exact": true, "projected_gradient_exact": true, "shapes_correct": true, "float_dtypes_correct": true, "active_mask_values_valid": true, "zero_columns_indices_valid": true, "reported_positive_solver_success": true, "stored_vector_gap_accepted": true, "reported_acceptance_consistent": true, "solver_parameters_match_frozen_source": true, "declared_dimensions_clock_valid": true }, "diagnostic_recalculations": { "frank_wolfe_gap": { "recomputed": 4.996245183536768e-08, "reported": 4.996245183536768e-08, "exact_equal": true, "absolute_difference": 0.0 }, "frank_wolfe_gap_direct_formula": { "recomputed": 4.996245183547243e-08, "reported": 4.996245183547243e-08, "exact_equal": true, "absolute_difference": 0.0 }, "projected_gradient_inf_norm": { "recomputed": 3.37062230962859e-05, "reported": 3.37062230962859e-05, "exact_equal": true, "absolute_difference": 0.0 }, "max_box_violation": { "recomputed": 0.0, "reported": 0.0, "exact_equal": true, "absolute_difference": 0.0 }, "zero_observed_column_count": { "recomputed": 0, "reported": 0, "exact_equal": true, "absolute_difference": 0 } }, "active_mask_counts": { "-1": 1, "0": 1166, "1": 34 }, "zero_columns": [], "gain_range": [ 3.075448789633935e-09, 0.9999999999999999 ] }, { "case": "librispeech_237-134500-0029", "checks": { "retained_arrays_finite": true, "numeric_diagnostics_finite": true, "gains_exact_box_feasible": true, "gains32_exact_box_feasible": true, "rounded_gain_conversion_exact": true, "projected_gradient_exact": true, "shapes_correct": true, "float_dtypes_correct": true, "active_mask_values_valid": true, "zero_columns_indices_valid": true, "reported_positive_solver_success": true, "stored_vector_gap_accepted": true, "reported_acceptance_consistent": true, "solver_parameters_match_frozen_source": true, "declared_dimensions_clock_valid": true }, "diagnostic_recalculations": { "frank_wolfe_gap": { "recomputed": 8.153382584506756e-08, "reported": 8.153382584506756e-08, "exact_equal": true, "absolute_difference": 0.0 }, "frank_wolfe_gap_direct_formula": { "recomputed": 8.153382583669933e-08, "reported": 8.153382583669933e-08, "exact_equal": true, "absolute_difference": 0.0 }, "projected_gradient_inf_norm": { "recomputed": 4.7512837539676056e-05, "reported": 4.7512837539676056e-05, "exact_equal": true, "absolute_difference": 0.0 }, "max_box_violation": { "recomputed": 0.0, "reported": 0.0, "exact_equal": true, "absolute_difference": 0.0 }, "zero_observed_column_count": { "recomputed": 0, "reported": 0, "exact_equal": true, "absolute_difference": 0 } }, "active_mask_counts": { "-1": 1, "0": 329, "1": 84 }, "zero_columns": [], "gain_range": [ 6.552810483813956e-09, 0.9999999999999999 ] }, { "case": "librispeech_237-134500-0031", "checks": { "retained_arrays_finite": true, "numeric_diagnostics_finite": true, "gains_exact_box_feasible": true, "gains32_exact_box_feasible": true, "rounded_gain_conversion_exact": true, "projected_gradient_exact": true, "shapes_correct": true, "float_dtypes_correct": true, "active_mask_values_valid": true, "zero_columns_indices_valid": true, "reported_positive_solver_success": true, "stored_vector_gap_accepted": true, "reported_acceptance_consistent": true, "solver_parameters_match_frozen_source": true, "declared_dimensions_clock_valid": true }, "diagnostic_recalculations": { "frank_wolfe_gap": { "recomputed": 1.4979151801880413e-07, "reported": 1.4979151801880413e-07, "exact_equal": true, "absolute_difference": 0.0 }, "frank_wolfe_gap_direct_formula": { "recomputed": 1.4979151802263502e-07, "reported": 1.4979151802263502e-07, "exact_equal": true, "absolute_difference": 0.0 }, "projected_gradient_inf_norm": { "recomputed": 3.664449367823952e-05, "reported": 3.664449367823952e-05, "exact_equal": true, "absolute_difference": 0.0 }, "max_box_violation": { "recomputed": 0.0, "reported": 0.0, "exact_equal": true, "absolute_difference": 0.0 }, "zero_observed_column_count": { "recomputed": 0, "reported": 0, "exact_equal": true, "absolute_difference": 0 } }, "active_mask_counts": { "-1": 1, "0": 1162, "1": 38 }, "zero_columns": [], "gain_range": [ 6.131080778279183e-10, 0.9999999999999999 ] }, { "case": "librispeech_260-123286-0008", "checks": { "retained_arrays_finite": true, "numeric_diagnostics_finite": true, "gains_exact_box_feasible": true, "gains32_exact_box_feasible": true, "rounded_gain_conversion_exact": true, "projected_gradient_exact": true, "shapes_correct": true, "float_dtypes_correct": true, "active_mask_values_valid": true, "zero_columns_indices_valid": true, "reported_positive_solver_success": true, "stored_vector_gap_accepted": true, "reported_acceptance_consistent": true, "solver_parameters_match_frozen_source": true, "declared_dimensions_clock_valid": true }, "diagnostic_recalculations": { "frank_wolfe_gap": { "recomputed": 1.3528324420952969e-07, "reported": 1.3528324420952969e-07, "exact_equal": true, "absolute_difference": 0.0 }, "frank_wolfe_gap_direct_formula": { "recomputed": 1.3528324420419846e-07, "reported": 1.3528324420419846e-07, "exact_equal": true, "absolute_difference": 0.0 }, "projected_gradient_inf_norm": { "recomputed": 6.592008668515614e-05, "reported": 6.592008668515614e-05, "exact_equal": true, "absolute_difference": 0.0 }, "max_box_violation": { "recomputed": 0.0, "reported": 0.0, "exact_equal": true, "absolute_difference": 0.0 }, "zero_observed_column_count": { "recomputed": 0, "reported": 0, "exact_equal": true, "absolute_difference": 0 } }, "active_mask_counts": { "-1": 0, "0": 729, "1": 19 }, "zero_columns": [], "gain_range": [ 4.286569503544659e-07, 0.9999999999999999 ] }, { "case": "librispeech_260-123288-0003", "checks": { "retained_arrays_finite": true, "numeric_diagnostics_finite": true, "gains_exact_box_feasible": true, "gains32_exact_box_feasible": true, "rounded_gain_conversion_exact": true, "projected_gradient_exact": true, "shapes_correct": true, "float_dtypes_correct": true, "active_mask_values_valid": true, "zero_columns_indices_valid": true, "reported_positive_solver_success": true, "stored_vector_gap_accepted": true, "reported_acceptance_consistent": true, "solver_parameters_match_frozen_source": true, "declared_dimensions_clock_valid": true }, "diagnostic_recalculations": { "frank_wolfe_gap": { "recomputed": 8.250666108758347e-08, "reported": 8.250666108758347e-08, "exact_equal": true, "absolute_difference": 0.0 }, "frank_wolfe_gap_direct_formula": { "recomputed": 8.250666109349547e-08, "reported": 8.250666109349547e-08, "exact_equal": true, "absolute_difference": 0.0 }, "projected_gradient_inf_norm": { "recomputed": 2.7413232419948308e-05, "reported": 2.7413232419948308e-05, "exact_equal": true, "absolute_difference": 0.0 }, "max_box_violation": { "recomputed": 0.0, "reported": 0.0, "exact_equal": true, "absolute_difference": 0.0 }, "zero_observed_column_count": { "recomputed": 0, "reported": 0, "exact_equal": true, "absolute_difference": 0 } }, "active_mask_counts": { "-1": 1, "0": 1194, "1": 6 }, "zero_columns": [], "gain_range": [ 7.910223112819585e-15, 0.9999999999999999 ] }, { "case": "librispeech_260-123440-0020", "checks": { "retained_arrays_finite": true, "numeric_diagnostics_finite": true, "gains_exact_box_feasible": true, "gains32_exact_box_feasible": true, "rounded_gain_conversion_exact": true, "projected_gradient_exact": true, "shapes_correct": true, "float_dtypes_correct": true, "active_mask_values_valid": true, "zero_columns_indices_valid": true, "reported_positive_solver_success": true, "stored_vector_gap_accepted": true, "reported_acceptance_consistent": true, "solver_parameters_match_frozen_source": true, "declared_dimensions_clock_valid": true }, "diagnostic_recalculations": { "frank_wolfe_gap": { "recomputed": 4.159282566035523e-08, "reported": 4.159282566035523e-08, "exact_equal": true, "absolute_difference": 0.0 }, "frank_wolfe_gap_direct_formula": { "recomputed": 4.159282566973399e-08, "reported": 4.159282566973399e-08, "exact_equal": true, "absolute_difference": 0.0 }, "projected_gradient_inf_norm": { "recomputed": 2.9231829069109594e-05, "reported": 2.9231829069109594e-05, "exact_equal": true, "absolute_difference": 0.0 }, "max_box_violation": { "recomputed": 0.0, "reported": 0.0, "exact_equal": true, "absolute_difference": 0.0 }, "zero_observed_column_count": { "recomputed": 0, "reported": 0, "exact_equal": true, "absolute_difference": 0 } }, "active_mask_counts": { "-1": 3, "0": 827, "1": 170 }, "zero_columns": [], "gain_range": [ 2.7175580509450908e-18, 0.9999999999999999 ] }, { "case": "librispeech_2830-3980-0000", "checks": { "retained_arrays_finite": true, "numeric_diagnostics_finite": true, "gains_exact_box_feasible": true, "gains32_exact_box_feasible": true, "rounded_gain_conversion_exact": true, "projected_gradient_exact": true, "shapes_correct": true, "float_dtypes_correct": true, "active_mask_values_valid": true, "zero_columns_indices_valid": true, "reported_positive_solver_success": true, "stored_vector_gap_accepted": true, "reported_acceptance_consistent": true, "solver_parameters_match_frozen_source": true, "declared_dimensions_clock_valid": true }, "diagnostic_recalculations": { "frank_wolfe_gap": { "recomputed": 3.0679256298992905e-08, "reported": 3.0679256298992905e-08, "exact_equal": true, "absolute_difference": 0.0 }, "frank_wolfe_gap_direct_formula": { "recomputed": 3.0679256298599134e-08, "reported": 3.0679256298599134e-08, "exact_equal": true, "absolute_difference": 0.0 }, "projected_gradient_inf_norm": { "recomputed": 3.181325452161765e-05, "reported": 3.181325452161765e-05, "exact_equal": true, "absolute_difference": 0.0 }, "max_box_violation": { "recomputed": 0.0, "reported": 0.0, "exact_equal": true, "absolute_difference": 0.0 }, "zero_observed_column_count": { "recomputed": 0, "reported": 0, "exact_equal": true, "absolute_difference": 0 } }, "active_mask_counts": { "-1": 28, "0": 597, "1": 122 }, "zero_columns": [], "gain_range": [ 3.8097222190946265e-23, 0.9999999999999999 ] }, { "case": "librispeech_2830-3980-0038", "checks": { "retained_arrays_finite": true, "numeric_diagnostics_finite": true, "gains_exact_box_feasible": true, "gains32_exact_box_feasible": true, "rounded_gain_conversion_exact": true, "projected_gradient_exact": true, "shapes_correct": true, "float_dtypes_correct": true, "active_mask_values_valid": true, "zero_columns_indices_valid": true, "reported_positive_solver_success": true, "stored_vector_gap_accepted": true, "reported_acceptance_consistent": true, "solver_parameters_match_frozen_source": true, "declared_dimensions_clock_valid": true }, "diagnostic_recalculations": { "frank_wolfe_gap": { "recomputed": 1.2952585513811048e-08, "reported": 1.2952585513811048e-08, "exact_equal": true, "absolute_difference": 0.0 }, "frank_wolfe_gap_direct_formula": { "recomputed": 1.2952585511094572e-08, "reported": 1.2952585511094572e-08, "exact_equal": true, "absolute_difference": 0.0 }, "projected_gradient_inf_norm": { "recomputed": 2.2970346751471915e-05, "reported": 2.2970346751471915e-05, "exact_equal": true, "absolute_difference": 0.0 }, "max_box_violation": { "recomputed": 0.0, "reported": 0.0, "exact_equal": true, "absolute_difference": 0.0 }, "zero_observed_column_count": { "recomputed": 0, "reported": 0, "exact_equal": true, "absolute_difference": 0 } }, "active_mask_counts": { "-1": 3, "0": 421, "1": 685 }, "zero_columns": [], "gain_range": [ 2.1097952665783605e-15, 0.9999999999999999 ] }, { "case": "librispeech_2830-3980-0042", "checks": { "retained_arrays_finite": true, "numeric_diagnostics_finite": true, "gains_exact_box_feasible": true, "gains32_exact_box_feasible": true, "rounded_gain_conversion_exact": true, "projected_gradient_exact": true, "shapes_correct": true, "float_dtypes_correct": true, "active_mask_values_valid": true, "zero_columns_indices_valid": true, "reported_positive_solver_success": true, "stored_vector_gap_accepted": true, "reported_acceptance_consistent": true, "solver_parameters_match_frozen_source": true, "declared_dimensions_clock_valid": true }, "diagnostic_recalculations": { "frank_wolfe_gap": { "recomputed": 4.1131142052772e-08, "reported": 4.1131142052772e-08, "exact_equal": true, "absolute_difference": 0.0 }, "frank_wolfe_gap_direct_formula": { "recomputed": 4.113114204090662e-08, "reported": 4.113114204090662e-08, "exact_equal": true, "absolute_difference": 0.0 }, "projected_gradient_inf_norm": { "recomputed": 2.2662651869009842e-05, "reported": 2.2662651869009842e-05, "exact_equal": true, "absolute_difference": 0.0 }, "max_box_violation": { "recomputed": 0.0, "reported": 0.0, "exact_equal": true, "absolute_difference": 0.0 }, "zero_observed_column_count": { "recomputed": 0, "reported": 0, "exact_equal": true, "absolute_difference": 0 } }, "active_mask_counts": { "-1": 3, "0": 211, "1": 391 }, "zero_columns": [], "gain_range": [ 2.6939830634615174e-14, 0.9999999999999999 ] }, { "case": "librispeech_2961-960-0010", "checks": { "retained_arrays_finite": true, "numeric_diagnostics_finite": true, "gains_exact_box_feasible": true, "gains32_exact_box_feasible": true, "rounded_gain_conversion_exact": true, "projected_gradient_exact": true, "shapes_correct": true, "float_dtypes_correct": true, "active_mask_values_valid": true, "zero_columns_indices_valid": true, "reported_positive_solver_success": true, "stored_vector_gap_accepted": true, "reported_acceptance_consistent": true, "solver_parameters_match_frozen_source": true, "declared_dimensions_clock_valid": true }, "diagnostic_recalculations": { "frank_wolfe_gap": { "recomputed": 4.0185355843497276e-08, "reported": 4.0185355843497276e-08, "exact_equal": true, "absolute_difference": 0.0 }, "frank_wolfe_gap_direct_formula": { "recomputed": 4.0185355845018256e-08, "reported": 4.0185355845018256e-08, "exact_equal": true, "absolute_difference": 0.0 }, "projected_gradient_inf_norm": { "recomputed": 1.2802535945377613e-05, "reported": 1.2802535945377613e-05, "exact_equal": true, "absolute_difference": 0.0 }, "max_box_violation": { "recomputed": 0.0, "reported": 0.0, "exact_equal": true, "absolute_difference": 0.0 }, "zero_observed_column_count": { "recomputed": 0, "reported": 0, "exact_equal": true, "absolute_difference": 0 } }, "active_mask_counts": { "-1": 1, "0": 634, "1": 566 }, "zero_columns": [], "gain_range": [ 5.5623991611661775e-12, 0.9999999999999999 ] }, { "case": "librispeech_2961-960-0019", "checks": { "retained_arrays_finite": true, "numeric_diagnostics_finite": true, "gains_exact_box_feasible": true, "gains32_exact_box_feasible": true, "rounded_gain_conversion_exact": true, "projected_gradient_exact": true, "shapes_correct": true, "float_dtypes_correct": true, "active_mask_values_valid": true, "zero_columns_indices_valid": true, "reported_positive_solver_success": true, "stored_vector_gap_accepted": true, "reported_acceptance_consistent": true, "solver_parameters_match_frozen_source": true, "declared_dimensions_clock_valid": true }, "diagnostic_recalculations": { "frank_wolfe_gap": { "recomputed": 5.0266750348743544e-08, "reported": 5.0266750348743544e-08, "exact_equal": true, "absolute_difference": 0.0 }, "frank_wolfe_gap_direct_formula": { "recomputed": 5.02667503489429e-08, "reported": 5.02667503489429e-08, "exact_equal": true, "absolute_difference": 0.0 }, "projected_gradient_inf_norm": { "recomputed": 3.147866640884622e-05, "reported": 3.147866640884622e-05, "exact_equal": true, "absolute_difference": 0.0 }, "max_box_violation": { "recomputed": 0.0, "reported": 0.0, "exact_equal": true, "absolute_difference": 0.0 }, "zero_observed_column_count": { "recomputed": 0, "reported": 0, "exact_equal": true, "absolute_difference": 0 } }, "active_mask_counts": { "-1": 3, "0": 781, "1": 417 }, "zero_columns": [], "gain_range": [ 6.297916126296213e-10, 0.9999999999999999 ] }, { "case": "librispeech_2961-961-0011", "checks": { "retained_arrays_finite": true, "numeric_diagnostics_finite": true, "gains_exact_box_feasible": true, "gains32_exact_box_feasible": true, "rounded_gain_conversion_exact": true, "projected_gradient_exact": true, "shapes_correct": true, "float_dtypes_correct": true, "active_mask_values_valid": true, "zero_columns_indices_valid": true, "reported_positive_solver_success": true, "stored_vector_gap_accepted": true, "reported_acceptance_consistent": true, "solver_parameters_match_frozen_source": true, "declared_dimensions_clock_valid": true }, "diagnostic_recalculations": { "frank_wolfe_gap": { "recomputed": 2.7248967038262378e-08, "reported": 2.7248967038262378e-08, "exact_equal": true, "absolute_difference": 0.0 }, "frank_wolfe_gap_direct_formula": { "recomputed": 2.7248967041093586e-08, "reported": 2.7248967041093586e-08, "exact_equal": true, "absolute_difference": 0.0 }, "projected_gradient_inf_norm": { "recomputed": 2.3011456904975525e-05, "reported": 2.3011456904975525e-05, "exact_equal": true, "absolute_difference": 0.0 }, "max_box_violation": { "recomputed": 0.0, "reported": 0.0, "exact_equal": true, "absolute_difference": 0.0 }, "zero_observed_column_count": { "recomputed": 0, "reported": 0, "exact_equal": true, "absolute_difference": 0 } }, "active_mask_counts": { "-1": 1, "0": 1082, "1": 118 }, "zero_columns": [], "gain_range": [ 8.543595598224987e-09, 0.9999999999999999 ] }, { "case": "librispeech_3570-5694-0001", "checks": { "retained_arrays_finite": true, "numeric_diagnostics_finite": true, "gains_exact_box_feasible": true, "gains32_exact_box_feasible": true, "rounded_gain_conversion_exact": true, "projected_gradient_exact": true, "shapes_correct": true, "float_dtypes_correct": true, "active_mask_values_valid": true, "zero_columns_indices_valid": true, "reported_positive_solver_success": true, "stored_vector_gap_accepted": true, "reported_acceptance_consistent": true, "solver_parameters_match_frozen_source": true, "declared_dimensions_clock_valid": true }, "diagnostic_recalculations": { "frank_wolfe_gap": { "recomputed": 1.2641528981209774e-07, "reported": 1.2641528981209774e-07, "exact_equal": true, "absolute_difference": 0.0 }, "frank_wolfe_gap_direct_formula": { "recomputed": 1.2641528981255368e-07, "reported": 1.2641528981255368e-07, "exact_equal": true, "absolute_difference": 0.0 }, "projected_gradient_inf_norm": { "recomputed": 3.486628325344299e-05, "reported": 3.486628325344299e-05, "exact_equal": true, "absolute_difference": 0.0 }, "max_box_violation": { "recomputed": 0.0, "reported": 0.0, "exact_equal": true, "absolute_difference": 0.0 }, "zero_observed_column_count": { "recomputed": 0, "reported": 0, "exact_equal": true, "absolute_difference": 0 } }, "active_mask_counts": { "-1": 0, "0": 1104, "1": 32 }, "zero_columns": [], "gain_range": [ 6.069393682173195e-08, 0.9999999999999999 ] }, { "case": "librispeech_3570-5694-0004", "checks": { "retained_arrays_finite": true, "numeric_diagnostics_finite": true, "gains_exact_box_feasible": true, "gains32_exact_box_feasible": true, "rounded_gain_conversion_exact": true, "projected_gradient_exact": true, "shapes_correct": true, "float_dtypes_correct": true, "active_mask_values_valid": true, "zero_columns_indices_valid": true, "reported_positive_solver_success": true, "stored_vector_gap_accepted": true, "reported_acceptance_consistent": true, "solver_parameters_match_frozen_source": true, "declared_dimensions_clock_valid": true }, "diagnostic_recalculations": { "frank_wolfe_gap": { "recomputed": 3.4808398813717994e-08, "reported": 3.4808398813717994e-08, "exact_equal": true, "absolute_difference": 0.0 }, "frank_wolfe_gap_direct_formula": { "recomputed": 3.4808398809149654e-08, "reported": 3.4808398809149654e-08, "exact_equal": true, "absolute_difference": 0.0 }, "projected_gradient_inf_norm": { "recomputed": 2.3135457031808748e-05, "reported": 2.3135457031808748e-05, "exact_equal": true, "absolute_difference": 0.0 }, "max_box_violation": { "recomputed": 0.0, "reported": 0.0, "exact_equal": true, "absolute_difference": 0.0 }, "zero_observed_column_count": { "recomputed": 0, "reported": 0, "exact_equal": true, "absolute_difference": 0 } }, "active_mask_counts": { "-1": 1, "0": 615, "1": 451 }, "zero_columns": [], "gain_range": [ 7.753900633116833e-10, 0.9999999999999999 ] }, { "case": "librispeech_3570-5696-0010", "checks": { "retained_arrays_finite": true, "numeric_diagnostics_finite": true, "gains_exact_box_feasible": true, "gains32_exact_box_feasible": true, "rounded_gain_conversion_exact": true, "projected_gradient_exact": true, "shapes_correct": true, "float_dtypes_correct": true, "active_mask_values_valid": true, "zero_columns_indices_valid": true, "reported_positive_solver_success": true, "stored_vector_gap_accepted": true, "reported_acceptance_consistent": true, "solver_parameters_match_frozen_source": true, "declared_dimensions_clock_valid": true }, "diagnostic_recalculations": { "frank_wolfe_gap": { "recomputed": 5.2689296593508725e-08, "reported": 5.2689296593508725e-08, "exact_equal": true, "absolute_difference": 0.0 }, "frank_wolfe_gap_direct_formula": { "recomputed": 5.268929659935084e-08, "reported": 5.268929659935084e-08, "exact_equal": true, "absolute_difference": 0.0 }, "projected_gradient_inf_norm": { "recomputed": 1.5172349177139388e-05, "reported": 1.5172349177139388e-05, "exact_equal": true, "absolute_difference": 0.0 }, "max_box_violation": { "recomputed": 0.0, "reported": 0.0, "exact_equal": true, "absolute_difference": 0.0 }, "zero_observed_column_count": { "recomputed": 0, "reported": 0, "exact_equal": true, "absolute_difference": 0 } }, "active_mask_counts": { "-1": 2, "0": 683, "1": 516 }, "zero_columns": [], "gain_range": [ 1.230188401655984e-10, 0.9999999999999999 ] }, { "case": "librispeech_3575-170457-0034", "checks": { "retained_arrays_finite": true, "numeric_diagnostics_finite": true, "gains_exact_box_feasible": true, "gains32_exact_box_feasible": true, "rounded_gain_conversion_exact": true, "projected_gradient_exact": true, "shapes_correct": true, "float_dtypes_correct": true, "active_mask_values_valid": true, "zero_columns_indices_valid": true, "reported_positive_solver_success": true, "stored_vector_gap_accepted": true, "reported_acceptance_consistent": true, "solver_parameters_match_frozen_source": true, "declared_dimensions_clock_valid": true }, "diagnostic_recalculations": { "frank_wolfe_gap": { "recomputed": 9.291658795796263e-08, "reported": 9.291658795796263e-08, "exact_equal": true, "absolute_difference": 0.0 }, "frank_wolfe_gap_direct_formula": { "recomputed": 9.29165879549887e-08, "reported": 9.29165879549887e-08, "exact_equal": true, "absolute_difference": 0.0 }, "projected_gradient_inf_norm": { "recomputed": 3.659972311220727e-05, "reported": 3.659972311220727e-05, "exact_equal": true, "absolute_difference": 0.0 }, "max_box_violation": { "recomputed": 0.0, "reported": 0.0, "exact_equal": true, "absolute_difference": 0.0 }, "zero_observed_column_count": { "recomputed": 0, "reported": 0, "exact_equal": true, "absolute_difference": 0 } }, "active_mask_counts": { "-1": 0, "0": 628, "1": 72 }, "zero_columns": [], "gain_range": [ 4.214223095330633e-08, 0.9999999999999999 ] }, { "case": "librispeech_3575-170457-0041", "checks": { "retained_arrays_finite": true, "numeric_diagnostics_finite": true, "gains_exact_box_feasible": true, "gains32_exact_box_feasible": true, "rounded_gain_conversion_exact": true, "projected_gradient_exact": true, "shapes_correct": true, "float_dtypes_correct": true, "active_mask_values_valid": true, "zero_columns_indices_valid": true, "reported_positive_solver_success": true, "stored_vector_gap_accepted": true, "reported_acceptance_consistent": true, "solver_parameters_match_frozen_source": true, "declared_dimensions_clock_valid": true }, "diagnostic_recalculations": { "frank_wolfe_gap": { "recomputed": 2.0819864702359091e-07, "reported": 2.0819864702359091e-07, "exact_equal": true, "absolute_difference": 0.0 }, "frank_wolfe_gap_direct_formula": { "recomputed": 2.0819864702051327e-07, "reported": 2.0819864702051327e-07, "exact_equal": true, "absolute_difference": 0.0 }, "projected_gradient_inf_norm": { "recomputed": 3.229862517206694e-05, "reported": 3.229862517206694e-05, "exact_equal": true, "absolute_difference": 0.0 }, "max_box_violation": { "recomputed": 0.0, "reported": 0.0, "exact_equal": true, "absolute_difference": 0.0 }, "zero_observed_column_count": { "recomputed": 0, "reported": 0, "exact_equal": true, "absolute_difference": 0 } }, "active_mask_counts": { "-1": 6, "0": 1093, "1": 102 }, "zero_columns": [], "gain_range": [ 9.534679310327235e-19, 0.9999999982250589 ] }, { "case": "librispeech_3575-170457-0054", "checks": { "retained_arrays_finite": true, "numeric_diagnostics_finite": true, "gains_exact_box_feasible": true, "gains32_exact_box_feasible": true, "rounded_gain_conversion_exact": true, "projected_gradient_exact": true, "shapes_correct": true, "float_dtypes_correct": true, "active_mask_values_valid": true, "zero_columns_indices_valid": true, "reported_positive_solver_success": true, "stored_vector_gap_accepted": true, "reported_acceptance_consistent": true, "solver_parameters_match_frozen_source": true, "declared_dimensions_clock_valid": true }, "diagnostic_recalculations": { "frank_wolfe_gap": { "recomputed": 5.839626312059151e-08, "reported": 5.839626312059151e-08, "exact_equal": true, "absolute_difference": 0.0 }, "frank_wolfe_gap_direct_formula": { "recomputed": 5.839626312023616e-08, "reported": 5.839626312023616e-08, "exact_equal": true, "absolute_difference": 0.0 }, "projected_gradient_inf_norm": { "recomputed": 3.2004258664120044e-05, "reported": 3.2004258664120044e-05, "exact_equal": true, "absolute_difference": 0.0 }, "max_box_violation": { "recomputed": 0.0, "reported": 0.0, "exact_equal": true, "absolute_difference": 0.0 }, "zero_observed_column_count": { "recomputed": 0, "reported": 0, "exact_equal": true, "absolute_difference": 0 } }, "active_mask_counts": { "-1": 10, "0": 1133, "1": 58 }, "zero_columns": [], "gain_range": [ 8.344741338210772e-13, 0.9999999999999999 ] } ], "preselected_full_basis": { "case": "librispeech_2094-142345-0032", "method": "Independent NumPy column placement from retained native centers and already-windowed blocks, observed-prefix clipping; no solver or candidate import. Normalize coefficients by reciprocal scale, sum retained-column contributions, subtract retained PCM/scale, and take per-column inner products.", "input_finite": true, "input_shapes": { "blocks": [ 649, 240 ], "centers": [ 649 ], "pcm": [ 77760 ] }, "matrix_nnz": { "recomputed": 154224, "reported": 154224 }, "zero_columns_exact": true, "array_comparisons": { "predicted_prefix_float64": { "exact_equal": true, "max_abs_difference": 0.0, "compared_elements": 77760 }, "rounded_gain_predicted_prefix_float64": { "exact_equal": true, "max_abs_difference": 0.0, "compared_elements": 77760 }, "normalized_residual_float64": { "exact_equal": false, "max_abs_difference": 6.938893903907228e-18, "compared_elements": 77760 }, "normalized_gradient_float64": { "exact_equal": false, "max_abs_difference": 4.336808689942018e-19, "compared_elements": 649 }, "projected_gradient_float64": { "exact_equal": true, "max_abs_difference": 0.0, "compared_elements": 649 } }, "scalar_comparisons": { "pcm_norm": { "recomputed": 22.95974159195257, "reported": 22.95974159195258, "absolute_difference": 7.105427357601002e-15, "exact_equal": false }, "normalization_scale": { "recomputed": 22.95974159195257, "reported": 22.95974159195258, "absolute_difference": 7.105427357601002e-15, "exact_equal": false }, "normalized_cost": { "recomputed": 0.025802216309135106, "reported": 0.025802216309135095, "absolute_difference": 1.0408340855860843e-17, "exact_equal": false }, "normalized_residual_norm": { "recomputed": 0.22716609037941868, "reported": 0.22716609037941862, "absolute_difference": 5.551115123125783e-17, "exact_equal": false }, "pcm_residual_norm": { "recomputed": 5.215674733565597, "reported": 5.215674733565597, "absolute_difference": 0.0, "exact_equal": true }, "frank_wolfe_gap": { "recomputed": 4.143004221005185e-08, "reported": 4.143004220992099e-08, "absolute_difference": 1.3085997290588898e-19, "exact_equal": false }, "projected_gradient_inf_norm": { "recomputed": 3.2454908970636076e-05, "reported": 3.2454908970636076e-05, "absolute_difference": 0.0, "exact_equal": true } }, "reconstructed_gradient_gap_in_declared_range": true, "stored_scale_isolation": { "description": "Using reported normalization_scale isolates norm-reduction differences; not an independent scale verification.", "normalized_residual_exact_equal": true, "normalized_residual_max_abs_difference": 0.0 } }, "frozen_formula_source": { "path": "soft_carrier_packet/gain-quality-v2-results/extracted/owner-1/source/gain-source/bounded_gain.py", "sha256": "f7b8339cd2be9c5c01f7aa3a82d47adb2a567e0d01b6a0694fe951fa65cf8dfe" }, "summary": { "case_count": 24, "all_explicit_small_vector_checks_pass": true, "all_small_vector_derived_scalar_diagnostics_exact": true, "full_basis_reconstruction_count": 1, "full_optimization_revalidation_claimed": false } }