| { |
| "exact_words": 6270, |
| "exact_prefixes": 18738, |
| "arithmetic": "fractions.Fraction", |
| "status": "PASS", |
| "complex_words": 400, |
| "complex_prefixes": 2573, |
| "local_unitary_cases": 96, |
| "topological_transition_samples": 513, |
| "sampled_transition_winding": -1.0, |
| "maximum_balance_error": 3.1233117677629557e-15, |
| "maximum_local_unitarity_error": 7.313718605403384e-16, |
| "python": "3.12.14", |
| "numpy": "2.3.5", |
| "seed": 704107, |
| "version": "3.0.0", |
| "relational_extension": { |
| "seed": 26100429, |
| "counts": { |
| "global_factor_and_blind_witness_cases": 192, |
| "anchor_and_exact_breakdown_cases": 384, |
| "recognized_perturbation_cases": 382, |
| "sharp_inverse_margin_examples": 96, |
| "nonorthogonal_atlas_witness_cases": 84, |
| "orthonormal_atlas_and_deficient_atlas_dimensions": 7, |
| "pair_transport_and_cycle_cases": 256, |
| "relational_matrix_completion_cases": 192, |
| "nonlinear_phase_loss_counterexamples": 1, |
| "quantitative_blind_region_cases": 192, |
| "synthetic_haar_rays": 84000, |
| "integrated_path_steps": 4608, |
| "path_resolution_comparisons": 3 |
| }, |
| "maximum_residuals": { |
| "factor": 1.2680511809273537e-15, |
| "distance": 5.551115123125783e-16, |
| "pair": 5.240421196468487e-15, |
| "decode": 9.827296528613448e-16, |
| "vectorization": 4.476131157373991e-15 |
| }, |
| "triangle_phase_radians": 0.7853981633974483, |
| "haar_ball_checks": [ |
| { |
| "n": 2, |
| "samples": 12000, |
| "count": 2999, |
| "predicted_fraction": 0.25, |
| "sampled_fraction": 0.24991666666666668 |
| }, |
| { |
| "n": 3, |
| "samples": 12000, |
| "count": 2915, |
| "predicted_fraction": 0.25000000000000006, |
| "sampled_fraction": 0.24291666666666667 |
| }, |
| { |
| "n": 4, |
| "samples": 12000, |
| "count": 2935, |
| "predicted_fraction": 0.2500000000000001, |
| "sampled_fraction": 0.24458333333333335 |
| }, |
| { |
| "n": 5, |
| "samples": 12000, |
| "count": 3026, |
| "predicted_fraction": 0.2499999999999999, |
| "sampled_fraction": 0.25216666666666665 |
| }, |
| { |
| "n": 6, |
| "samples": 12000, |
| "count": 2991, |
| "predicted_fraction": 0.24999999999999997, |
| "sampled_fraction": 0.24925 |
| }, |
| { |
| "n": 7, |
| "samples": 12000, |
| "count": 2985, |
| "predicted_fraction": 0.2499999999999999, |
| "sampled_fraction": 0.24875 |
| }, |
| { |
| "n": 8, |
| "samples": 12000, |
| "count": 3074, |
| "predicted_fraction": 0.25000000000000017, |
| "sampled_fraction": 0.25616666666666665 |
| } |
| ], |
| "path_integration_checks": [ |
| { |
| "theta": 0.3, |
| "errors_512_1024": [ |
| 5.317178471138385e-06, |
| 1.3292953852635848e-06 |
| ], |
| "convergence_ratio": 3.9999976905690127 |
| }, |
| { |
| "theta": 0.7853981633974483, |
| "errors_512_1024": [ |
| 9.856574241182722e-06, |
| 2.4641539977433662e-06 |
| ], |
| "convergence_ratio": 3.999983057150332 |
| }, |
| { |
| "theta": 1.1, |
| "errors_512_1024": [ |
| 7.5850455410952964e-06, |
| 1.8962691661236172e-06 |
| ], |
| "convergence_ratio": 3.999983587035149 |
| } |
| ], |
| "scope": "Finite and synthetic checks support explicit constructions; proofs establish universal bounds. No empirical science or proof-assistant certification is claimed." |
| }, |
| "continuous_factorization_extension": { |
| "status": "PASS", |
| "seed": 30001004, |
| "exact_monomial_subspaces": 494, |
| "exact_monomial_jet_determinants": 6124, |
| "exact_integer_polynomial_subspaces": 64, |
| "repair_cases": 224, |
| "reference_cases": 224, |
| "blind_witnesses": 252, |
| "inside_radius_cases": 224, |
| "wronskian_atlas_cases": 224, |
| "coordinate_atlas_cases": 224, |
| "transport_cycles": 224, |
| "noisy_decoder_cases": 224, |
| "inverse_margin_cases": 140, |
| "gap_boundary_rejections": 28, |
| "structured_blind_families": 28, |
| "maximum_errors": { |
| "repaired_gram_error": 5.496715111541425e-15, |
| "reference_gram_error": 5.7295201615193524e-15, |
| "blind_distance_error": 7.771561172376096e-16, |
| "transport_error": 2.712334408548656e-13, |
| "decoder_error": 9.132859199938697e-15, |
| "cauchy_binet_error": 2.886579864025407e-15 |
| }, |
| "sampled_minimum_wronskian_atlas_margin": 0.23017908524708902, |
| "wronskian_margin_scope": "sample statistic, not a uniform certificate", |
| "four_reference_blind_counterexample": "Gr(2,4), nodes -2,-1,1,2", |
| "noncommuting_holonomy_commutator_norm": 0.04653835104854928, |
| "exact_holonomy_commutator_norm": "162/3481", |
| "topological_scope": "finite checks do not prove the global lower bounds" |
| }, |
| "scope": "finite checks support the analytic proofs; topology is not proved by sampling" |
| } |
|
|
