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      "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
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    "maximum_residuals": {
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    "path_integration_checks": [
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        "convergence_ratio": 3.999983587035149
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    ],
    "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,
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    "inside_radius_cases": 224,
    "wronskian_atlas_cases": 224,
    "coordinate_atlas_cases": 224,
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    "gap_boundary_rejections": 28,
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    "maximum_errors": {
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      "blind_distance_error": 7.771561172376096e-16,
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    "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"
}