{
  "scope": "Separate local verification of source formulas; not external independent assessment or hardware quantum validation",
  "checks": {
    "metric_all_125_triangles": true,
    "metric_separation_symmetry": true,
    "mirror_involution_isometry": true,
    "anchor_unique_fixed_point": true,
    "closed_walks_recurrence_lengths_1_to_40": true,
    "scalar_gradient": true,
    "rank_gradient": true,
    "100_balanced_pairs_distinct_and_roundtrip": true,
    "729_addresses_unique": true,
    "observer_recovery_441_cases": true,
    "phase_reference_constructive_destructive": true,
    "zero_projection_active_density_trace": true,
    "bell_coefficient_rank_two": true,
    "calibration_formula_rounds_to_0297": true,
    "five_state_not_closed_under_payload_addition": true,
    "raw_negation_not_closed": true,
    "hex_fold_all_4096_inputs": true,
    "hex_fold_entropy": true,
    "existence_magnitude_decoupling": true,
    "phase_tagged_map_roundtrip": true
  },
  "all_checks_passed": true,
  "closed_walk_counts": [
    {
      "length": 1,
      "dynamic_program_count": 0,
      "formula": 0
    },
    {
      "length": 2,
      "dynamic_program_count": 8,
      "formula": 8
    },
    {
      "length": 3,
      "dynamic_program_count": 0,
      "formula": 0
    },
    {
      "length": 4,
      "dynamic_program_count": 20,
      "formula": 20
    },
    {
      "length": 5,
      "dynamic_program_count": 0,
      "formula": 0
    },
    {
      "length": 6,
      "dynamic_program_count": 56,
      "formula": 56
    },
    {
      "length": 7,
      "dynamic_program_count": 0,
      "formula": 0
    },
    {
      "length": 8,
      "dynamic_program_count": 164,
      "formula": 164
    },
    {
      "length": 9,
      "dynamic_program_count": 0,
      "formula": 0
    },
    {
      "length": 10,
      "dynamic_program_count": 488,
      "formula": 488
    },
    {
      "length": 11,
      "dynamic_program_count": 0,
      "formula": 0
    },
    {
      "length": 12,
      "dynamic_program_count": 1460,
      "formula": 1460
    },
    {
      "length": 13,
      "dynamic_program_count": 0,
      "formula": 0
    },
    {
      "length": 14,
      "dynamic_program_count": 4376,
      "formula": 4376
    },
    {
      "length": 15,
      "dynamic_program_count": 0,
      "formula": 0
    },
    {
      "length": 16,
      "dynamic_program_count": 13124,
      "formula": 13124
    },
    {
      "length": 17,
      "dynamic_program_count": 0,
      "formula": 0
    },
    {
      "length": 18,
      "dynamic_program_count": 39368,
      "formula": 39368
    },
    {
      "length": 19,
      "dynamic_program_count": 0,
      "formula": 0
    },
    {
      "length": 20,
      "dynamic_program_count": 118100,
      "formula": 118100
    },
    {
      "length": 21,
      "dynamic_program_count": 0,
      "formula": 0
    },
    {
      "length": 22,
      "dynamic_program_count": 354296,
      "formula": 354296
    },
    {
      "length": 23,
      "dynamic_program_count": 0,
      "formula": 0
    },
    {
      "length": 24,
      "dynamic_program_count": 1062884,
      "formula": 1062884
    },
    {
      "length": 25,
      "dynamic_program_count": 0,
      "formula": 0
    },
    {
      "length": 26,
      "dynamic_program_count": 3188648,
      "formula": 3188648
    },
    {
      "length": 27,
      "dynamic_program_count": 0,
      "formula": 0
    },
    {
      "length": 28,
      "dynamic_program_count": 9565940,
      "formula": 9565940
    },
    {
      "length": 29,
      "dynamic_program_count": 0,
      "formula": 0
    },
    {
      "length": 30,
      "dynamic_program_count": 28697816,
      "formula": 28697816
    },
    {
      "length": 31,
      "dynamic_program_count": 0,
      "formula": 0
    },
    {
      "length": 32,
      "dynamic_program_count": 86093444,
      "formula": 86093444
    },
    {
      "length": 33,
      "dynamic_program_count": 0,
      "formula": 0
    },
    {
      "length": 34,
      "dynamic_program_count": 258280328,
      "formula": 258280328
    },
    {
      "length": 35,
      "dynamic_program_count": 0,
      "formula": 0
    },
    {
      "length": 36,
      "dynamic_program_count": 774840980,
      "formula": 774840980
    },
    {
      "length": 37,
      "dynamic_program_count": 0,
      "formula": 0
    },
    {
      "length": 38,
      "dynamic_program_count": 2324522936,
      "formula": 2324522936
    },
    {
      "length": 39,
      "dynamic_program_count": 0,
      "formula": 0
    },
    {
      "length": 40,
      "dynamic_program_count": 6973568804,
      "formula": 6973568804
    }
  ],
  "observer_cases": 441,
  "calibration_formula": {
    "k": 0.6321205588285577,
    "log_cosh_k_over_k": 0.2970137033667769,
    "claimed": 0.297,
    "difference": 1.3703366776918191e-05
  },
  "quantum_reference": "Standard two-path and Bell reference calculations, not native KEX runtime execution"
}
