{
  "schema": "KEDDEH_RESEARCH_FALSIFICATION_V2",
  "seed": 20261010,
  "scope": "Local source execution and separately defined reference experiments; no external independent assessment",
  "groups": {
    "original_suite": {
      "tests": 37,
      "passed": 37,
      "exception_codes": 13
    },
    "proof_correction": {
      "original_failures": 7,
      "corrected_rejections": 7,
      "regression_tests_passed": 37,
      "status": "LOCAL CORRECTION CANDIDATE; source Drive archive unchanged"
    },
    "codec_adversarial": {
      "roundtrip_cases": 2000,
      "single_bit_mutations": 408,
      "typed_rejected": 252,
      "structurally_valid_mutations": 156,
      "trusted_digest_detected": 408,
      "all_mutated_digests_differ": true
    },
    "addressing": {
      "grids": 512,
      "coordinates_checked": 46144,
      "collisions": 0,
      "origin_reserved": true
    },
    "transported_algebra": {
      "triples_checked": 9261,
      "additive_origin": 1,
      "multiplicative_unit": 2,
      "domain": "Unbounded native integer states; finite five-state view is not closed",
      "counterpart_composition": "Separate operator; do not conflate with transported addition"
    },
    "nested_frames": {
      "cases": 5000,
      "maximum_recovery_error": 3.567979245389097e-13,
      "rationale": "Declared context, never treated as a metric scale",
      "identity": "Stable local identity survives invertible frame relocation"
    },
    "metric_curvature": {
      "shell_radii": 30,
      "counts": [
        {
          "radius": 1,
          "square": 8,
          "diamond": 4
        },
        {
          "radius": 2,
          "square": 16,
          "diamond": 8
        },
        {
          "radius": 3,
          "square": 24,
          "diamond": 12
        },
        {
          "radius": 4,
          "square": 32,
          "diamond": 16
        },
        {
          "radius": 5,
          "square": 40,
          "diamond": 20
        },
        {
          "radius": 6,
          "square": 48,
          "diamond": 24
        },
        {
          "radius": 7,
          "square": 56,
          "diamond": 28
        },
        {
          "radius": 8,
          "square": 64,
          "diamond": 32
        },
        {
          "radius": 9,
          "square": 72,
          "diamond": 36
        },
        {
          "radius": 10,
          "square": 80,
          "diamond": 40
        },
        {
          "radius": 11,
          "square": 88,
          "diamond": 44
        },
        {
          "radius": 12,
          "square": 96,
          "diamond": 48
        },
        {
          "radius": 13,
          "square": 104,
          "diamond": 52
        },
        {
          "radius": 14,
          "square": 112,
          "diamond": 56
        },
        {
          "radius": 15,
          "square": 120,
          "diamond": 60
        },
        {
          "radius": 16,
          "square": 128,
          "diamond": 64
        },
        {
          "radius": 17,
          "square": 136,
          "diamond": 68
        },
        {
          "radius": 18,
          "square": 144,
          "diamond": 72
        },
        {
          "radius": 19,
          "square": 152,
          "diamond": 76
        },
        {
          "radius": 20,
          "square": 160,
          "diamond": 80
        },
        {
          "radius": 21,
          "square": 168,
          "diamond": 84
        },
        {
          "radius": 22,
          "square": 176,
          "diamond": 88
        },
        {
          "radius": 23,
          "square": 184,
          "diamond": 92
        },
        {
          "radius": 24,
          "square": 192,
          "diamond": 96
        },
        {
          "radius": 25,
          "square": 200,
          "diamond": 100
        },
        {
          "radius": 26,
          "square": 208,
          "diamond": 104
        },
        {
          "radius": 27,
          "square": 216,
          "diamond": 108
        },
        {
          "radius": 28,
          "square": 224,
          "diamond": 112
        },
        {
          "radius": 29,
          "square": 232,
          "diamond": 116
        },
        {
          "radius": 30,
          "square": 240,
          "diamond": 120
        }
      ],
      "polygon_convergence": [
        {
          "vertices": 4,
          "total_turn": 6.283185307179586,
          "circle_perimeter_relative_error": 0.09968368384289394
        },
        {
          "vertices": 8,
          "total_turn": 6.283185307179586,
          "circle_perimeter_relative_error": 0.025504641595567312
        },
        {
          "vertices": 16,
          "total_turn": 6.283185307179586,
          "circle_perimeter_relative_error": 0.006413148855794248
        },
        {
          "vertices": 32,
          "total_turn": 6.283185307179586,
          "circle_perimeter_relative_error": 0.0016056069643816118
        },
        {
          "vertices": 64,
          "total_turn": 6.283185307179586,
          "circle_perimeter_relative_error": 0.00040154685032089965
        },
        {
          "vertices": 128,
          "total_turn": 6.283185307179586,
          "circle_perimeter_relative_error": 0.00010039578385823145
        },
        {
          "vertices": 256,
          "total_turn": 6.283185307179586,
          "circle_perimeter_relative_error": 2.5099512949933178e-05
        }
      ],
      "native_scope": "Reference norm/turning experiments; original ZCG codec does not implement curvature transport"
    },
    "observer_references": {
      "trials_per_level": 12000,
      "measured_mse": {
        "1": 1.013832431976434,
        "2": 0.5076297772457259,
        "4": 0.2557896209046728,
        "8": 0.12516642753539764,
        "16": 0.06198731344187295
      },
      "predicted_iid_mse": {
        "1": 1.0,
        "2": 0.5,
        "4": 0.25,
        "8": 0.125,
        "16": 0.0625
      },
      "counterexample": {
        "truth": 10,
        "first_reading": 10,
        "added_independent_biased_reading": 14,
        "old_gap": 0,
        "new_equal_weight_gap": 2
      }
    },
    "bell_density": {
      "locations_tested": [
        -3,
        0,
        1,
        5
      ],
      "scales_tested": [
        0.2,
        1,
        3
      ],
      "symmetric_origin_one": true,
      "density_peak_at_mu_one_sigma_one": 0.3989422804014327,
      "whole_integral": 1,
      "density_unit": "inverse x-unit",
      "environment_model": "Illustrative logistic growth da/dt=(rho-1-.15rho\u00b2)*a-a\u00b3; not recovered native physics",
      "growth_at_density": {
        "0": -1.0,
        "1": -0.15,
        "2": 0.4,
        "4": 0.6000000000000001,
        "8": -2.5999999999999996
      }
    },
    "scheduler": {
      "blocked_node": "A",
      "independent_runnable_executed": [
        "B",
        "C",
        "D",
        "B",
        "C",
        "D"
      ],
      "identities_retained": 4,
      "scope": "Reference scheduler invariant, not native BRAINK deployment"
    },
    "compression_cases": [
      {
        "case": "empty",
        "input": 0,
        "zcg": 11,
        "zlib": 8,
        "roundtrip": true
      },
      {
        "case": "long-run",
        "input": 4096,
        "zcg": 15,
        "zlib": 28,
        "roundtrip": true
      },
      {
        "case": "alternating",
        "input": 4096,
        "zcg": 8206,
        "zlib": 28,
        "roundtrip": true
      },
      {
        "case": "all-bytes",
        "input": 4096,
        "zcg": 8206,
        "zlib": 315,
        "roundtrip": true
      },
      {
        "case": "seeded-random",
        "input": 4096,
        "zcg": 8192,
        "zlib": 4107,
        "roundtrip": true
      }
    ]
  },
  "findings": [
    {
      "id": "F01",
      "claim": "Every proof validation failure is typed",
      "result": "FALSIFIED in original",
      "evidence": [
        {
          "field": "run_length",
          "original_outcome": "error"
        },
        {
          "field": "state_revision",
          "original_outcome": "error"
        },
        {
          "field": "coefficient_numerator",
          "original_outcome": "error"
        },
        {
          "field": "coefficient_denominator",
          "original_outcome": "error"
        },
        {
          "field": "bounds",
          "original_outcome": "error"
        },
        {
          "field": "coordinate",
          "original_outcome": "error"
        },
        {
          "field": "coefficient_version",
          "original_outcome": "UnicodeEncodeError"
        }
      ],
      "address": "Add explicit uint64/uint32 bounds and convert invalid UTF-8 to InvalidStateError in a separate correction candidate."
    },
    {
      "id": "F02",
      "claim": "Concurrent random corpus exercises varied bytes",
      "result": "FALSIFIED",
      "original_unique_symbols": 1,
      "corrected_unique_symbols": 256,
      "address": "Seed once outside comprehension; added 2,000 reproducible diverse round trips."
    },
    {
      "id": "F03",
      "claim": "A decodable stream is necessarily unchanged",
      "result": "FALSIFIED",
      "original": "100 A bytes",
      "mutated": "100 B bytes",
      "address": "Verify a trusted out-of-band SHA-256 before decoding; a digest supplied by the same untrusted sender is insufficient."
    },
    {
      "id": "F04",
      "claim": "A naked magnitude survives frame transfer",
      "result": "FALSIFIED",
      "example": "local 2 at scale 10 is shared 20; reporting 2 without scale loses recoverability",
      "address": "Carry frame id, unit, transform, polarity, parent and lineage; reject missing/singular transforms."
    },
    {
      "id": "F05",
      "claim": "Equal-radius L\u221e and L1 shells are just the same lattice shell rotated",
      "result": "FALSIFIED",
      "example": "radius 2 gives 16 square states and 8 diamond states; continuous area is 16 vs 8",
      "address": "Distinguish norm change from rigid rotation with radius/scale correction; retain substrate ids."
    },
    {
      "id": "F06",
      "claim": "More independent references guarantee a smaller gap in every realised case",
      "result": "FALSIFIED as an unconditional numeric prediction",
      "address": "Keep the source A3 axiom distinct; test expected error under declared bias/covariance and estimator assumptions. Independence alone does not ensure accuracy."
    },
    {
      "id": "F07",
      "claim": "A bell curve alone uniquely derives coordinate origin 1",
      "result": "NOT ESTABLISHED; shifted bell curves are counterexamples to uniqueness",
      "address": "Retain whole normalization \u222bp=1, anchor identity U=1, mode location \u03bc and physical environmental density as distinct typed quantities. Test emergence through interventions, not recentering."
    },
    {
      "id": "F08",
      "claim": "Increasing environmental density always favours emergence",
      "result": "FALSIFIED in a declared crowding model, not a falsification of a supplied native law",
      "address": "Measure coupling, dispersion and crowding; density can support, impede or shift an emergence threshold."
    }
  ],
  "status": "All declared regression and bounded verification checks passed; falsified broad claims and source defects retained as findings."
}