{
  "version": "4.27.0",
  "theorems": [
    "fundamental_dimension",
    "symmetric2_dimension",
    "symmetric3_dimension",
    "adjoint_dimension",
    "fundamental_coefficients",
    "symmetric2_coefficients",
    "adjoint_coefficients",
    "symmetric3_coefficients",
    "adjoint_parity_resolution",
    "printed_gauge_coefficients",
    "background_gauge_coefficients",
    "seed_shift_d8",
    "seed_shift_a4",
    "seed_shift_w",
    "seed_shift_preserves_law_combination",
    "quartet_lower_weight_is_required",
    "same_matter_preserves_d8_shift",
    "same_matter_preserves_a4_shift",
    "same_matter_preserves_w",
    "dirac_chirality_trace_cancels_parity",
    "eight_generator_moments",
    "universal_matter_congruence",
    "published_seed_congruence",
    "candidate_seed_congruence",
    "published_seed_odd",
    "candidate_seed_even"
  ],
  "passed": 26,
  "axioms": "12 declarations are axiom-free; 14 use only Lean standard propext and Quot.sound.",
  "sourceSHA256": "51e49c4d79ae1932326fa8e596fd7978ec9182f07724ba8acaf6ad05a1c37cfc",
  "logSHA256": "76125b5a56f4360c7e03f2fe43d6b1e8f3fda793dc6f606a47b91d0aed925c01",
  "scope": "Exact finite weight identities and universal same-matter seed shifts. Infinite Fourier analysis and physical assumptions are not formalized in Lean.",
  "compatibilityNote": "List.bind renamed to List.flatMap; theorem statements unchanged. See proof/replay.json for a fresh kernel and axiom check.",
  "axiom_dependencies": {
    "GHU.fundamental_dimension": [],
    "GHU.symmetric2_dimension": [
      "propext"
    ],
    "GHU.symmetric3_dimension": [
      "propext"
    ],
    "GHU.adjoint_dimension": [],
    "GHU.fundamental_coefficients": [],
    "GHU.symmetric2_coefficients": [
      "propext"
    ],
    "GHU.adjoint_coefficients": [],
    "GHU.symmetric3_coefficients": [
      "propext"
    ],
    "GHU.adjoint_parity_resolution": [],
    "GHU.printed_gauge_coefficients": [],
    "GHU.background_gauge_coefficients": [],
    "GHU.seed_shift_d8": [],
    "GHU.seed_shift_a4": [],
    "GHU.seed_shift_w": [],
    "GHU.seed_shift_preserves_law_combination": [],
    "GHU.quartet_lower_weight_is_required": [
      "propext"
    ],
    "GHU.same_matter_preserves_d8_shift": [
      "propext",
      "Quot.sound"
    ],
    "GHU.same_matter_preserves_a4_shift": [
      "propext",
      "Quot.sound"
    ],
    "GHU.same_matter_preserves_w": [],
    "GHU.dirac_chirality_trace_cancels_parity": [
      "propext",
      "Quot.sound"
    ],
    "GHU.eight_generator_moments": [
      "propext"
    ],
    "GHU.universal_matter_congruence": [
      "propext",
      "Quot.sound"
    ],
    "GHU.published_seed_congruence": [
      "propext",
      "Quot.sound"
    ],
    "GHU.candidate_seed_congruence": [
      "propext",
      "Quot.sound"
    ],
    "GHU.published_seed_odd": [
      "propext",
      "Quot.sound"
    ],
    "GHU.candidate_seed_even": [
      "propext",
      "Quot.sound"
    ]
  },
  "historicalRecord": "proof/su7/lean-4.10.0-record.json"
}