{
  "passed": true,
  "lean_version": "Lean (version 4.27.0, x86_64-w64-windows-gnu, commit db93fe1608548721853390a10cd40580fe7d22ae, Release)",
  "lean": [
    {
      "path": "proof/su7/SU7Certificates.lean",
      "theorems": 26,
      "sha256": "51e49c4d79ae1932326fa8e596fd7978ec9182f07724ba8acaf6ad05a1c37cfc",
      "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"
        ]
      },
      "passed": true
    },
    {
      "path": "proof/quantization/GHUQuantization.lean",
      "theorems": 8,
      "sha256": "607663f02ec3206b406e64e53503a310e5ed2dca1d22b4c1379f9a76bec33609",
      "axiom_dependencies": {
        "GHUQuantization.integral_basis_criterion": [
          "propext",
          "Classical.choice",
          "Quot.sound"
        ],
        "GHUQuantization.quotient_witness": [],
        "GHUQuantization.cover_witness": [],
        "GHUQuantization.cover_misses_fraction": [
          "propext",
          "Quot.sound"
        ],
        "GHUQuantization.parent_annihilator": [
          "propext",
          "Quot.sound"
        ],
        "GHUQuantization.standard_tensor_obstruction": [
          "propext",
          "Quot.sound"
        ],
        "GHUQuantization.no_standard_tensor_parent_match": [
          "propext",
          "Quot.sound"
        ],
        "GHUQuantization.residue_mod_three": [
          "propext",
          "Quot.sound"
        ]
      },
      "passed": true
    },
    {
      "path": "proof/quantization/SpinPeriod.lean",
      "theorems": 7,
      "sha256": "aaee15d1932bc82a34b4147d5c2e47aebe63864b353053730ebc9efd959bb67e",
      "axiom_dependencies": {
        "SpinPeriod.universal_basis": [
          "propext",
          "Classical.choice",
          "Quot.sound"
        ],
        "SpinPeriod.spin_basis": [
          "propext",
          "Classical.choice",
          "Quot.sound"
        ],
        "SpinPeriod.universal_implies_spin": [
          "propext",
          "Classical.choice",
          "Quot.sound"
        ],
        "SpinPeriod.half_square_spin": [
          "propext"
        ],
        "SpinPeriod.half_square_not_universal": [
          "propext",
          "Quot.sound"
        ],
        "SpinPeriod.q6_congruence": [
          "propext",
          "Classical.choice",
          "Quot.sound"
        ],
        "SpinPeriod.q6_implies_six": [
          "propext",
          "Quot.sound"
        ]
      },
      "passed": true
    },
    {
      "path": "proof/u2/U2Certificate.lean",
      "theorems": 8,
      "sha256": "1ae108981f60143dc37e174a412c5620dba338312c37c6d5265440a9faa55974",
      "axiom_dependencies": {
        "U2Certificate.positive_identity": [
          "propext",
          "Classical.choice",
          "Quot.sound"
        ],
        "U2Certificate.positive_joint": [
          "propext",
          "Classical.choice",
          "Quot.sound"
        ],
        "U2Certificate.positive_not_separate": [
          "propext",
          "Quot.sound"
        ],
        "U2Certificate.corrected_criterion": [
          "propext",
          "Classical.choice",
          "Quot.sound"
        ],
        "U2Certificate.separate_sufficient": [
          "propext",
          "Classical.choice",
          "Quot.sound"
        ],
        "U2Certificate.joint_does_not_imply_separate": [
          "propext",
          "Classical.choice",
          "Quot.sound"
        ],
        "U2Certificate.rational_corrected_criterion": [
          "propext",
          "Classical.choice",
          "Quot.sound"
        ],
        "U2Certificate.two_samples_suffice": [
          "propext",
          "Classical.choice",
          "Quot.sound"
        ]
      },
      "passed": true
    },
    {
      "path": "proof/hypothesis/HypothesisAlgebra.lean",
      "theorems": 10,
      "sha256": "ebf9c91fc0172e126553c725fa56ed987cfd0c077b1dd0101e93301db24c7b50",
      "axiom_dependencies": {
        "HypothesisAlgebra.canonical_quartic": [
          "propext",
          "Classical.choice",
          "Quot.sound"
        ],
        "HypothesisAlgebra.mass_coefficient": [
          "propext",
          "Classical.choice",
          "Quot.sound"
        ],
        "HypothesisAlgebra.log_second_numerator": [
          "propext",
          "Classical.choice",
          "Quot.sound"
        ],
        "HypothesisAlgebra.log_third_recurrence": [
          "propext",
          "Classical.choice",
          "Quot.sound"
        ],
        "HypothesisAlgebra.log_fourth_recurrence": [
          "propext",
          "Classical.choice",
          "Quot.sound"
        ],
        "HypothesisAlgebra.vacuum_offset_cancels": [
          "propext",
          "Classical.choice",
          "Quot.sound"
        ],
        "HypothesisAlgebra.normalization_null_column": [
          "propext",
          "Classical.choice",
          "Quot.sound"
        ],
        "HypothesisAlgebra.covariance_pullback_two": [
          "propext",
          "Classical.choice",
          "Quot.sound"
        ],
        "HypothesisAlgebra.gram_minor_two": [
          "propext",
          "Classical.choice",
          "Quot.sound"
        ],
        "HypothesisAlgebra.covariance_unit_minor": [
          "propext",
          "Classical.choice",
          "Quot.sound"
        ]
      },
      "passed": true
    }
  ],
  "checks": [
    {
      "command": [
        "python",
        "proof/quantization/verify_lean.py",
        "--check"
      ],
      "passed": true,
      "output": "{\"passed\": true, \"theorems\": 8}"
    },
    {
      "command": [
        "python",
        "proof/quantization/verify_spin.py",
        "--check"
      ],
      "passed": true,
      "output": "{\"passed\": true, \"theorems\": 7}"
    },
    {
      "command": [
        "python",
        "proof/u2/verify_lean.py",
        "--check"
      ],
      "passed": true,
      "output": "{\"passed\": true, \"theorems\": 8, \"read_only\": true}"
    },
    {
      "command": [
        "node",
        "proof/quantization/test_lab.mjs",
        "--check"
      ],
      "passed": true,
      "output": "{\"passed\":true,\"checks\":10}"
    },
    {
      "command": [
        "node",
        "proof/quantization/test_spin.mjs",
        "--check"
      ],
      "passed": true,
      "output": "{\"passed\":true,\"checks\":7}"
    },
    {
      "command": [
        "python",
        "proof/lifts/background_lift_checks.py"
      ],
      "passed": true,
      "output": "{\"passed\": true, \"check_count\": 3290, \"arithmetic\": \"integer phases modulo four; independent Jordan-Wigner basis action\", \"source\": \"action_source.txt\", \"source_sha256\": \"618b9217f73c63d9ae139675c2264e038f604bc703b66e08746cf03582c73722\", \"source_definition\": \"U6=prod(cg[12:]);Ua=-1j*U6@prod(cg[:10]);Ub=-U6@prod(cg[:4])\", \"raw_degrees\": [8, 18, 12], \"raw_squares\": [1, -1, 1], \"representation_squares\": [1, 1, 1], \"negative_control\": \"Removing -i from Ua gives square -1\", \"scope\": \"Local Clifford and representation identities only; no proof of global bundle admissibility, anomaly cancellation or novelty\", \"lean_certified\": false}"
    },
    {
      "command": [
        "python",
        "proof/lifts/background_lift_checks.py",
        "--check"
      ],
      "passed": true,
      "output": "{\"passed\": true, \"check_count\": 3290, \"arithmetic\": \"integer phases modulo four; independent Jordan-Wigner basis action\", \"source\": \"action_source.txt\", \"source_sha256\": \"618b9217f73c63d9ae139675c2264e038f604bc703b66e08746cf03582c73722\", \"source_definition\": \"U6=prod(cg[12:]);Ua=-1j*U6@prod(cg[:10]);Ub=-U6@prod(cg[:4])\", \"raw_degrees\": [8, 18, 12], \"raw_squares\": [1, -1, 1], \"representation_squares\": [1, 1, 1], \"negative_control\": \"Removing -i from Ua gives square -1\", \"scope\": \"Local Clifford and representation identities only; no proof of global bundle admissibility, anomaly cancellation or novelty\", \"lean_certified\": false}"
    },
    {
      "command": [
        "python",
        "proof/boundary-research/certify.py",
        "--check"
      ],
      "passed": true,
      "output": "{\n  \"passed\": true,\n  \"checks\": 113,\n  \"certifiedGramLambdaMinLowerBound\": 0.11058751227528704,\n  \"rootBrackets\": 10\n}"
    },
    {
      "command": [
        "node",
        "proof/u2/lab_crosscheck.mjs",
        "--check"
      ],
      "passed": true,
      "output": "{\"passed\":true,\"checks\":4,\"read_only\":true}"
    },
    {
      "command": [
        "python",
        "proof/quantization/literature_checks.py",
        "--check"
      ],
      "passed": true,
      "output": "{\"passed\": true, \"checks\": 10, \"u2_cases\": 138}"
    },
    {
      "command": [
        "python",
        "proof/hypothesis/certify.py",
        "--check"
      ],
      "passed": true,
      "output": "{\"passed\": true, \"checks\": 296, \"lean_theorems\": 10, \"exact_covariance_dimension\": 15, \"pointwise_enclosures\": 3, \"full_potential_certified\": false}"
    }
  ],
  "scope": "Arithmetic replay and scoped computational checks; topology and full physical consistency not formalized"
}
