{
  "status": "passed",
  "check_count": 29,
  "checks": [
    "noncommuting word retained",
    "inversion fixes the whole word",
    "inversion preserves product order",
    "inversion does not invert A",
    "C-times-C product-to-sum",
    "exact even/odd decomposition",
    "odd projector squares to itself",
    "even component fixed",
    "half-integral raw lift gives integral normal representative",
    "doubled tetrahedron coefficient is integral",
    "parity kernel generators independent",
    "parity kernel isotropic over F2",
    "zero-odd-model: simultaneous inversion",
    "zero-odd-model: allowed parity support",
    "zero-odd-model: exact unit normalization",
    "zero-odd-model: balanced vacuum zero",
    "zero-odd-model: native insertion antisymmetry",
    "zero-odd-model: noncommuting skein word invisible",
    "zero-odd-model: functional factors through odd projector",
    "nonzero-odd-model: simultaneous inversion",
    "nonzero-odd-model: allowed parity support",
    "nonzero-odd-model: exact unit normalization",
    "nonzero-odd-model: balanced vacuum zero",
    "nonzero-odd-model: native insertion antisymmetry",
    "nonzero-odd-model: noncommuting skein word invisible",
    "nonzero-odd-model: functional factors through odd projector",
    "constraints permit zero oriented value",
    "constraints permit nonzero oriented value",
    "oriented differences double the value"
  ],
  "formal_countermodels": {
    "Z0: B(E_t)/c_l": "0",
    "Z1: B(E_t)/c_l": "A^4"
  },
  "scope": "Exact quantum torus algebra and formal boundary witnesses only. No topological input is enumerated. These witnesses are not actual normal indices.",
  "proof_only_dependencies": [
    "GHHR integral normal-homology theorem",
    "retained all-input convergence",
    "retained native named-action dictionary",
    "GHHR simultaneous boundary inversion"
  ]
}
