{
  "arithmetic": "exact integer, rational, and Q(sqrt(5)); SymPy 1.14.0",
  "proof_status": "Executable checks plus source proofs; this audit has not been run through Lean.",
  "tests": [
    {
      "test": "Q recurrence",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "root quarter-turn",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "G root",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "welded mirrors",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "axial square",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "axial signed metric",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "axial reversal",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "golden chart dilation",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "projective mirror",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "new change of basis P H P^-1 = M",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "new conjugated carriage reverses",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "central lift",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "carry identity p=0, n mod4=0",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "carry identity p=0, n mod4=1",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "carry identity p=0, n mod4=2",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "carry identity p=0, n mod4=3",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "carry identity p=1, n mod4=0",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "carry identity p=1, n mod4=1",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "carry identity p=1, n mod4=2",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "carry identity p=1, n mod4=3",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "carry identity p=2, n mod4=0",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "carry identity p=2, n mod4=1",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "carry identity p=2, n mod4=2",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "carry identity p=2, n mod4=3",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "carry identity p=3, n mod4=0",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "carry identity p=3, n mod4=1",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "carry identity p=3, n mod4=2",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "carry identity p=3, n mod4=3",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "four-step lift as source-defined carry",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "eight occurrence addresses",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "all unordered pairs",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "every occurrence degree seven",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "two-cycle decomposition",
      "status": "PASS",
      "detail": "[6, 16, 6]"
    },
    {
      "test": "seven complete matchings",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "matching partition equals K8",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "CRT scanner bijection",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "CRT inverse",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "potential difference rank",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "triangle constraint rank",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "triangle telescoping",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "triangle-potential dimensions",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "declared 3D display affine rank",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "2D display keeps eight vertices",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "no vertex lies inside an unrelated edge",
      "status": "PASS",
      "detail": "[]"
    },
    {
      "test": "published SVG matching for edge (0, 7)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published SVG matching for edge (1, 6)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published SVG matching for edge (2, 5)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published SVG matching for edge (3, 4)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published SVG matching for edge (1, 7)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published SVG matching for edge (0, 2)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published SVG matching for edge (3, 6)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published SVG matching for edge (4, 5)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published SVG matching for edge (2, 7)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published SVG matching for edge (1, 3)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published SVG matching for edge (0, 4)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published SVG matching for edge (5, 6)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published SVG matching for edge (3, 7)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published SVG matching for edge (2, 4)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published SVG matching for edge (1, 5)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published SVG matching for edge (0, 6)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published SVG matching for edge (4, 7)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published SVG matching for edge (3, 5)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published SVG matching for edge (2, 6)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published SVG matching for edge (0, 1)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published SVG matching for edge (5, 7)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published SVG matching for edge (4, 6)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published SVG matching for edge (0, 3)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published SVG matching for edge (1, 2)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published SVG matching for edge (6, 7)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published SVG matching for edge (0, 5)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published SVG matching for edge (1, 4)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published SVG matching for edge (2, 3)",
      "status": "PASS",
      "detail": ""
    },
    {
      "test": "published cover edge set",
      "status": "PASS",
      "detail": ""
    }
  ],
  "count": 73,
  "summary": {
    "vertices": 8,
    "edges": 28,
    "vertex_degree": 7,
    "within_first_cycle": 6,
    "cross_cycle": 16,
    "within_second_cycle": 6,
    "matching_dimensions": [
      4,
      4,
      4,
      4,
      4,
      4,
      4
    ],
    "triangle_rank": 21,
    "potential_rank": 7
  },
  "new_basis_change": {
    "P": "Matrix([[1, 2 + sqrt(5)], [0, sqrt(5)]])",
    "L_M": "Matrix([[1 + sqrt(5), -sqrt(5) - 2], [1, -1]])",
    "scope": "Exact matrix conjugacy; separately derived here."
  }
}