{
  "release": "AXIORYN-CRYSTAL 1.0.0",
  "arithmetic": "exact rational; no floating tolerances",
  "environment": {
    "python": "3.13.5",
    "sympy": "1.14.0"
  },
  "two_active_normal_components": {
    "matrix": [
      [
        "34/25",
        "12/25",
        "0"
      ],
      [
        "-6/25",
        "17/25",
        "0"
      ],
      [
        "0",
        "0",
        "1"
      ]
    ],
    "gram": [
      [
        "52/25",
        "0",
        "0"
      ],
      [
        "0",
        "13/25",
        "0"
      ],
      [
        "0",
        "0",
        "1"
      ]
    ],
    "active_normal_components": 2,
    "support": [
      0,
      1
    ],
    "ratios": {
      "0": "2",
      "1": "1/2"
    },
    "same_jacobian": false,
    "determinant_ratio": "26/25"
  },
  "scale_compiler": {
    "positive_components": 4,
    "basis": [
      [
        "1",
        "0",
        "0",
        "0"
      ],
      [
        "0",
        "1",
        "0",
        "0"
      ],
      [
        "0",
        "0",
        "1",
        "0"
      ],
      [
        "0",
        "0",
        "0",
        "1"
      ],
      [
        "0",
        "1",
        "0",
        "0"
      ],
      [
        "0",
        "0",
        "1",
        "0"
      ]
    ]
  },
  "pl_reconstruction": {
    "integrable": true,
    "coordinates": [
      [
        "0",
        "0",
        "0"
      ],
      [
        "0",
        "2",
        "0"
      ],
      [
        "0",
        "0",
        "3"
      ],
      [
        "-1",
        "0",
        "0"
      ],
      [
        "2",
        "0",
        "0"
      ]
    ],
    "jacobians": [
      [
        [
          "1",
          "0",
          "0"
        ],
        [
          "0",
          "2",
          "0"
        ],
        [
          "0",
          "0",
          "3"
        ]
      ],
      [
        [
          "2",
          "0",
          "0"
        ],
        [
          "0",
          "2",
          "0"
        ],
        [
          "0",
          "0",
          "3"
        ]
      ]
    ],
    "determinants": [
      "6",
      "12"
    ],
    "global_injectivity": "NOT_CERTIFIED",
    "hexahedral_extraction": "NOT_PERFORMED"
  },
  "real_gauge_quotient": {
    "B": [
      [
        "2"
      ],
      [
        "0"
      ]
    ],
    "C": [
      [
        "0",
        "1"
      ]
    ],
    "right_inverse": [
      [
        "0"
      ],
      [
        "1"
      ]
    ],
    "note": "No mod-2 obstruction with real chart origins."
  },
  "coupled_optimum": {
    "alpha": [
      [
        "1"
      ]
    ],
    "cost": "2601/20000",
    "active_state": [
      0
    ],
    "active_sets_examined": 3,
    "integer_target": [
      [
        "1"
      ],
      [
        "2"
      ]
    ],
    "targets_examined": 2,
    "feasible_targets": 1
  },
  "claims_not_tested": [
    "general hex extraction",
    "HexMe performance",
    "external peer review",
    "historical novelty"
  ]
}