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      "beta_at_zero_pairing": "0",
      "beta_epsilon_linear_pairing": "8/3",
      "B_pairing": "1/3"
    },
    {
      "id": "n6-asymmetric-2211",
      "mu": [
        "1/10",
        "1/5",
        "3/10",
        "2/5",
        "9/20",
        "11/20"
      ],
      "parts": [
        [
          0,
          4
        ],
        [
          1,
          5
        ],
        [
          2
        ],
        [
          3
        ]
      ],
      "kappa_pairing": "1",
      "beta_at_zero_pairing": "0",
      "beta_epsilon_linear_pairing": "2",
      "B_pairing": "1/4"
    }
  ],
  "sl2_fixtures": [
    {
      "id": "integer-noncommuting",
      "D": [
        [
          "5",
          "-7"
        ],
        [
          "-2",
          "3"
        ]
      ],
      "traces": {
        "a": "2",
        "b": "2",
        "c": "4",
        "d": "8",
        "x": "3",
        "y": "5",
        "z": "6"
      },
      "Fricke_residual": "0",
      "Phi_z": "3",
      "twist_numerator": "-3",
      "chart_nondegenerate": true,
      "scope": "Algebraic SL2 fixture; no global hyperbolic surface realization is asserted."
    },
    {
      "id": "rational-noncommuting",
      "D": [
        [
          "-31/3",
          "15/2"
        ],
        [
          "-19/3",
          "9/2"
        ]
      ],
      "traces": {
        "a": "5/2",
        "b": "3",
        "c": "0",
        "d": "-35/6",
        "x": "16/3",
        "y": "-1",
        "z": "-20/3"
      },
      "Fricke_residual": "0",
      "Phi_z": "-49/12",
      "twist_numerator": "49/12",
      "chart_nondegenerate": true,
      "scope": "Algebraic SL2 fixture; no global hyperbolic surface realization is asserted."
    },
    {
      "id": "identity-chart-degeneracy",
      "D": [
        [
          "1",
          "-1"
        ],
        [
          "-1",
          "2"
        ]
      ],
      "traces": {
        "a": "2",
        "b": "2",
        "c": "2",
        "d": "3",
        "x": "2",
        "y": "2",
        "z": "3"
      },
      "Fricke_residual": "0",
      "Phi_z": "0",
      "twist_numerator": "0",
      "chart_nondegenerate": false,
      "scope": "Algebraic SL2 fixture; no global hyperbolic surface realization is asserted."
    }
  ],
  "coverage_limits": [
    "The stated intersection relations and source theorems are inputs, not computer-proved geometry.",
    "Top intersections cover only n=4,5; three n=6 F-curve probes do not prove a general divisor identity.",
    "No numerical quadrature, all-genus volume engine, hyperideal cell solver, or global surface realization.",
    "Finite cohomology agreement does not prove local metric, measure, or pointwise convergence.",
    "Balanced walls use strict light subsets; each final polynomial is restricted to its stated chamber."
  ],
  "checks_passed": true,
  "elapsed_seconds": 0.09267837507650256
}