{
  "status": "PASS",
  "seed": 20261001,
  "trials": 10000,
  "seconds": 0.744632234999699,
  "scope": "Random trials with repeats possible; n=3..10, K=3..16. Optima enumerate all binary orders. Every new record is checked by the independent cycle LP oracle. No universal guarantee follows from this experiment.",
  "records": {
    "small": [
      {
        "K": 14,
        "x": [
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          14,
          14
        ],
        "y": [
          7,
          1,
          1,
          2,
          6,
          3,
          4,
          4,
          7,
          1
        ],
        "order": [
          1,
          1,
          1,
          1,
          1,
          14,
          1,
          1,
          1,
          14
        ],
        "cost": 15,
        "optimal_order": [
          1,
          1,
          1,
          1,
          14,
          1,
          1,
          1,
          14,
          1
        ],
        "OPT": 14,
        "initial_lp": 7
      },
      {
        "K": 11,
        "x": [
          1,
          1,
          1,
          1,
          1,
          11,
          11,
          11,
          11
        ],
        "y": [
          6,
          1,
          4,
          10,
          1,
          2,
          16,
          3,
          6
        ],
        "order": [
          1,
          1,
          1,
          11,
          1,
          11,
          1,
          11,
          11
        ],
        "cost": 19,
        "optimal_order": [
          11,
          1,
          1,
          11,
          1,
          1,
          11,
          11,
          1
        ],
        "OPT": 16,
        "initial_lp": 16
      },
      {
        "K": 14,
        "x": [
          1,
          1,
          1,
          14,
          14,
          14
        ],
        "y": [
          2,
          5,
          10,
          15,
          7,
          6
        ],
        "order": [
          1,
          1,
          14,
          14,
          14,
          1
        ],
        "cost": 18,
        "optimal_order": [
          1,
          14,
          1,
          14,
          14,
          1
        ],
        "OPT": 15,
        "initial_lp": 15
      },
      {
        "K": 7,
        "x": [
          1,
          1,
          1,
          1,
          1,
          7,
          7,
          7,
          7
        ],
        "y": [
          6,
          2,
          1,
          1,
          2,
          5,
          10,
          1,
          5
        ],
        "order": [
          1,
          7,
          1,
          1,
          1,
          7,
          7,
          1,
          7
        ],
        "cost": 13,
        "optimal_order": [
          7,
          7,
          1,
          1,
          1,
          1,
          7,
          7,
          1
        ],
        "OPT": 10,
        "initial_lp": 10
      },
      {
        "K": 12,
        "x": [
          1,
          1,
          1,
          1,
          12,
          12
        ],
        "y": [
          3,
          2,
          7,
          1,
          11,
          4
        ],
        "order": [
          1,
          1,
          12,
          1,
          1,
          12
        ],
        "cost": 17,
        "optimal_order": [
          1,
          1,
          1,
          12,
          1,
          12
        ],
        "OPT": 13,
        "initial_lp": 11
      },
      {
        "K": 3,
        "x": [
          1,
          1,
          3,
          3,
          3
        ],
        "y": [
          2,
          2,
          3,
          2,
          2
        ],
        "order": [
          1,
          3,
          1,
          3,
          3
        ],
        "cost": 4,
        "optimal_order": [
          3,
          1,
          3,
          3,
          1
        ],
        "OPT": 3,
        "initial_lp": 3
      },
      {
        "K": 5,
        "x": [
          1,
          1,
          1,
          5,
          5,
          5
        ],
        "y": [
          2,
          2,
          3,
          5,
          4,
          2
        ],
        "order": [
          1,
          1,
          5,
          1,
          5,
          5
        ],
        "cost": 7,
        "optimal_order": [
          5,
          1,
          1,
          5,
          5,
          1
        ],
        "OPT": 5,
        "initial_lp": 5
      }
    ],
    "large": [
      {
        "K": 14,
        "x": [
          14,
          14,
          14,
          1,
          1,
          1,
          1,
          1,
          1
        ],
        "y": [
          2,
          2,
          15,
          10,
          3,
          2,
          3,
          4,
          7
        ],
        "order": [
          14,
          1,
          1,
          14,
          1,
          14,
          1,
          1,
          1
        ],
        "cost": 17,
        "optimal_order": [
          1,
          1,
          14,
          14,
          1,
          1,
          14,
          1,
          1
        ],
        "OPT": 15,
        "initial_lp": 15
      },
      {
        "K": 13,
        "x": [
          13,
          13,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1
        ],
        "y": [
          1,
          8,
          2,
          3,
          3,
          4,
          1,
          10,
          1,
          1
        ],
        "order": [
          1,
          1,
          1,
          1,
          13,
          1,
          1,
          1,
          13,
          1
        ],
        "cost": 15,
        "optimal_order": [
          13,
          1,
          1,
          1,
          1,
          13,
          1,
          1,
          1,
          1
        ],
        "OPT": 13,
        "initial_lp": 10
      },
      {
        "K": 16,
        "x": [
          16,
          16,
          16,
          1,
          1,
          1,
          1
        ],
        "y": [
          1,
          10,
          18,
          11,
          4,
          6,
          2
        ],
        "order": [
          16,
          1,
          16,
          16,
          1,
          1,
          1
        ],
        "cost": 22,
        "optimal_order": [
          1,
          1,
          16,
          16,
          1,
          16,
          1
        ],
        "OPT": 18,
        "initial_lp": 18
      },
      {
        "K": 9,
        "x": [
          9,
          9,
          9,
          9,
          1,
          1,
          1,
          1,
          1,
          1
        ],
        "y": [
          4,
          11,
          1,
          5,
          3,
          9,
          1,
          4,
          3,
          1
        ],
        "order": [
          9,
          9,
          9,
          1,
          1,
          9,
          1,
          1,
          1,
          1
        ],
        "cost": 14,
        "optimal_order": [
          1,
          9,
          9,
          1,
          1,
          9,
          9,
          1,
          1,
          1
        ],
        "OPT": 11,
        "initial_lp": 11
      },
      {
        "K": 9,
        "x": [
          9,
          9,
          9,
          1,
          1,
          1,
          1,
          1,
          1,
          1
        ],
        "y": [
          1,
          1,
          5,
          9,
          1,
          5,
          6,
          2,
          1,
          3
        ],
        "order": [
          9,
          1,
          1,
          9,
          9,
          1,
          1,
          1,
          1,
          1
        ],
        "cost": 13,
        "optimal_order": [
          1,
          1,
          1,
          9,
          9,
          1,
          1,
          9,
          1,
          1
        ],
        "OPT": 10,
        "initial_lp": 9
      },
      {
        "K": 10,
        "x": [
          10,
          10,
          10,
          1,
          1,
          1,
          1,
          1
        ],
        "y": [
          5,
          11,
          2,
          4,
          6,
          3,
          3,
          1
        ],
        "order": [
          10,
          10,
          10,
          1,
          1,
          1,
          1,
          1
        ],
        "cost": 15,
        "optimal_order": [
          1,
          10,
          10,
          1,
          1,
          10,
          1,
          1
        ],
        "OPT": 11,
        "initial_lp": 11
      },
      {
        "K": 5,
        "x": [
          5,
          5,
          1,
          1,
          1,
          1,
          1,
          1,
          1,
          1
        ],
        "y": [
          3,
          1,
          1,
          5,
          1,
          2,
          1,
          2,
          1,
          1
        ],
        "order": [
          5,
          1,
          1,
          5,
          1,
          1,
          1,
          1,
          1,
          1
        ],
        "cost": 7,
        "optimal_order": [
          1,
          5,
          1,
          1,
          5,
          1,
          1,
          1,
          1,
          1
        ],
        "OPT": 5,
        "initial_lp": 5
      },
      {
        "K": 16,
        "x": [
          16,
          16,
          16,
          1,
          1,
          1,
          1,
          1,
          1,
          1
        ],
        "y": [
          7,
          3,
          3,
          2,
          8,
          2,
          2,
          6,
          16,
          6
        ],
        "order": [
          16,
          1,
          1,
          1,
          1,
          16,
          1,
          1,
          16,
          1
        ],
        "cost": 24,
        "optimal_order": [
          1,
          1,
          1,
          16,
          1,
          1,
          1,
          1,
          16,
          16
        ],
        "OPT": 16,
        "initial_lp": 16
      }
    ]
  }
}