{
  "desired": {
    "net": [
      [
        -1,
        -1
      ],
      [
        1,
        4
      ]
    ],
    "boundary_determinant": -3,
    "search": {
      "status": "yes",
      "attempted": 5,
      "admissible": 1,
      "witness": {
        "certificate": {
          "left": [
            [
              1,
              1
            ],
            [
              0,
              0
            ]
          ],
          "right": [
            [
              0,
              0
            ],
            [
              1,
              4
            ]
          ],
          "entities": [
            0,
            1
          ],
          "reactions": [
            0,
            1
          ],
          "flow": [
            -5,
            2
          ]
        },
        "verification": {
          "accepted": true,
          "certificate": "motif; PAC existence follows by finite descent",
          "minimality": "not checked",
          "production": [
            "3",
            "3"
          ],
          "reasons": []
        },
        "determinant": -3,
        "integer_flow_bound": 8,
        "max_flow_bits": 3,
        "minimality": "PAC certified by exhaustive exclusion of every smaller square witness"
      }
    }
  },
  "crossed": {
    "net": [
      [
        -1,
        2
      ],
      [
        1,
        -2
      ]
    ],
    "boundary_determinant": 0,
    "search": {
      "status": "no_exhaustive",
      "attempted": 5,
      "admissible": 1,
      "scope": "Every square support was checked; this is exponential enumeration, not a polynomial-time solver."
    }
  }
}