{
  "format": "triangle-packing-finite-domain-proofs/v1",
  "version": "2.0.0",
  "proofs": [
    {
      "proofId": "finite-right-grid-control-v1",
      "linkedRecordId": "iso-a90-r0p75",
      "relation": "same_piece_family_control",
      "claim": "Optimal only within the declared finite candidate domain; not a global packing claim.",
      "certificate": {
        "format": "triangle-packing-certificate/v3",
        "type": "finite_candidate_domain",
        "claim": "optimal_within_declared_finite_candidate_domain",
        "globallyOptimal": false,
        "domain": {
          "format": "tpa-finite-candidate-domain/v1",
          "problem": {
            "width": 3,
            "height": 2,
            "sides": [
              1,
              1,
              1.414213562373095
            ]
          },
          "specification": {
            "generator": "cartesian-grid/v1",
            "xStep": 1,
            "yStep": 1,
            "angles": [
              0,
              6.283185307179586
            ],
            "reflections": [
              false
            ],
            "quantum": 1e-9
          },
          "candidates": [
            {
              "x": 0,
              "y": 0,
              "angle": 0,
              "reflect": false
            },
            {
              "x": 0,
              "y": 0,
              "angle": 6.283185307,
              "reflect": false
            },
            {
              "x": 0,
              "y": 1,
              "angle": 0,
              "reflect": false
            },
            {
              "x": 0,
              "y": 1,
              "angle": 6.283185307,
              "reflect": false
            },
            {
              "x": 1,
              "y": 0,
              "angle": 0,
              "reflect": false
            },
            {
              "x": 1,
              "y": 0,
              "angle": 6.283185307,
              "reflect": false
            },
            {
              "x": 1,
              "y": 1,
              "angle": 0,
              "reflect": false
            },
            {
              "x": 1,
              "y": 1,
              "angle": 6.283185307,
              "reflect": false
            }
          ],
          "candidateCount": 8,
          "canonicalPayload": "{\"candidates\":[{\"angle\":0,\"reflect\":false,\"x\":0,\"y\":0},{\"angle\":6.283185307,\"reflect\":false,\"x\":0,\"y\":0},{\"angle\":0,\"reflect\":false,\"x\":0,\"y\":1},{\"angle\":6.283185307,\"reflect\":false,\"x\":0,\"y\":1},{\"angle\":0,\"reflect\":false,\"x\":1,\"y\":0},{\"angle\":6.283185307,\"reflect\":false,\"x\":1,\"y\":0},{\"angle\":0,\"reflect\":false,\"x\":1,\"y\":1},{\"angle\":6.283185307,\"reflect\":false,\"x\":1,\"y\":1}],\"problem\":{\"height\":2,\"sides\":[1,1,1.414213562373095],\"width\":3},\"specification\":{\"angles\":[0,6.283185307179586],\"generator\":\"cartesian-grid/v1\",\"quantum\":1e-9,\"reflections\":[false],\"xStep\":1,\"yStep\":1}}",
          "sha256": "7e5df5ed2aa8221bcafd7292e6d8c814ff0b1dbf5838c786b36cba3e7fa2a432"
        },
        "conflictGraph": {
          "format": "tpa-finite-conflict-graph/v1",
          "domainSha256": "7e5df5ed2aa8221bcafd7292e6d8c814ff0b1dbf5838c786b36cba3e7fa2a432",
          "adjacency": [
            [
              1,
              4,
              5
            ],
            [
              0,
              4,
              5
            ],
            [
              3,
              6,
              7
            ],
            [
              2,
              6,
              7
            ],
            [
              0,
              1,
              5
            ],
            [
              0,
              1,
              4
            ],
            [
              2,
              3,
              7
            ],
            [
              2,
              3,
              6
            ]
          ],
          "edgeCount": 12,
          "sha256": "b38ea11316b3664ce8f63f5a27b2a0633815208f902d85778b7f9cd02e3118b0"
        },
        "selectedIndices": [
          0,
          2
        ],
        "cliqueCover": [
          [
            0,
            1,
            4,
            5
          ],
          [
            2,
            3,
            6,
            7
          ]
        ],
        "optimum": 2,
        "solver": {
          "algorithm": "component-aware-bitset-branch-and-bound/v1",
          "components": 2,
          "componentSizes": [
            4,
            4
          ],
          "independentSetNodes": 14,
          "cliqueCoverNodes": 10,
          "maxSearchNodes": 100000
        },
        "canonicalPayload": "{\"claim\":\"optimal_within_declared_finite_candidate_domain\",\"cliqueCover\":[[0,1,4,5],[2,3,6,7]],\"conflictGraph\":{\"adjacency\":[[1,4,5],[0,4,5],[3,6,7],[2,6,7],[0,1,5],[0,1,4],[2,3,7],[2,3,6]],\"domainSha256\":\"7e5df5ed2aa8221bcafd7292e6d8c814ff0b1dbf5838c786b36cba3e7fa2a432\",\"edgeCount\":12,\"format\":\"tpa-finite-conflict-graph/v1\",\"sha256\":\"b38ea11316b3664ce8f63f5a27b2a0633815208f902d85778b7f9cd02e3118b0\"},\"domain\":{\"candidateCount\":8,\"candidates\":[{\"angle\":0,\"reflect\":false,\"x\":0,\"y\":0},{\"angle\":6.283185307,\"reflect\":false,\"x\":0,\"y\":0},{\"angle\":0,\"reflect\":false,\"x\":0,\"y\":1},{\"angle\":6.283185307,\"reflect\":false,\"x\":0,\"y\":1},{\"angle\":0,\"reflect\":false,\"x\":1,\"y\":0},{\"angle\":6.283185307,\"reflect\":false,\"x\":1,\"y\":0},{\"angle\":0,\"reflect\":false,\"x\":1,\"y\":1},{\"angle\":6.283185307,\"reflect\":false,\"x\":1,\"y\":1}],\"canonicalPayload\":\"{\\\"candidates\\\":[{\\\"angle\\\":0,\\\"reflect\\\":false,\\\"x\\\":0,\\\"y\\\":0},{\\\"angle\\\":6.283185307,\\\"reflect\\\":false,\\\"x\\\":0,\\\"y\\\":0},{\\\"angle\\\":0,\\\"reflect\\\":false,\\\"x\\\":0,\\\"y\\\":1},{\\\"angle\\\":6.283185307,\\\"reflect\\\":false,\\\"x\\\":0,\\\"y\\\":1},{\\\"angle\\\":0,\\\"reflect\\\":false,\\\"x\\\":1,\\\"y\\\":0},{\\\"angle\\\":6.283185307,\\\"reflect\\\":false,\\\"x\\\":1,\\\"y\\\":0},{\\\"angle\\\":0,\\\"reflect\\\":false,\\\"x\\\":1,\\\"y\\\":1},{\\\"angle\\\":6.283185307,\\\"reflect\\\":false,\\\"x\\\":1,\\\"y\\\":1}],\\\"problem\\\":{\\\"height\\\":2,\\\"sides\\\":[1,1,1.414213562373095],\\\"width\\\":3},\\\"specification\\\":{\\\"angles\\\":[0,6.283185307179586],\\\"generator\\\":\\\"cartesian-grid/v1\\\",\\\"quantum\\\":1e-9,\\\"reflections\\\":[false],\\\"xStep\\\":1,\\\"yStep\\\":1}}\",\"format\":\"tpa-finite-candidate-domain/v1\",\"problem\":{\"height\":2,\"sides\":[1,1,1.414213562373095],\"width\":3},\"sha256\":\"7e5df5ed2aa8221bcafd7292e6d8c814ff0b1dbf5838c786b36cba3e7fa2a432\",\"specification\":{\"angles\":[0,6.283185307179586],\"generator\":\"cartesian-grid/v1\",\"quantum\":1e-9,\"reflections\":[false],\"xStep\":1,\"yStep\":1}},\"format\":\"triangle-packing-certificate/v3\",\"globallyOptimal\":false,\"optimum\":2,\"selectedIndices\":[0,2],\"solver\":{\"algorithm\":\"component-aware-bitset-branch-and-bound/v1\",\"cliqueCoverNodes\":10,\"componentSizes\":[4,4],\"components\":2,\"independentSetNodes\":14,\"maxSearchNodes\":100000},\"type\":\"finite_candidate_domain\"}",
        "sha256": "2704f0905af9f088b6b61f60f90f08c666ce5c1804d4602c655b54b6ed010305"
      }
    }
  ]
}
