Finite verification record; does not score physical data. {
  "PSR": {
    "nodes": [
      "v0",
      "v1",
      "v2",
      "v3",
      "e01",
      "e02",
      "e03",
      "e12",
      "e13",
      "e23"
    ],
    "columns_tree_then_heldout": [
      [
        "v0",
        "e01"
      ],
      [
        "v0",
        "e02"
      ],
      [
        "v2",
        "e02"
      ],
      [
        "v3",
        "e03"
      ],
      [
        "v1",
        "e12"
      ],
      [
        "v2",
        "e12"
      ],
      [
        "v1",
        "e13"
      ],
      [
        "v2",
        "e23"
      ],
      [
        "v3",
        "e23"
      ],
      [
        "v1",
        "e01"
      ],
      [
        "v0",
        "e03"
      ],
      [
        "v3",
        "e13"
      ]
    ],
    "parity_matrix": [
      [
        1,
        1,
        1,
        0,
        1,
        1,
        0,
        0,
        0,
        1,
        0,
        0
      ],
      [
        0,
        1,
        1,
        1,
        0,
        0,
        0,
        1,
        1,
        0,
        1,
        0
      ],
      [
        0,
        0,
        0,
        0,
        1,
        1,
        1,
        1,
        1,
        0,
        0,
        1
      ]
    ],
    "weight_enumerator": {
      "0": 1,
      "2": 6,
      "3": 32,
      "4": 63,
      "5": 96,
      "6": 116,
      "7": 96,
      "8": 63,
      "9": 32,
      "10": 6,
      "12": 1
    },
    "single_error_syndrome_classes": {
      "1 0 0": [
        [
          "v0",
          "e01"
        ],
        [
          "v1",
          "e01"
        ]
      ],
      "1 1 0": [
        [
          "v0",
          "e02"
        ],
        [
          "v2",
          "e02"
        ]
      ],
      "0 1 0": [
        [
          "v3",
          "e03"
        ],
        [
          "v0",
          "e03"
        ]
      ],
      "1 0 1": [
        [
          "v1",
          "e12"
        ],
        [
          "v2",
          "e12"
        ]
      ],
      "0 0 1": [
        [
          "v1",
          "e13"
        ],
        [
          "v3",
          "e13"
        ]
      ],
      "0 1 1": [
        [
          "v2",
          "e23"
        ],
        [
          "v3",
          "e23"
        ]
      ]
    },
    "parameters": [
      12,
      9,
      2
    ],
    "frozen_split_sha256": "af979f74d99e7941b6c7bdfe92353fdf643f064727dc8afe004184960deab6fb"
  },
  "S4": {
    "basis": [
      "0",
      "1",
      "2",
      "3",
      "01",
      "02",
      "03",
      "12",
      "13",
      "23",
      "012",
      "013",
      "023",
      "123",
      "0123"
    ],
    "isotypic_ranks": {
      "trivial": 1,
      "standard": 6,
      "standard_sign": 6,
      "sign": 2
    },
    "characters": [
      {
        "permutation": [
          0,
          1,
          2,
          3
        ],
        "cycle_type": [
          1,
          1,
          1,
          1
        ],
        "chain_characters": [
          4,
          6,
          4,
          1
        ]
      },
      {
        "permutation": [
          0,
          1,
          3,
          2
        ],
        "cycle_type": [
          2,
          1,
          1
        ],
        "chain_characters": [
          "2",
          "0",
          "-2",
          -1
        ]
      },
      {
        "permutation": [
          0,
          2,
          1,
          3
        ],
        "cycle_type": [
          2,
          1,
          1
        ],
        "chain_characters": [
          "2",
          "0",
          "-2",
          -1
        ]
      },
      {
        "permutation": [
          0,
          2,
          3,
          1
        ],
        "cycle_type": [
          3,
          1
        ],
        "chain_characters": [
          "1",
          "0",
          "1",
          1
        ]
      },
      {
        "permutation": [
          0,
          3,
          1,
          2
        ],
        "cycle_type": [
          3,
          1
        ],
        "chain_characters": [
          "1",
          "0",
          "1",
          1
        ]
      },
      {
        "permutation": [
          0,
          3,
          2,
          1
        ],
        "cycle_type": [
          2,
          1,
          1
        ],
        "chain_characters": [
          "2",
          "0",
          "-2",
          -1
        ]
      },
      {
        "permutation": [
          1,
          0,
          2,
          3
        ],
        "cycle_type": [
          2,
          1,
          1
        ],
        "chain_characters": [
          "2",
          "0",
          "-2",
          -1
        ]
      },
      {
        "permutation": [
          1,
          0,
          3,
          2
        ],
        "cycle_type": [
          2,
          2
        ],
        "chain_characters": [
          "0",
          "-2",
          "0",
          1
        ]
      },
      {
        "permutation": [
          1,
          2,
          0,
          3
        ],
        "cycle_type": [
          3,
          1
        ],
        "chain_characters": [
          "1",
          "0",
          "1",
          1
        ]
      },
      {
        "permutation": [
          1,
          2,
          3,
          0
        ],
        "cycle_type": [
          4
        ],
        "chain_characters": [
          "0",
          "0",
          "0",
          -1
        ]
      },
      {
        "permutation": [
          1,
          3,
          0,
          2
        ],
        "cycle_type": [
          4
        ],
        "chain_characters": [
          "0",
          "0",
          "0",
          -1
        ]
      },
      {
        "permutation": [
          1,
          3,
          2,
          0
        ],
        "cycle_type": [
          3,
          1
        ],
        "chain_characters": [
          "1",
          "0",
          "1",
          1
        ]
      },
      {
        "permutation": [
          2,
          0,
          1,
          3
        ],
        "cycle_type": [
          3,
          1
        ],
        "chain_characters": [
          "1",
          "0",
          "1",
          1
        ]
      },
      {
        "permutation": [
          2,
          0,
          3,
          1
        ],
        "cycle_type": [
          4
        ],
        "chain_characters": [
          "0",
          "0",
          "0",
          -1
        ]
      },
      {
        "permutation": [
          2,
          1,
          0,
          3
        ],
        "cycle_type": [
          2,
          1,
          1
        ],
        "chain_characters": [
          "2",
          "0",
          "-2",
          -1
        ]
      },
      {
        "permutation": [
          2,
          1,
          3,
          0
        ],
        "cycle_type": [
          3,
          1
        ],
        "chain_characters": [
          "1",
          "0",
          "1",
          1
        ]
      },
      {
        "permutation": [
          2,
          3,
          0,
          1
        ],
        "cycle_type": [
          2,
          2
        ],
        "chain_characters": [
          "0",
          "-2",
          "0",
          1
        ]
      },
      {
        "permutation": [
          2,
          3,
          1,
          0
        ],
        "cycle_type": [
          4
        ],
        "chain_characters": [
          "0",
          "0",
          "0",
          -1
        ]
      },
      {
        "permutation": [
          3,
          0,
          1,
          2
        ],
        "cycle_type": [
          4
        ],
        "chain_characters": [
          "0",
          "0",
          "0",
          -1
        ]
      },
      {
        "permutation": [
          3,
          0,
          2,
          1
        ],
        "cycle_type": [
          3,
          1
        ],
        "chain_characters": [
          "1",
          "0",
          "1",
          1
        ]
      },
      {
        "permutation": [
          3,
          1,
          0,
          2
        ],
        "cycle_type": [
          3,
          1
        ],
        "chain_characters": [
          "1",
          "0",
          "1",
          1
        ]
      },
      {
        "permutation": [
          3,
          1,
          2,
          0
        ],
        "cycle_type": [
          2,
          1,
          1
        ],
        "chain_characters": [
          "2",
          "0",
          "-2",
          -1
        ]
      },
      {
        "permutation": [
          3,
          2,
          0,
          1
        ],
        "cycle_type": [
          4
        ],
        "chain_characters": [
          "0",
          "0",
          "0",
          -1
        ]
      },
      {
        "permutation": [
          3,
          2,
          1,
          0
        ],
        "cycle_type": [
          2,
          2
        ],
        "chain_characters": [
          "0",
          "-2",
          "0",
          1
        ]
      }
    ],
    "grade_projector_ranks": {
      "trivial": [
        1,
        0,
        0,
        0
      ],
      "standard": [
        3,
        3,
        0,
        0
      ],
      "standard_sign": [
        0,
        3,
        3,
        0
      ],
      "sign": [
        0,
        0,
        1,
        1
      ]
    },
    "symbolic_classification": "A(a,b,c)=a A1+b A2+c A3; A^2=-4(a^2 P_V+b^2 P_Vsign+c^2 P_sign)",
    "unit_characteristic_polynomial": "lambda*(lambda^2+4)^7"
  },
  "Smith": {
    "K4": {
      "edges": [
        [
          0,
          1
        ],
        [
          0,
          2
        ],
        [
          0,
          3
        ],
        [
          1,
          2
        ],
        [
          1,
          3
        ],
        [
          2,
          3
        ]
      ],
      "deleted_vertex": 0,
      "reduced_laplacian": [
        [
          3,
          -1,
          -1
        ],
        [
          -1,
          3,
          -1
        ],
        [
          -1,
          -1,
          3
        ]
      ],
      "determinantal_divisors_including_Delta0": [
        1,
        1,
        4,
        16
      ],
      "Smith_diagonal": [
        1,
        4,
        4
      ],
      "group_order": 16
    },
    "K1_4": {
      "edges": [
        [
          0,
          1
        ],
        [
          0,
          2
        ],
        [
          0,
          3
        ],
        [
          0,
          4
        ]
      ],
      "deleted_vertex": 0,
      "reduced_laplacian": [
        [
          1,
          0,
          0,
          0
        ],
        [
          0,
          1,
          0,
          0
        ],
        [
          0,
          0,
          1,
          0
        ],
        [
          0,
          0,
          0,
          1
        ]
      ],
      "determinantal_divisors_including_Delta0": [
        1,
        1,
        1,
        1,
        1
      ],
      "Smith_diagonal": [
        1,
        1,
        1,
        1
      ],
      "group_order": 1
    },
    "K5_minus_34": {
      "edges": [
        [
          0,
          1
        ],
        [
          0,
          2
        ],
        [
          0,
          3
        ],
        [
          0,
          4
        ],
        [
          1,
          2
        ],
        [
          1,
          3
        ],
        [
          1,
          4
        ],
        [
          2,
          3
        ],
        [
          2,
          4
        ]
      ],
      "deleted_vertex": 0,
      "reduced_laplacian": [
        [
          4,
          -1,
          -1,
          -1
        ],
        [
          -1,
          4,
          -1,
          -1
        ],
        [
          -1,
          -1,
          3,
          0
        ],
        [
          -1,
          -1,
          0,
          3
        ]
      ],
      "determinantal_divisors_including_Delta0": [
        1,
        1,
        1,
        5,
        75
      ],
      "Smith_diagonal": [
        1,
        1,
        5,
        15
      ],
      "group_order": 75
    }
  },
  "status": "PASS",
  "physical_promotion": 0,
  "independent_review": false,
  "empirical_data_used": false,
  "checks": [
    "PSR tree/heldout counts",
    "PSR frozen root",
    "PSR parity systematic right block",
    "PSR H F = 0 over F2",
    "PSR exactly 512 relative classes",
    "PSR distance two",
    "PSR all codewords pass parity",
    "PSR every single error detected",
    "PSR six indistinguishable pairs",
    "PSR each ambiguous pair shares edge amplitude",
    "S4 signed action orthogonal (0, 1, 2, 3)",
    "S4 boundary equivariance (0, 1, 2, 3)",
    "S4 signed action orthogonal (0, 1, 3, 2)",
    "S4 boundary equivariance (0, 1, 3, 2)",
    "S4 signed action orthogonal (0, 2, 1, 3)",
    "S4 boundary equivariance (0, 2, 1, 3)",
    "S4 signed action orthogonal (0, 2, 3, 1)",
    "S4 boundary equivariance (0, 2, 3, 1)",
    "S4 signed action orthogonal (0, 3, 1, 2)",
    "S4 boundary equivariance (0, 3, 1, 2)",
    "S4 signed action orthogonal (0, 3, 2, 1)",
    "S4 boundary equivariance (0, 3, 2, 1)",
    "S4 signed action orthogonal (1, 0, 2, 3)",
    "S4 boundary equivariance (1, 0, 2, 3)",
    "S4 signed action orthogonal (1, 0, 3, 2)",
    "S4 boundary equivariance (1, 0, 3, 2)",
    "S4 signed action orthogonal (1, 2, 0, 3)",
    "S4 boundary equivariance (1, 2, 0, 3)",
    "S4 signed action orthogonal (1, 2, 3, 0)",
    "S4 boundary equivariance (1, 2, 3, 0)",
    "S4 signed action orthogonal (1, 3, 0, 2)",
    "S4 boundary equivariance (1, 3, 0, 2)",
    "S4 signed action orthogonal (1, 3, 2, 0)",
    "S4 boundary equivariance (1, 3, 2, 0)",
    "S4 signed action orthogonal (2, 0, 1, 3)",
    "S4 boundary equivariance (2, 0, 1, 3)",
    "S4 signed action orthogonal (2, 0, 3, 1)",
    "S4 boundary equivariance (2, 0, 3, 1)",
    "S4 signed action orthogonal (2, 1, 0, 3)",
    "S4 boundary equivariance (2, 1, 0, 3)",
    "S4 signed action orthogonal (2, 1, 3, 0)",
    "S4 boundary equivariance (2, 1, 3, 0)",
    "S4 signed action orthogonal (2, 3, 0, 1)",
    "S4 boundary equivariance (2, 3, 0, 1)",
    "S4 signed action orthogonal (2, 3, 1, 0)",
    "S4 boundary equivariance (2, 3, 1, 0)",
    "S4 signed action orthogonal (3, 0, 1, 2)",
    "S4 boundary equivariance (3, 0, 1, 2)",
    "S4 signed action orthogonal (3, 0, 2, 1)",
    "S4 boundary equivariance (3, 0, 2, 1)",
    "S4 signed action orthogonal (3, 1, 0, 2)",
    "S4 boundary equivariance (3, 1, 0, 2)",
    "S4 signed action orthogonal (3, 1, 2, 0)",
    "S4 boundary equivariance (3, 1, 2, 0)",
    "S4 signed action orthogonal (3, 2, 0, 1)",
    "S4 boundary equivariance (3, 2, 0, 1)",
    "S4 signed action orthogonal (3, 2, 1, 0)",
    "S4 boundary equivariance (3, 2, 1, 0)",
    "S4 boundary nilpotency",
    "S4 absent 2D projector",
    "S4 projectors resolve identity",
    "S4 symmetric idempotent trivial",
    "S4 projector commutes A trivial",
    "S4 projector equivariance trivial 0",
    "S4 projector equivariance trivial 1",
    "S4 projector equivariance trivial 2",
    "S4 projector equivariance trivial 3",
    "S4 projector equivariance trivial 4",
    "S4 projector equivariance trivial 5",
    "S4 projector equivariance trivial 6",
    "S4 projector equivariance trivial 7",
    "S4 projector equivariance trivial 8",
    "S4 projector equivariance trivial 9",
    "S4 projector equivariance trivial 10",
    "S4 projector equivariance trivial 11",
    "S4 projector equivariance trivial 12",
    "S4 projector equivariance trivial 13",
    "S4 projector equivariance trivial 14",
    "S4 projector equivariance trivial 15",
    "S4 projector equivariance trivial 16",
    "S4 projector equivariance trivial 17",
    "S4 projector equivariance trivial 18",
    "S4 projector equivariance trivial 19",
    "S4 projector equivariance trivial 20",
    "S4 projector equivariance trivial 21",
    "S4 projector equivariance trivial 22",
    "S4 projector equivariance trivial 23",
    "S4 symmetric idempotent standard",
    "S4 projector commutes A standard",
    "S4 projector equivariance standard 0",
    "S4 projector equivariance standard 1",
    "S4 projector equivariance standard 2",
    "S4 projector equivariance standard 3",
    "S4 projector equivariance standard 4",
    "S4 projector equivariance standard 5",
    "S4 projector equivariance standard 6",
    "S4 projector equivariance standard 7",
    "S4 projector equivariance standard 8",
    "S4 projector equivariance standard 9",
    "S4 projector equivariance standard 10",
    "S4 projector equivariance standard 11",
    "S4 projector equivariance standard 12",
    "S4 projector equivariance standard 13",
    "S4 projector equivariance standard 14",
    "S4 projector equivariance standard 15",
    "S4 projector equivariance standard 16",
    "S4 projector equivariance standard 17",
    "S4 projector equivariance standard 18",
    "S4 projector equivariance standard 19",
    "S4 projector equivariance standard 20",
    "S4 projector equivariance standard 21",
    "S4 projector equivariance standard 22",
    "S4 projector equivariance standard 23",
    "S4 symmetric idempotent standard_sign",
    "S4 projector commutes A standard_sign",
    "S4 projector equivariance standard_sign 0",
    "S4 projector equivariance standard_sign 1",
    "S4 projector equivariance standard_sign 2",
    "S4 projector equivariance standard_sign 3",
    "S4 projector equivariance standard_sign 4",
    "S4 projector equivariance standard_sign 5",
    "S4 projector equivariance standard_sign 6",
    "S4 projector equivariance standard_sign 7",
    "S4 projector equivariance standard_sign 8",
    "S4 projector equivariance standard_sign 9",
    "S4 projector equivariance standard_sign 10",
    "S4 projector equivariance standard_sign 11",
    "S4 projector equivariance standard_sign 12",
    "S4 projector equivariance standard_sign 13",
    "S4 projector equivariance standard_sign 14",
    "S4 projector equivariance standard_sign 15",
    "S4 projector equivariance standard_sign 16",
    "S4 projector equivariance standard_sign 17",
    "S4 projector equivariance standard_sign 18",
    "S4 projector equivariance standard_sign 19",
    "S4 projector equivariance standard_sign 20",
    "S4 projector equivariance standard_sign 21",
    "S4 projector equivariance standard_sign 22",
    "S4 projector equivariance standard_sign 23",
    "S4 symmetric idempotent sign",
    "S4 projector commutes A sign",
    "S4 projector equivariance sign 0",
    "S4 projector equivariance sign 1",
    "S4 projector equivariance sign 2",
    "S4 projector equivariance sign 3",
    "S4 projector equivariance sign 4",
    "S4 projector equivariance sign 5",
    "S4 projector equivariance sign 6",
    "S4 projector equivariance sign 7",
    "S4 projector equivariance sign 8",
    "S4 projector equivariance sign 9",
    "S4 projector equivariance sign 10",
    "S4 projector equivariance sign 11",
    "S4 projector equivariance sign 12",
    "S4 projector equivariance sign 13",
    "S4 projector equivariance sign 14",
    "S4 projector equivariance sign 15",
    "S4 projector equivariance sign 16",
    "S4 projector equivariance sign 17",
    "S4 projector equivariance sign 18",
    "S4 projector equivariance sign 19",
    "S4 projector equivariance sign 20",
    "S4 projector equivariance sign 21",
    "S4 projector equivariance sign 22",
    "S4 projector equivariance sign 23",
    "S4 orthogonal trivial standard",
    "S4 orthogonal trivial standard_sign",
    "S4 orthogonal trivial sign",
    "S4 orthogonal standard standard_sign",
    "S4 orthogonal standard sign",
    "S4 orthogonal standard_sign sign",
    "S4 isotypic ranks",
    "S4 boundary projector formula standard",
    "S4 cross block product (0, 1)",
    "S4 cross block product (0, 2)",
    "S4 boundary projector formula standard_sign",
    "S4 cross block product (1, 0)",
    "S4 cross block product (1, 2)",
    "S4 boundary projector formula sign",
    "S4 cross block product (2, 0)",
    "S4 cross block product (2, 1)",
    "S4 unit weight square",
    "S4 unequal frequency witness",
    "Smith factors K4",
    "Smith determinant K4",
    "Smith divisibility K4",
    "Smith factors K1_4",
    "Smith determinant K1_4",
    "Smith divisibility K1_4",
    "Smith factors K5_minus_34",
    "Smith determinant K5_minus_34",
    "Smith divisibility K5_minus_34"
  ],
  "check_count": 192
}
