{
  "status": "PASS",
  "checks": 17263,
  "groups": {
    "complete representation dimensions": 1,
    "representation multiplication": 108,
    "unitary matrices": 18,
    "matrix coefficient orthogonality": 36,
    "delta convolution direction": 36,
    "full bilinear convolution on basis": 36,
    "all ternary S3 inversion": 729,
    "direct versus weighted block rank": 729,
    "complex support rank inequality": 729,
    "real Plancherel": 729,
    "class function iff scalar blocks": 729,
    "complex irrational inversion": 36,
    "complex ordered convolution": 36,
    "complex Plancherel": 36,
    "group involution adjoint": 36,
    "noncentral nilpotent block": 1,
    "nonzero nilpotent convolution": 1,
    "nilpotent unit two sided inverse": 1,
    "explicit general kernel inverse": 1,
    "original group inverse verification": 1,
    "shear singular square polynomial": 1,
    "block and direct compatibility": 56,
    "block solution original residual": 32,
    "all solution freedom complete": 32,
    "kernel freedom original residual": 32,
    "changed basis algebraic inversion": 12,
    "changed basis ranks": 12,
    "nonunitary basis changes raw Frobenius norm": 1,
    "arbitrary field support rank": 4174,
    "actual translate basis support cover": 4170,
    "all S3 subgroups": 1,
    "subgroup equality all fields": 18,
    "exact retained row coset criterion": 1152,
    "uniform erasure guarantee": 1152,
    "erasure ambiguity dimension": 1152,
    "erasure original message recovery": 582,
    "incompatible retained data rejected": 648,
    "modular simple block loses nonzero rank": 1,
    "invalid contract rejected": 6
  },
  "records": {
    "group_order": [
      "e",
      "r",
      "r^2",
      "s",
      "rs",
      "r^2s"
    ],
    "noncentral_nilpotent": {
      "values": [
        "0",
        "-1",
        "1",
        "0",
        "1",
        "-1"
      ],
      "blocks": [
        [
          [
            "0"
          ]
        ],
        [
          [
            "0"
          ]
        ],
        [
          [
            "0",
            "2*sqrt(3)"
          ],
          [
            "0",
            "0"
          ]
        ]
      ],
      "rank": 2,
      "support": 4
    },
    "general_inverse": {
      "kernel": [
        "2",
        "1",
        "0",
        "1",
        "0",
        "0"
      ],
      "inverse": [
        "5/8",
        "-3/8",
        "1/8",
        "-3/8",
        "1/8",
        "1/8"
      ],
      "blocks": [
        [
          [
            "4"
          ]
        ],
        [
          [
            "2"
          ]
        ],
        [
          [
            "5/2",
            "-1/2*sqrt(3)"
          ],
          [
            "1/2*sqrt(3)",
            "1/2"
          ]
        ]
      ]
    },
    "singular_kernel": {
      "values": [
        "1",
        "0",
        "0",
        "-1",
        "0",
        "0"
      ],
      "blocks": [
        [
          [
            "0"
          ]
        ],
        [
          [
            "2"
          ]
        ],
        [
          [
            "0",
            "0"
          ],
          [
            "0",
            "2"
          ]
        ]
      ],
      "rank": 3
    }
  },
  "scope": "Exact S3 arithmetic over Q(sqrt(3),i); original-matrix rank over F2/F3/F5 and finite erasure tests. General proofs, arbitrary complex input and arbitrary groups are justified by the articles, not by finite enumeration."
}