{
  "status": "passed",
  "arithmetic": "exact Z[omega] 9x9 matrices",
  "backend_sha256": "074fa5beaa92d8579f90fb5f0658b567f1ab9bf166d88d759dce5a2e5933c7a9",
  "candidate_C4": true,
  "candidate_C3": false,
  "all_pauli_classes_checked_at_each_successful_recursive_node": 81,
  "recursive_edge_checks_by_level": {
    "2": 29899,
    "3": 6751,
    "4": 81
  },
  "cached_nodes": 455,
  "pauli_preserving_labels": [
    [
      0,
      0,
      0,
      0
    ],
    [
      0,
      0,
      1,
      0
    ],
    [
      0,
      0,
      2,
      0
    ]
  ],
  "semi_clifford_necessary_minimum": 9,
  "semi_clifford": false,
  "explicit_non_C3_double_conjugation_labels": [
    [
      1,
      0,
      0,
      0
    ],
    [
      0,
      1,
      0,
      0
    ]
  ],
  "explicit_non_C3_phase_formula": "4*x^2 - 6*x + 2*y + 3 (mod p)",
  "higher_prime_backend_checks": [
    {
      "prime": 3,
      "pauli_labels_checked": 81,
      "basis_points_per_label": 9,
      "pauli_images": 3
    },
    {
      "prime": 5,
      "pauli_labels_checked": 625,
      "basis_points_per_label": 25,
      "pauli_images": 5
    },
    {
      "prime": 7,
      "pauli_labels_checked": 2401,
      "basis_points_per_label": 49,
      "pauli_images": 7
    },
    {
      "prime": 11,
      "pauli_labels_checked": 14641,
      "basis_points_per_label": 121,
      "pauli_images": 11
    }
  ],
  "seconds": 2.741649334000158,
  "scope": "Complete p=3 counterexample; arbitrary-prime extension requires the algebraic proof."
}
