{
  "phase_algebra": {
    "P4_is_identity": true,
    "P_transpose_is_P3": true,
    "KPK_is_P3": true,
    "N4_is_zero": true,
    "N_ranks": [
      4,
      3,
      2,
      1,
      0
    ],
    "generated_operator_count": 16,
    "invertible_phase_operator_count": 8,
    "centralizer_of_P_count": 16,
    "centralizer_equals_generated_algebra": true
  },
  "gate_inventory": {
    "all": 65536,
    "invertible_8x8_block_gates": 24576,
    "orthogonal_8x8_block_gates": 512,
    "projective_reversible_bases": 192,
    "projective_orthogonal_bases": 4
  },
  "bell": {
    "tables": {
      "ZZ": [
        1,
        0,
        0,
        1
      ],
      "ZX": [
        1,
        1,
        1,
        0
      ],
      "ZY": [
        0,
        1,
        1,
        1
      ],
      "XZ": [
        1,
        1,
        1,
        0
      ],
      "XX": [
        0,
        1,
        1,
        1
      ],
      "XY": [
        1,
        0,
        0,
        1
      ],
      "YZ": [
        0,
        1,
        1,
        1
      ],
      "YX": [
        1,
        0,
        0,
        1
      ],
      "YY": [
        1,
        1,
        1,
        0
      ]
    },
    "compatible_global_assignments": 0,
    "explicit_contradiction": "ZZ fixes common z; XY fixes bY=x; YX fixes bX=y; ZX/XZ/YY forbid 11 and ZY/XX/YZ forbid 00, forcing three pairwise-unequal Boolean values."
  },
  "contextuality": {
    "measurement_bases_per_party": 192,
    "strong_classes": 4,
    "logical_not_strong_classes": 6,
    "local_nonzero_classes": 4,
    "zero_classes": 1,
    "state_counts": {
      "strong": 26214,
      "logical_not_strong": 34056,
      "local_nonzero": 5265
    }
  },
  "bell_delta": {
    "generated_by_Hrot_then_CNOT": true,
    "state_branches": [
      1,
      0,
      0,
      5
    ],
    "embedded_3_basis_global_assignments": 8,
    "embedded_3_basis_uncovered": 0,
    "complete_192_basis": {
      "satisfiable": true,
      "clauses": 10240,
      "possible_sections": 137216,
      "extendable_possible_sections": 100352,
      "uncovered_possible_sections": 36864,
      "first_uncovered": [
        0,
        0,
        1,
        1
      ]
    }
  },
  "teleportation": {
    "bell_analyzer_f2": [
      [
        0,
        1,
        1,
        1
      ],
      [
        1,
        0,
        1,
        1
      ],
      [
        0,
        1,
        1,
        0
      ],
      [
        1,
        0,
        0,
        1
      ]
    ],
    "global_analyzer_dimension": "32x32",
    "support_bell_branch_ranks": [
      8,
      8,
      8,
      8
    ],
    "support_bell_branch_block_selectors": [
      [
        0,
        1,
        1,
        1
      ],
      [
        1,
        1,
        0,
        1
      ],
      [
        0,
        1,
        1,
        0
      ],
      [
        1,
        0,
        0,
        1
      ]
    ],
    "support_bell_correction_block_selectors": [
      [
        1,
        1,
        1,
        0
      ],
      [
        1,
        1,
        0,
        1
      ],
      [
        0,
        1,
        1,
        0
      ],
      [
        1,
        0,
        0,
        1
      ]
    ],
    "exhaustive_exact_checks": 1024,
    "universal_resource_count": 24576,
    "universal_iff_resource_boolean_rank8": true,
    "delta_resource_boolean_rank": 6,
    "delta_standard_bell_analyzer_branch_ranks": [
      6,
      6,
      6,
      6
    ],
    "delta_natural_inverse_preparation_analyzer_branch_ranks": [
      4,
      4,
      4,
      4
    ],
    "delta_natural_branch_block_selectors": [
      [
        1,
        0,
        0,
        0
      ],
      [
        0,
        5,
        5,
        0
      ],
      [
        5,
        0,
        0,
        5
      ],
      [
        0,
        1,
        0,
        0
      ]
    ]
  },
  "ghz": {
    "support_generated_natively": true,
    "delta_generated_natively": true,
    "support_embedded_3_basis": {
      "global_assignments": 0,
      "uncovered_possible_sections": 112,
      "minimum_unsat_context_count": 6,
      "minimum_unsat_contexts": [
        {
          "A": "Z",
          "B": "Z",
          "C": "Z",
          "table": [
            1,
            0,
            0,
            0,
            0,
            0,
            0,
            1
          ]
        },
        {
          "A": "Z",
          "B": "X",
          "C": "X",
          "table": [
            1,
            1,
            1,
            1,
            1,
            0,
            0,
            0
          ]
        },
        {
          "A": "X",
          "B": "Z",
          "C": "Y",
          "table": [
            0,
            1,
            1,
            1,
            0,
            1,
            0,
            0
          ]
        },
        {
          "A": "X",
          "B": "X",
          "C": "X",
          "table": [
            0,
            1,
            1,
            1,
            1,
            1,
            1,
            1
          ]
        },
        {
          "A": "Y",
          "B": "Y",
          "C": "Z",
          "table": [
            0,
            1,
            0,
            1,
            0,
            1,
            1,
            1
          ]
        },
        {
          "A": "Y",
          "B": "Y",
          "C": "Y",
          "table": [
            1,
            1,
            1,
            1,
            1,
            1,
            1,
            0
          ]
        }
      ]
    },
    "delta_embedded_3_basis": {
      "global_assignments": 16,
      "uncovered_possible_sections": 0,
      "minimum_unsat_context_count": null,
      "minimum_unsat_contexts": null
    },
    "support_4_orthogonal_bases": {
      "global_assignments": 44,
      "uncovered_possible_sections": 0
    },
    "delta_4_orthogonal_bases": {
      "global_assignments": 23,
      "uncovered_possible_sections": 0
    }
  },
  "prior_raw_regression": {
    "contextuality_table_exact_match": true,
    "contextuality_mismatches": [],
    "bell_table_exact_match": true,
    "ghz_support_table_exact_match": true,
    "ghz_delta_table_exact_match": true
  },
  "new_native_deductions": {
    "phase_algebra_is_full_centralizer_of_P": true,
    "N_interpretation": "N=P XOR I is a one-step rotation-difference operator; N^4=0 and rank(N^a)=4-a.",
    "rotation_class_profile_formula": "For canonical (a,b), rank after N^j filtering is max(4-a-j,0)+max(4-b-j,0).",
    "teleportation_native_criterion": "Universal exact one-bit transfer iff the 8x8 Boolean resource transfer matrix has full rank 8.",
    "delta_rank_loss": "The (0,2) resource is diag(I4,N^2), rank 6: two of eight Boolean phase dimensions are collapsed before correction.",
    "orthogonality_reinterpretation": "The 512 previously intrinsic-unitary gates are exactly ordinary 8x8 Boolean orthogonal block matrices in this representation."
  },
  "elapsed_seconds": 28.352529048919678
}
