{
  "P": [
    [
      0,
      0,
      0,
      1
    ],
    [
      1,
      0,
      0,
      0
    ],
    [
      0,
      1,
      0,
      0
    ],
    [
      0,
      0,
      1,
      0
    ]
  ],
  "P2": [
    [
      0,
      0,
      1,
      0
    ],
    [
      0,
      0,
      0,
      1
    ],
    [
      1,
      0,
      0,
      0
    ],
    [
      0,
      1,
      0,
      0
    ]
  ],
  "P3": [
    [
      0,
      1,
      0,
      0
    ],
    [
      0,
      0,
      1,
      0
    ],
    [
      0,
      0,
      0,
      1
    ],
    [
      1,
      0,
      0,
      0
    ]
  ],
  "P4_is_I": true,
  "P2_is_not_I": true,
  "P_transpose_is_inverse": true,
  "transpose_reflection_K": [
    [
      1,
      0,
      0,
      0
    ],
    [
      0,
      0,
      0,
      1
    ],
    [
      0,
      0,
      1,
      0
    ],
    [
      0,
      1,
      0,
      0
    ]
  ],
  "K2_is_I": true,
  "KPK_is_P_inverse": true,
  "generated_symmetry_group_note": "P and K satisfy P^4=K^2=I and KPK=P^-1 (dihedral D4 relations).",
  "N_P_xor_I": [
    [
      1,
      0,
      0,
      1
    ],
    [
      1,
      1,
      0,
      0
    ],
    [
      0,
      1,
      1,
      0
    ],
    [
      0,
      0,
      1,
      1
    ]
  ],
  "N_nilpotency": {
    "N1_nonzero": true,
    "N2_nonzero": true,
    "N3_nonzero": true,
    "N4_zero": true
  },
  "Delta_operator_I_xor_P2": [
    [
      1,
      0,
      1,
      0
    ],
    [
      0,
      1,
      0,
      1
    ],
    [
      1,
      0,
      1,
      0
    ],
    [
      0,
      1,
      0,
      1
    ]
  ],
  "Delta_operator_square_zero": true,
  "Omega_operator": [
    [
      1,
      1,
      1,
      1
    ],
    [
      1,
      1,
      1,
      1
    ],
    [
      1,
      1,
      1,
      1
    ],
    [
      1,
      1,
      1,
      1
    ]
  ],
  "Omega_operator_square_zero": true,
  "operator_algebra_size": 16,
  "operator_algebra_units_count": 8,
  "operator_algebra_unit_masks": [
    1,
    2,
    4,
    7,
    8,
    11,
    13,
    14
  ],
  "operator_composition_matches_cyclic_mask_for_all_256_pairs": true,
  "strict_branch_shear_C2": [
    [
      1,
      0
    ],
    [
      1,
      1
    ]
  ],
  "C2_squared_is_I": true,
  "C2_on_e0": [
    1,
    1
  ],
  "C2_on_e1": [
    0,
    1
  ],
  "GL2_F2_count": 6,
  "GL2_maps_splitting_both_basis_vectors_count": 0,
  "bell_from_shear_then_CNOT": [
    1,
    0,
    0,
    1
  ],
  "bell_expected_1001": true,
  "C8_squared_is_I": true,
  "H8_squared_is_I": true,
  "H8_symmetric_split": [
    {
      "input_branch": "0",
      "branch0": [
        1,
        0,
        0,
        0
      ],
      "branch1": [
        1,
        0,
        1,
        0
      ]
    },
    {
      "input_branch": "1",
      "branch0": [
        1,
        0,
        1,
        0
      ],
      "branch1": [
        1,
        0,
        0,
        0
      ]
    }
  ],
  "controlled_rotation_shear_interference": [
    {
      "k": 0,
      "branch0": [
        1,
        0,
        0,
        0
      ],
      "branch1": [
        0,
        0,
        0,
        0
      ],
      "branch1_weight": 0
    },
    {
      "k": 1,
      "branch0": [
        1,
        0,
        0,
        0
      ],
      "branch1": [
        1,
        1,
        0,
        0
      ],
      "branch1_weight": 2
    },
    {
      "k": 2,
      "branch0": [
        1,
        0,
        0,
        0
      ],
      "branch1": [
        1,
        0,
        1,
        0
      ],
      "branch1_weight": 2
    },
    {
      "k": 3,
      "branch0": [
        1,
        0,
        0,
        0
      ],
      "branch1": [
        1,
        0,
        0,
        1
      ],
      "branch1_weight": 2
    }
  ],
  "controlled_rotation_symmetric_interference": [
    {
      "k": 0,
      "branch0": [
        1,
        0,
        0,
        0
      ],
      "branch1": [
        0,
        0,
        0,
        0
      ],
      "branch1_weight": 0
    },
    {
      "k": 1,
      "branch0": [
        1,
        0,
        0,
        0
      ],
      "branch1": [
        1,
        1,
        1,
        1
      ],
      "branch1_weight": 4
    },
    {
      "k": 2,
      "branch0": [
        1,
        0,
        0,
        0
      ],
      "branch1": [
        0,
        0,
        0,
        0
      ],
      "branch1_weight": 0
    },
    {
      "k": 3,
      "branch0": [
        1,
        0,
        0,
        0
      ],
      "branch1": [
        1,
        1,
        1,
        1
      ],
      "branch1_weight": 4
    }
  ]
}
