{
  "license": "CC0-1.0; font terms are separate",
  "group": "Z/2",
  "singleton_Haar_mass": 3,
  "singleton_dual_Haar_mass": "1/6",
  "total_Haar_mass": 6,
  "coefficient_density": [
    2,
    5
  ],
  "action": "flip conjugation",
  "coordinate_order": [
    "(0,1)",
    "(0,2)",
    "(1,1)",
    "(1,2)"
  ],
  "kernel_blocks": [
    [
      [
        [
          "1",
          "2"
        ],
        [
          "0",
          "I"
        ]
      ],
      [
        [
          "0",
          "1"
        ],
        [
          "2",
          "0"
        ]
      ]
    ],
    [
      [
        [
          "1",
          "0"
        ],
        [
          "3",
          "I"
        ]
      ],
      [
        [
          "I",
          "0"
        ],
        [
          "1",
          "2"
        ]
      ]
    ]
  ],
  "normalized_matrix_B": [
    [
      "3",
      "6",
      "0",
      "3"
    ],
    [
      "0",
      "3*I",
      "6",
      "0"
    ],
    [
      "3",
      "0",
      "3*I",
      "0"
    ],
    [
      "9",
      "3*I",
      "3",
      "6"
    ]
  ],
  "reference_density_Q": [
    2,
    5,
    2,
    5
  ],
  "second_dual_density_R": [
    2,
    5,
    5,
    2
  ],
  "correct_column_contributions": [
    [
      27,
      22
    ],
    [
      25,
      18
    ]
  ],
  "incorrect_row_contributions": [
    [
      27,
      13
    ],
    [
      52,
      18
    ]
  ],
  "correct_weight": 828,
  "incorrect_weight": 990,
  "relative_half_power_norm_squared": 828,
  "equations": {
    "matrix": "B_rs = 3 K_rs",
    "cocycle": "C_t = R^(it) Q^(-it)",
    "weight": "9 sum_(r,s) Tr(D_s K_rs* K_rs)",
    "relative_vector": "Delta_(W,Omega)^(1/2) Lambda_Omega(B*) = R^(1/2) B*"
  },
  "proof_locators": [
    "OA-FLOW-L33.md#l33-finite-model",
    "OA-FLOW-L33.md#l33-kernel-diagnostic"
  ],
  "human_antecedent": "Takesaki, Theory of Operator Algebras II, X.2 formula (16), p.260; the proof discussion on p.263 points to VIII.3.15",
  "verification": "Exact SymPy matrix arithmetic, including direct full-matrix and relative-square-root calculations"
}