{
  "license": "CC0-1.0 to the extent of rights held; numerical facts are not claimed as exclusive property.",
  "model": {
    "G": "Z/3Z",
    "H": "Z/3Z",
    "pairing": "chi_k(s)=omega^(ks)",
    "omega": "exp(2*pi*i/3)",
    "D_diagonal_exponents": [
      0,
      1
    ],
    "u1_diagonal_exponents_by_block": [
      [
        0,
        1
      ],
      [
        1,
        2
      ],
      [
        2,
        0
      ]
    ],
    "z_scalar_exponents_by_block": [
      0,
      1,
      2
    ],
    "alpha1_matrix_unit_exponents": [
      [
        0,
        2
      ],
      [
        1,
        0
      ]
    ],
    "beta1_projection_destination": [
      1,
      2,
      0
    ],
    "original_group_singleton_mass": 1,
    "dual_group_singleton_mass": "1/3",
    "Euclidean_target_coordinate": "eta_hat_k=eta(k)/sqrt(3)",
    "W_block_k_t": "omega^(k*t)*u_t/sqrt(3)",
    "Hilbert_dimension": 18,
    "algebra_dimension": 12
  },
  "exact_projection_values": [
    [
      1,
      0,
      0
    ],
    [
      0,
      1,
      0
    ],
    [
      0,
      0,
      1
    ]
  ],
  "exact_phase_covariance_checked_for_all_27_triples": true,
  "exact_root_basis": "(1,omega) with omega^2=-1-omega",
  "numerical_checks": {
    "W_star_W_minus_identity": 3.3306690738754696e-16,
    "W_W_star_minus_identity": 3.253848972186392e-16,
    "sum_central_projections_minus_identity": 3.4980578905787326e-16,
    "unitary_representation_s0_t0": 0.0,
    "unitary_representation_s0_t1": 0.0,
    "unitary_representation_s0_t2": 0.0,
    "eigencharacter_k0_s0": 0.0,
    "eigencharacter_k1_s0": 0.0,
    "eigencharacter_k2_s0": 0.0,
    "group_intertwiner_s0": 3.253848972186392e-16,
    "unitary_representation_s1_t0": 0.0,
    "unitary_representation_s1_t1": 2.2254223746127275e-16,
    "unitary_representation_s1_t2": 1.9022240837416075e-15,
    "eigencharacter_k0_s1": 0.0,
    "eigencharacter_k1_s1": 6.093986062563353e-16,
    "eigencharacter_k2_s1": 6.181460191301303e-16,
    "group_intertwiner_s1": 1.1102230246251565e-15,
    "unitary_representation_s2_t0": 0.0,
    "unitary_representation_s2_t1": 1.9022240837416075e-15,
    "unitary_representation_s2_t2": 1.8481726070021634e-15,
    "eigencharacter_k0_s2": 0.0,
    "eigencharacter_k1_s2": 1.2041750190242758e-15,
    "eigencharacter_k2_s2": 1.2225062931717347e-15,
    "group_intertwiner_s2": 2.0358293740687926e-15,
    "projection_block_j0": 3.1619165601783647e-16,
    "projection_idempotence_j0": 3.161916560178364e-16,
    "projection_block_j1": 2.340555645717801e-16,
    "projection_idempotence_j1": 2.3405556457178003e-16,
    "projection_block_j2": 3.3572256015987104e-16,
    "projection_idempotence_j2": 3.3572256015987104e-16,
    "coefficient_intertwiner_e11": 3.9876396450950914e-16,
    "coefficient_action_e11": 0.0,
    "coefficient_intertwiner_e12": 4.3802724817048847e-16,
    "coefficient_action_e12": 5.551115123125783e-17,
    "coefficient_intertwiner_e21": 4.554928218193396e-16,
    "coefficient_action_e21": 0.0,
    "coefficient_intertwiner_e22": 4.441722337838912e-16,
    "coefficient_action_e22": 1.1102230246251565e-16
  },
  "numeric_tolerance": 1e-12,
  "generated_matrix_space_rank": 12,
  "interpretation": "Exact finite model plus floating-point residual diagnostics. The arbitrary-group proof is OA-FLOW-L29, Section 5."
}