{
  "license": "CC0-1.0",
  "proof_locator": "OA-FLOW-L41.md#oa-flow.cstd.example; E1-E13",
  "group": "C2={e,s}, s^2=e",
  "base_action": "T_s(0)=1, T_s(1)=0",
  "base_masses": [
    "1/3",
    "2/3"
  ],
  "density_matrix_diagonals": [
    [
      "2/3",
      "1/3"
    ],
    [
      "1/4",
      "3/4"
    ]
  ],
  "target_columns": [
    0,
    1
  ],
  "source_for_each_target": [
    1,
    0
  ],
  "fibre_arrows": "u(s,x)b=b between the labelled Hilbert-Schmidt copies",
  "pushforward_density_at_target": [
    "2",
    "1/2"
  ],
  "global_unitary": "U_s(eta_0,eta_1)=(sqrt(2)*eta_1,eta_0/sqrt(2))",
  "transported_vector_squared_diagonal_entries": [
    [
      "1/2",
      "3/2"
    ],
    [
      "1/3",
      "1/6"
    ]
  ],
  "transported_conditional_masses_h": [
    "2",
    "1/2"
  ],
  "transported_central_masses": [
    "2/3",
    "1/3"
  ],
  "normalized_vector_squared_diagonal_entries": [
    [
      "1/4",
      "3/4"
    ],
    [
      "2/3",
      "1/3"
    ]
  ],
  "exact_checks": [
    "mu(y)*j_s(y)=mu(T_s^-1 y)",
    "j_s(0)*j_s(1)=1",
    "sum diagonal squares=h_nu",
    "sum_y mu(y)*h_nu(y)=1",
    "normalized squared diagonal entries=rho_source"
  ],
  "numerical_checks": [
    "weighted norm preservation",
    "U_s^2=1",
    "U_s J=J U_s",
    "U_s L_a U_s*=L_alpha_s(a)",
    "positive-cone preservation"
  ],
  "numerical_absolute_tolerance": 1e-12
}