{
  "version": 1,
  "proof_locators": ["OA-FLOW-L40.md#oa-flow.istate.examples", "E1-E7", "E13-E15"],
  "matrix_model": {
    "group": "R under addition",
    "A": "M_2(C)",
    "state": "Tr(a)/2",
    "hilbert_inner_product_linear_first": "Tr(c* b)/2",
    "base_points": [1, 2],
    "base_masses_rational": [[1, 2], [1, 2]],
    "base_action": "T_t(j)=j",
    "measure_derivative": 1,
    "W_t_row_phase_exponents": [1, 0],
    "W_t_adjoint_column_phase_exponents": [-1, 0],
    "conjugation_entry_phase_exponents": [[0, 1], [-1, 0]],
    "fibre_1": {
      "input_column": ["b11", "b21"],
      "unitary_coordinate_phase_exponents": [0, -1],
      "scalar_phase_exponent_before_W_t": -1,
      "cyclic_vector": [1, 0]
    },
    "fibre_2": {
      "input_column": ["b12", "b22"],
      "unitary_coordinate_phase_exponents": [1, 0],
      "scalar_phase_exponent_before_W_t": 0,
      "cyclic_vector": [0, 1]
    },
    "expectation": "(T1,T2) -> (<T1 e1,e1>I, <T2 e2,e2>I)",
    "positive_nonfaithfulness_witness": "(E22,0)",
    "original_algebra": "{(a,a): a in M2}",
    "whole_field_algebra": "M2 direct_sum M2"
  },
  "boundary_model": {
    "compact_spectrum": "[0,1]",
    "ideal": "{f in C([0,1]): f(0)=0}",
    "probability_measure": "Lebesgue",
    "action": "trivial R action",
    "approximate_identity": "a_n(t)=min(1,n*t)",
    "integrated_approximate_identity": "1-1/(2*n)",
    "restriction_norm_at_zero": 0,
    "restriction_norm_at_positive_points": 1,
    "exact_full_norm_locus": "(0,1]",
    "removed_set_measure": 0
  },
  "arrow_convention": "Vertical arrows in the matrix diagram act on vectors inside one fixed labelled fibre. They do not move the base or carry a positive density multiplier.",
  "license": "CC0-1.0 for original diagram geometry, source code, mathematical labels and data; the retained DejaVu font terms apply separately."
}