{
  "quantity": "-Arg(eigenvalue of product of polar MMN links)/(2*pi), modulo one",
  "subspace": "Four occupied spatial bands of eight-electron nonmagnetic scalar Si, no SOC",
  "connection": "Closed +b1 loops at each sampled fractional k2,k3",
  "interpretation": "Matrix phase extraction only; no spinful Kramers partner tracking, Z2, edge spectrum or gap validation",
  "numpy_version": "2.4.6",
  "cases": [
    {
      "grid": 4,
      "loop_direction": "+b1 including periodic G",
      "loops": 16,
      "loop_points": 4,
      "spatial_bands": 4,
      "min_link_singular_value": 0.6668967225520925,
      "reverse_overlap_error": 0.0,
      "max_unitarity_error": 3.1086244689504383e-15,
      "max_determinant_phase_error_rad": 4.4408688050905515e-16,
      "max_random_gauge_spectrum_error_mod1": 2.220446049250313e-16,
      "random_seed": 2026100204
    },
    {
      "grid": 6,
      "loop_direction": "+b1 including periodic G",
      "loops": 36,
      "loop_points": 6,
      "spatial_bands": 4,
      "min_link_singular_value": 0.7327458767942244,
      "reverse_overlap_error": 1.0000333894311098e-12,
      "max_unitarity_error": 6.439293542825908e-15,
      "max_determinant_phase_error_rad": 6.661388969678199e-16,
      "max_random_gauge_spectrum_error_mod1": 2.220446049250313e-16,
      "random_seed": 2026100206
    }
  ]
}