{
  "status": "PASS",
  "checks": 59956,
  "groups": {
    "factorized_square_root": 47,
    "logarithmic_derivative": 47,
    "integer_period_samples": 121,
    "single_loop_obstructions": 1,
    "changed_exponent_obstruction": 1,
    "basepoint_branch": 1,
    "sphere_inverse": 56,
    "scalar_matrix_equivalence": 56,
    "matrix_composition_order": 392,
    "three_point_calibration": 60,
    "invalid_mobius": 1,
    "boundary_disk_center": 1,
    "upper_half_plane_identity": 78,
    "upper_half_plane_inverse": 78,
    "right_half_plane_identity": 78,
    "slit_square_inverse": 78,
    "quadrant_target": 64,
    "quadrant_rational_inverse": 64,
    "quadrant_disk_identity": 64,
    "quadrant_basepoint": 1,
    "normalized_derivative": 1,
    "conformal_radius_squared": 1,
    "slit_base_derivative": 1,
    "transport_second_input": 1,
    "rational_unit_circle": 25,
    "circle_through_pole_to_line": 25,
    "constructed_disk_target": 1125,
    "derivative_pick_bound": 1125,
    "derivative_rigidity": 1125,
    "two_point_pick_bound": 28125,
    "two_point_rigidity": 27000,
    "square_map_strict_derivative": 25,
    "capstone_interpolation": 3,
    "feasible_output_disk": 3,
    "capstone_interpolation_values": 2,
    "transport_derivative_squared": 2,
    "missing_value_strict_gain": 39,
    "gain_excess_identity": 39
  },
  "integer_periods": {
    "around_plus_one": 2,
    "around_minus_one": 4,
    "logarithm": false,
    "root_orders": [
      1,
      2
    ],
    "positive_square_root_at_2": 9
  },
  "explicit_maps": {
    "quadrant_basepoint": [
      1,
      1
    ],
    "unnormalized_derivative": {
      "real": "1/2",
      "imag": "-1/2"
    },
    "normalized_derivative": "1/sqrt(2)",
    "quadrant_conformal_radius": "sqrt(2)",
    "slit_conformal_radius": "4"
  },
  "interpolation": [
    {
      "b": "2/3",
      "normalized_value": "3/7",
      "classification": "feasible",
      "scale": "6/7",
      "disk_derivative": "16/21",
      "quadrant_derivative_norm_squared": "128/441"
    },
    {
      "b": "5/7",
      "normalized_value": "1/2",
      "classification": "unique_automorphism",
      "scale": "1",
      "disk_derivative": "8/9",
      "quadrant_derivative_norm_squared": "32/81"
    },
    {
      "b": "3/4",
      "normalized_value": "5/9",
      "classification": "impossible"
    }
  ],
  "arithmetic": "exact Fraction pairs; no float comparison",
  "limitations": [
    "The loop integer formula and global branch classification are proved in prose, not inferred from sampled paths.",
    "Inverse checks concern explicit maps and their stated branches; no general domain mapping algorithm is claimed.",
    "Finite Pick checks do not prove the theorem for all holomorphic maps.",
    "Infinity is one sphere point, not a signed or directional infinity."
  ]
}