{
  "status": "PASS",
  "checks": 33666,
  "categories": {
    "archimedean_exact_rectangle": 432,
    "archimedean_margins": 39,
    "capstone_conditional_sample": 1,
    "capstone_continuous_four_cells": 1,
    "capstone_continuous_joint_cdf": 1,
    "capstone_other_threshold_not_minimal": 1,
    "capstone_three_threshold_attainment": 1,
    "circle_filled_uniform_marginal": 4914,
    "circle_partition_mass": 360,
    "circle_pointwise_lower_attainment": 360,
    "clayton_density_numerator": 144,
    "clayton_first_derivative_numerator": 144,
    "clayton_lower_diagonal_ratio": 87,
    "clayton_upper_diagonal_ratio": 87,
    "conditional_inverse_equation": 1521,
    "conditional_inverse_in_unit_interval": 1521,
    "convex_inverse_fixed_increment": 216,
    "fair_independent_jitter_value": 1,
    "fair_shared_jitter_value": 1,
    "generalized_inverse_recovers_atom": 1485,
    "high_dimensional_lower_rejected": 6,
    "jitter_nonnegative_cell_mass": 16128,
    "lower_function_half_cube_delta": 7,
    "mixture_lower_tail_ratio": 87,
    "mixture_upper_tail_ratio": 87,
    "modulo_3D_mass_one": 1,
    "modulo_nonnegative_3D_cells": 64,
    "modulo_pair_UV_independent": 121,
    "modulo_pair_UW_independent": 121,
    "modulo_pair_VW_independent": 121,
    "modulo_triple_conditional_probability": 63,
    "modulo_triple_triangle_mass": 63,
    "nonconvex_generator_rejected": 1,
    "nonexistent_tail_endpoint_ratio": 5,
    "nonexistent_tail_reflected_midpoint_ratio": 5,
    "randomized_transform_uniform_margins": 2268,
    "shared_jitter_covariance": 1,
    "shared_jitter_lower_tail_ratio": 87,
    "shared_jitter_upper_tail_ratio": 87,
    "sklar_discrete_grid_recovery": 3024,
    "zero_correlation_joint_upper_tail": 1,
    "zero_correlation_moment": 1
  },
  "sklar": {
    "tables": 126,
    "independent_jitter_at_quarter": "1/16",
    "shared_jitter_at_quarter": "1/8",
    "shared_covariance": "1/48",
    "shared_correlation": "1/4"
  },
  "frechet": {
    "constructed_models": 360,
    "half_cube_masses": {
      "2": "0",
      "3": "-1/2",
      "4": "-1",
      "5": "-3/2",
      "6": "-2",
      "7": "-5/2",
      "8": "-3"
    },
    "target_mass": "1/10",
    "same_model_center_mass": "25/672"
  },
  "archimedean": {
    "rectangles": 432,
    "nonconvex_rectangle": "-1/8",
    "four_cells": [
      "1/5",
      "3/10",
      "1/20",
      "9/20"
    ],
    "conditional_sample_v": "1/3"
  },
  "tail": {
    "reflection_subsequences": [
      {
        "k": 0,
        "endpoint_ratio": "1",
        "midpoint_ratio": "2/3"
      },
      {
        "k": 2,
        "endpoint_ratio": "1",
        "midpoint_ratio": "2/17"
      },
      {
        "k": 4,
        "endpoint_ratio": "1",
        "midpoint_ratio": "2/65537"
      },
      {
        "k": 6,
        "endpoint_ratio": "1",
        "midpoint_ratio": "2/18446744073709551617"
      },
      {
        "k": 8,
        "endpoint_ratio": "1",
        "midpoint_ratio": "2/115792089237316195423570985008687907853269984665640564039457584007913129639937"
      }
    ],
    "pairwise_independent_triple_at_one_tenth": "1/200",
    "fully_independent_triple_at_one_tenth": "1/1000",
    "triple_conditional": "1/2"
  },
  "scope": "Exact finite algebra, finite-support jitter integration, circle partitions and polygon clipping. Grid checks do not prove universal convexity or existence of a tail limit; those are supplied by the accompanying proofs."
}