{
  "status": "PASS",
  "checks": 88990,
  "groups": {
    "copy_gram_exact": 1,
    "cross_gram_exact": 1,
    "six_observed_scores": 1,
    "six_observed_selection": 1,
    "all_pair_gram_swaps": 64,
    "all_pair_score_antisymmetry": 64,
    "null_mean_swap_and_nonnull_boundary": 64,
    "conditional_eight_sign_FDR": 1,
    "reverse_one_step_budget": 495,
    "binomial_initial_budget": 30,
    "group_scan_vs_direct_definition": 45045,
    "finite_conditional_FDR_with_ties_zeros": 9828,
    "minimum_discovery_count": 11272,
    "common_sign_invalid_counterexample": 1,
    "offset_zero_one_null_counterexample": 1,
    "three_variable_conditional_generator": 1,
    "random_cross_covariance": 1,
    "random_copy_covariance": 1,
    "positive_definite_leading_minors": 3,
    "displayed_minors": 1,
    "conditional_mean_record": 1,
    "conditional_interaction_covariance": 1,
    "nondegenerate_nonnull_conditional_variances": 1,
    "interaction_score_and_selection": 1,
    "interaction_full_antisymmetry": 8,
    "singular_model_all_conditional_nulls": 1,
    "independent_whole_copy_FDR_failure": 1,
    "discrete_pair_law_normalized": 1,
    "discrete_all_subset_pair_exchangeability": 512,
    "discrete_response_conditional_targets": 2,
    "conditional_joint_sign_uniformity_from_full_law": 54,
    "discrete_modelx_actual_FDR": 6,
    "nonuniform_background_full_probability": 1,
    "extra_count_conditional_tail": 1,
    "six_point_conditional_kernel": 1,
    "conditional_kernel_reconstruction": 6,
    "incorrect_permutation_unconditional_error_lower": 1,
    "specified_monte_carlo_record": 1,
    "exact_monte_carlo_rank_level_for_discrete_laws": 190,
    "all_tied_rank_counting_arrays": 21321,
    "minimum_monte_carlo_resolution": 1,
    "one_allnull_run_FDR": 1,
    "five_valid_runs_postselection_FDR": 1
  },
  "results": {
    "fixed_design": {
      "W": [
        "6",
        "5",
        "4",
        "3",
        "-2",
        "1"
      ],
      "conditional_FDR": "7/40",
      "sign_table": [
        {
          "signs": [
            -1,
            -1,
            -1
          ],
          "threshold": null,
          "selected_1based": [],
          "FDP": "0"
        },
        {
          "signs": [
            -1,
            -1,
            1
          ],
          "threshold": null,
          "selected_1based": [],
          "FDP": "0"
        },
        {
          "signs": [
            -1,
            1,
            -1
          ],
          "threshold": null,
          "selected_1based": [],
          "FDP": "0"
        },
        {
          "signs": [
            -1,
            1,
            1
          ],
          "threshold": null,
          "selected_1based": [],
          "FDP": "0"
        },
        {
          "signs": [
            1,
            -1,
            -1
          ],
          "threshold": "3",
          "selected_1based": [
            1,
            2,
            3,
            4
          ],
          "FDP": "1/4"
        },
        {
          "signs": [
            1,
            -1,
            1
          ],
          "threshold": "3",
          "selected_1based": [
            1,
            2,
            3,
            4
          ],
          "FDP": "1/4"
        },
        {
          "signs": [
            1,
            1,
            -1
          ],
          "threshold": "2",
          "selected_1based": [
            1,
            2,
            3,
            4,
            5
          ],
          "FDP": "2/5"
        },
        {
          "signs": [
            1,
            1,
            1
          ],
          "threshold": "1",
          "selected_1based": [
            1,
            2,
            3,
            4,
            5,
            6
          ],
          "FDP": "1/2"
        }
      ]
    },
    "symbolic_sign_budget": {
      "conditional_configurations": 9828,
      "largest_risk_over_q": "73/96",
      "common_sign_FDR": "1/2",
      "no_offset_one_null_FDR": "1/2"
    },
    "nonlinear_gaussian": {
      "B": [
        [
          "1/3",
          "1/3",
          "0"
        ],
        [
          "2/9",
          "4/9",
          "2/9"
        ],
        [
          "0",
          "1/3",
          "1/3"
        ]
      ],
      "V": [
        [
          "2/3",
          "1/9",
          "0"
        ],
        [
          "1/9",
          "13/27",
          "1/9"
        ],
        [
          "0",
          "1/9",
          "2/3"
        ]
      ],
      "principal_minors": [
        [
          "1",
          "3/4",
          "9/16"
        ],
        [
          "3/2",
          "3/2",
          "4/3"
        ],
        [
          "2/3",
          "25/81",
          "16/81"
        ]
      ],
      "conditional_mean": [
        "1",
        "16/9",
        "5/3"
      ],
      "true_nulls_1based": [
        2
      ],
      "interaction_W": [
        "20",
        "16",
        "-8"
      ]
    },
    "discrete_modelx": {
      "invalid_independent_copy_FDR": "1/2",
      "valid_finite_model_risks": {
        "independent q=1/3": "1/144",
        "independent q=1/2": "11/144",
        "independent q=2/3": "11/144",
        "xor q=1/3": "1/432",
        "xor q=1/2": "13/432",
        "xor q=2/3": "13/432"
      }
    },
    "conditional_resampling": {
      "unconditional_background_tail": "144/625",
      "count_probability": "244/625",
      "count_conditioned_tail": "36/61",
      "count_expected_rejection_sampling_attempts": "625/244",
      "six_point_kernel": [
        {
          "ones_1based": [
            3,
            4
          ],
          "probability": "36/61"
        },
        {
          "ones_1based": [
            2,
            4
          ],
          "probability": "6/61"
        },
        {
          "ones_1based": [
            2,
            3
          ],
          "probability": "6/61"
        },
        {
          "ones_1based": [
            1,
            4
          ],
          "probability": "6/61"
        },
        {
          "ones_1based": [
            1,
            3
          ],
          "probability": "6/61"
        },
        {
          "ones_1based": [
            1,
            2
          ],
          "probability": "1/61"
        }
      ],
      "incorrect_permutation_error_lower": "19683/80000",
      "monte_carlo_record": "3/5"
    },
    "repeated_runs": {
      "one_run_FDR": "1/16",
      "five_run_report_FDR": "289201/1048576"
    }
  },
  "scope": "Exact finite matrix/distribution/rank certificates. No simulation, estimated design law, or unproved numerical tolerance. General theorems are proved in the companion pages."
}