{
  "jackknife_example": {
    "endpoints": [
      "-8/3",
      "4"
    ],
    "rows": [
      [
        0,
        "2",
        "2",
        "0",
        "4"
      ],
      [
        1,
        "2",
        "2",
        "0",
        "4"
      ],
      [
        2,
        "4/3",
        "2/3",
        "2/3",
        "2"
      ],
      [
        3,
        "2/3",
        "10/3",
        "-8/3",
        "4"
      ]
    ]
  },
  "cv_example": {
    "endpoints": [
      "-4",
      "6"
    ],
    "rows": [
      [
        0,
        "3",
        "3",
        "0",
        "6"
      ],
      [
        1,
        "3",
        "3",
        "0",
        "6"
      ],
      [
        2,
        "0",
        "2",
        "-2",
        "2"
      ],
      [
        3,
        "0",
        "4",
        "-4",
        "4"
      ]
    ]
  },
  "jackknife_exact_iid_coverages": [
    {
      "n": 2,
      "alpha": "1/10",
      "coverage": "1",
      "bound": "4/5"
    },
    {
      "n": 2,
      "alpha": "1/5",
      "coverage": "1",
      "bound": "3/5"
    },
    {
      "n": 2,
      "alpha": "1/4",
      "coverage": "1",
      "bound": "1/2"
    },
    {
      "n": 2,
      "alpha": "2/5",
      "coverage": "7/9",
      "bound": "1/5"
    },
    {
      "n": 3,
      "alpha": "1/10",
      "coverage": "1",
      "bound": "4/5"
    },
    {
      "n": 3,
      "alpha": "1/5",
      "coverage": "1",
      "bound": "3/5"
    },
    {
      "n": 3,
      "alpha": "1/4",
      "coverage": "23/27",
      "bound": "1/2"
    },
    {
      "n": 3,
      "alpha": "2/5",
      "coverage": "23/27",
      "bound": "1/5"
    },
    {
      "n": 4,
      "alpha": "1/10",
      "coverage": "1",
      "bound": "4/5"
    },
    {
      "n": 4,
      "alpha": "1/5",
      "coverage": "217/243",
      "bound": "3/5"
    },
    {
      "n": 4,
      "alpha": "1/4",
      "coverage": "217/243",
      "bound": "1/2"
    },
    {
      "n": 4,
      "alpha": "2/5",
      "coverage": "185/243",
      "bound": "1/5"
    },
    {
      "n": 5,
      "alpha": "1/10",
      "coverage": "1",
      "bound": "4/5"
    },
    {
      "n": 5,
      "alpha": "1/5",
      "coverage": "673/729",
      "bound": "3/5"
    },
    {
      "n": 5,
      "alpha": "1/4",
      "coverage": "673/729",
      "bound": "1/2"
    },
    {
      "n": 5,
      "alpha": "2/5",
      "coverage": "593/729",
      "bound": "1/5"
    }
  ],
  "cv_exact_iid_coverages": [
    {
      "alpha": "1/10",
      "coverage": "1",
      "bound": "19/30"
    },
    {
      "alpha": "1/5",
      "coverage": "221/243",
      "bound": "13/30"
    },
    {
      "alpha": "1/4",
      "coverage": "221/243",
      "bound": "1/3"
    },
    {
      "alpha": "2/5",
      "coverage": "71/81",
      "bound": "1/30"
    }
  ],
  "cqr_population_example": {
    "group_A_coverage": "558022029778704493791/640000000000000000000",
    "group_B_coverage": "97801731991659555881/640000000000000000000",
    "marginal_coverage": "4/5",
    "probability_B_interval_empty": "19739340894919641147/32000000000000000000",
    "group_A_decimal": 0.8719094215292258,
    "group_B_decimal": 0.15281520623696807,
    "empty_decimal": 0.6168544029662388
  },
  "crc_conditional_counterexample": {
    "n": 4,
    "alpha": "2/5",
    "risky_loss_probability": "1/2",
    "risky_selected_probability": "5/16",
    "expected_test_loss": "5/32",
    "probability_conditional_risk_above_alpha": "5/16"
  },
  "nonmonotone_crc_failure": {
    "n": 1,
    "alpha": "1/2",
    "candidate_count": 10,
    "per_candidate_risk": "9/10",
    "expected_selected_risk": "58618940391/100000000000"
  },
  "conditional_rank_plans": [
    {
      "n": 4,
      "alpha": "1/5",
      "delta": "1/20",
      "rank": 5,
      "bad_calibration_probability": "0"
    },
    {
      "n": 4,
      "alpha": "1/10",
      "delta": "1/20",
      "rank": 5,
      "bad_calibration_probability": "0"
    },
    {
      "n": 9,
      "alpha": "1/5",
      "delta": "1/20",
      "rank": 10,
      "bad_calibration_probability": "0"
    },
    {
      "n": 9,
      "alpha": "1/10",
      "delta": "1/20",
      "rank": 10,
      "bad_calibration_probability": "0"
    },
    {
      "n": 14,
      "alpha": "1/5",
      "delta": "1/20",
      "rank": 14,
      "bad_calibration_probability": "268435456/6103515625"
    },
    {
      "n": 14,
      "alpha": "1/10",
      "delta": "1/20",
      "rank": 15,
      "bad_calibration_probability": "0"
    },
    {
      "n": 19,
      "alpha": "1/5",
      "delta": "1/20",
      "rank": 19,
      "bad_calibration_probability": "274877906944/19073486328125"
    },
    {
      "n": 19,
      "alpha": "1/10",
      "delta": "1/20",
      "rank": 20,
      "bad_calibration_probability": "0"
    },
    {
      "n": 29,
      "alpha": "1/5",
      "delta": "1/20",
      "rank": 28,
      "bad_calibration_probability": "2377900603251621888/186264514923095703125"
    },
    {
      "n": 29,
      "alpha": "1/10",
      "delta": "1/20",
      "rank": 29,
      "bad_calibration_probability": "4710128697246244834921603689/100000000000000000000000000000"
    },
    {
      "n": 39,
      "alpha": "1/5",
      "delta": "1/20",
      "rank": 36,
      "bad_calibration_probability": "60403789682385631928385536/1818989403545856475830078125"
    },
    {
      "n": 39,
      "alpha": "1/10",
      "delta": "1/20",
      "rank": 39,
      "bad_calibration_probability": "16423203268260658146231467800709255289/1000000000000000000000000000000000000000"
    },
    {
      "n": 59,
      "alpha": "1/5",
      "delta": "1/20",
      "rank": 53,
      "bad_calibration_probability": "6080515335788042795458068376420018552832/173472347597680709441192448139190673828125"
    },
    {
      "n": 59,
      "alpha": "1/10",
      "delta": "1/20",
      "rank": 58,
      "bad_calibration_probability": "377150309858584328111408112366213403400433156396832948257/25000000000000000000000000000000000000000000000000000000000"
    },
    {
      "n": 99,
      "alpha": "1/5",
      "delta": "1/20",
      "rank": 87,
      "bad_calibration_probability": "44388581725046526084444345529422203823053543381214481508918699753472/1577721810442023610823457130565572459346412870218046009540557861328125"
    },
    {
      "n": 99,
      "alpha": "1/10",
      "delta": "1/20",
      "rank": 95,
      "bad_calibration_probability": "79388665170795674847332749963750014969078920995779089560454427674189967178395607506780733855401/3125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
    }
  ],
  "hoeffding_examples": [
    {
      "n": 4,
      "radius": "0.61193670767020413659400674121523122738416795504149925023878138211015494007320756",
      "middle_upper": "0.73693670767020413659400674121523122738416795504149925023878138211015494007320756"
    },
    {
      "n": 100,
      "radius": "0.12238734153404082731880134824304624547683359100829985004775627642203098801464151",
      "middle_upper": "0.24738734153404082731880134824304624547683359100829985004775627642203098801464151"
    }
  ],
  "capstone_99_calibration": {
    "90": "11611917503111310205710602269737049416139174231517550464989502226747819256317406194782988386330031/25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
    "94": "7643951277995603700381998601912236341294672013610077098781457632759643960282920078970494188205313/125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
    "95": "79388665170795674847332749963750014969078920995779089560454427674189967178395607506780733855401/3125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000"
  },
  "status": "PASS",
  "assertions": 3174526,
  "groups": {
    "jackknife_comparison_graph": 298248,
    "cv_fold_comparison_graph": 2657205,
    "crc_oracle_order": 179136,
    "crc_exchangeable_mean_budget": 37296,
    "rcps_suffix_exact_probability": 30,
    "rcps_arbitrary_search_failure": 30,
    "rcps_arbitrary_search_exceeds_delta": 27,
    "beta_density_integral": 210,
    "beta_mean_integral": 210,
    "beta_second_moment_integral": 210,
    "beta_binomial_identity": 840,
    "discrete_score_conservative_tail": 324,
    "hoeffding_displayed_choice": 2,
    "hoeffding_exact_unsafe_selection": 720,
    "cqr_negative_threshold": 1,
    "cqr_empty_output": 1,
    "calibration_80percent_counterexample": 1,
    "minimum_sample_80": 1,
    "minimum_sample_90": 1,
    "label_conditional_exact_coverage": 30,
    "label_conditional_empty_group": 1,
    "label_conditional_hand_set": 1,
    "capstone_99_minimum_rank": 1
  },
  "limits": [
    "Exact finite enumerations check implementations, while distribution-free statements use the published proofs in the entries.",
    "Decimal logarithms are high-precision numerical calculations, not interval certificates.",
    "No production-site rendering test is claimed."
  ]
}