{
  "status": "PASS",
  "range_task": {
    "with_replacement": {
      "0": "5/36",
      "1/3": "1/9",
      "2/3": "1/9",
      "1": "1/6",
      "4/3": "1/18",
      "5/3": "5/36",
      "2": "5/36",
      "7/3": "1/18",
      "8/3": "1/18",
      "3": "1/36"
    },
    "without_replacement": {
      "0": "1/5",
      "1/3": "3/20",
      "2/3": "3/20",
      "1": "1/5",
      "4/3": "1/20",
      "5/3": "3/20",
      "2": "1/10"
    },
    "root_quantiles": [
      "2",
      "4/3"
    ],
    "upper_endpoints": [
      "27/2",
      "81/7"
    ],
    "exact_quantile_bracket": [
      "3/5",
      "31/50"
    ],
    "exact_upper_endpoint_bracket": [
      "450/31",
      "15"
    ]
  },
  "subsampling_task": {
    "support_is_coefficient_of_sqrt3": true,
    "without_replacement": {
      "-1/6": "9/14",
      "1/2": "5/14"
    },
    "with_replacement": {
      "-1/6": "9/16",
      "1/2": "7/16"
    }
  },
  "regression_task": {
    "A": [
      [
        "7/25",
        "-1/25"
      ],
      [
        "-1/25",
        "1/50"
      ]
    ],
    "beta": [
      "7/25",
      "19/25"
    ],
    "residuals": [
      "37/25",
      "-7/25",
      "-1/25",
      "-9/5",
      "16/25"
    ],
    "leverages": [
      "19/50",
      "7/25",
      "11/50",
      "1/5",
      "23/25"
    ],
    "RSS": "148/25",
    "deleted_beta": [
      "3/5",
      "-1/5"
    ],
    "deleted_RSS": "4/5",
    "internal_square": "96/37",
    "external_square": "64/5",
    "Cook": "552/37",
    "changed_beta": [
      "-1/10",
      "19/50"
    ],
    "changed_deleted_beta": [
      "7/10",
      "-1/10"
    ],
    "heteroskedastic_HC2_expectation": "8/25",
    "heteroskedastic_true_variance": "17/25"
  },
  "wild_task": {
    "group_contrast_law": {
      "-8/3": "1/16",
      "-2": "1/8",
      "-4/3": "1/16",
      "-2/3": "1/8",
      "0": "1/4",
      "2/3": "1/8",
      "4/3": "1/16",
      "2": "1/8",
      "8/3": "1/16"
    },
    "group_covariances": [
      [
        [
          "2/9",
          "0"
        ],
        [
          "0",
          "2"
        ]
      ],
      [
        [
          "1/3",
          "0"
        ],
        [
          "0",
          "4"
        ]
      ],
      [
        [
          "1/2",
          "0"
        ],
        [
          "0",
          "8"
        ]
      ]
    ],
    "selected_star_beta": [
      "4/3",
      "5"
    ],
    "selected_star_residuals": [
      "-1/3",
      "2/3",
      "-1/3",
      "0",
      "0"
    ],
    "selected_star_variance": "2/27",
    "selected_studentized_square": "24",
    "pooled_finite_variance": "5/3",
    "true_n_variance_limit": "35/3",
    "pooled_n_variance_limit": "55/6"
  },
  "checks": 35006,
  "categories": {
    "with-replacement endpoint inclusion-exclusion": 249,
    "maximum exact CDF": 81,
    "without-replacement endpoint count": 266,
    "range law normalization": 2,
    "both original endpoints retained": 1,
    "range root quantiles": 1,
    "original n interval scale": 1,
    "exact Uniform range quantile bracket": 1,
    "range density normalization": 18,
    "range density integral": 378,
    "endpoint scaled mean": 84,
    "endpoint scaled variance": 84,
    "oracle subset CDF expectation": 2576,
    "random-block variance budget": 2576,
    "sequential uniform subset probability": 502,
    "absolute mean subset law": 1,
    "absolute mean replacement law": 1,
    "absolute mean quantile separation": 1,
    "hat matrix orthogonal projection": 7,
    "leverage bounds and trace": 7,
    "rank preserved exactly subunit leverage": 30,
    "OLS residual orthogonality": 928,
    "deleted coefficient direct refit": 4488,
    "deleted prediction residual": 4488,
    "deleted RSS direct refit": 4488,
    "HC3 uncentered deletion outer products": 901,
    "internal residual support bound": 4340,
    "Cook full fitted-vector norm": 4340,
    "external studentization algebra": 4008,
    "homoskedastic HC2 expectation": 6,
    "rank failure exactly unit leverage": 1,
    "unit leverage forces zero residual": 27,
    "high leverage terminal coefficients": 1,
    "high leverage terminal diagnostics": 1,
    "invertible feature change keeps diagnostics": 1,
    "changed coordinate coefficients": 1,
    "raw coefficient metric changes": 1,
    "heteroskedastic HC2 bias counterexample": 1,
    "wild direct refit equals linear update": 104,
    "exact wild conditional mean and covariance": 4,
    "group HC0 HC2 HC3": 1,
    "group selected wild record": 1,
    "refitted bootstrap studentization": 1,
    "frozen studentization is distinct": 1,
    "heteroskedastic pooling limit": 1,
    "Mammen exact moments": 5
  },
  "scope": "Exact finite laws and algebra. Asymptotic validity and Gaussian t laws are proved in the pages, not established by these finite checks."
}