files / problems / union-closed / compute / q3 / certs / certificate.json

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{
  "status": "dent",
  "record_inequality": "0.38305 > 0.38304 > 0.382709087918741",
  "claimed_c": 0.38305,
  "analytic_crossing": "0.3830513565868255825016468730022052750943",
  "crossing_minus_claimed": "0.00000135658682558250164687300220528",
  "grid": {
    "n_b": 9000,
    "n_a": 7000,
    "b_lo": 0.02,
    "b_hi": 0.499,
    "a_lo": 0.0,
    "a_hi": 0.499,
    "total_cells": 63000000,
    "retained_cells": 20440358,
    "retained_rows": 6821,
    "mean_tolerance": 1e-15
  },
  "python": {
    "algorithm": "Python row-boundary scan using ratio monotonicity in a",
    "min_ratio": 1.0000049143029008,
    "n_bad_cells": 0,
    "at": {
      "i_b": 5192,
      "i_a": 1728,
      "b": 0.29636048449827757,
      "a": 0.12319931418774112,
      "mean": 0.3830483902434842
    }
  },
  "c": {
    "algorithm": "C exhaustive nested-loop mesh",
    "min_ratio": 1.0000049143029008,
    "n_bad_cells": 0,
    "at": {
      "i_b": 5192,
      "i_a": 1728,
      "b": 0.29636048449827757,
      "a": 0.12319931418774112,
      "mean": 0.3830483902434842
    }
  },
  "joint_star_probe": {
    "interior_equality_b": "0.343708259565593633604564834261331729339",
    "note": "failed handle: the independent shared-union joint-entropy inequality reaches equality below the q1/q3 ray constant"
  },
  "checks": {
    "analytic_replay_ok": true,
    "failed_joint_handle_replays": true,
    "python_replay_ok": true,
    "c_replay_ok": true,
    "claimed_constant_matches": true,
    "grid_dimensions_match": true,
    "retained_cell_counts_match": true,
    "minimum_ratios_match": true,
    "minimum_indices_match": true,
    "minimum_coordinates_match": true,
    "both_minima_strictly_above_1": true,
    "both_have_zero_bad_cells": true,
    "claim_below_analytic_crossing": true,
    "claim_strictly_beats_q1": true,
    "claim_strictly_beats_liu": true
  },
  "all_ok": true,
  "scope": "pure Liu Example 4 on the two-point family {b,1}; the every-measure and 1/2 statements remain open"
}