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

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{
  "claimed_c": 0.38305,
  "q1_c": 0.38304,
  "liu_quote": 0.382709087918741,
  "record_inequality": "0.38305 > 0.38304 > 0.382709087918741",
  "b_star": "0.2964939235693375690307033837822290478675",
  "crossing": "0.3830513565868255825016468730022052750943",
  "crossing_float": 0.3830513565868256,
  "crossing_minus_claimed": "0.00000135658682558250164687300220528",
  "critical_eq_residual": "1.05421979432e-81",
  "g_second_derivative": "-7.35897097258475540845923306712",
  "saturation_ratio_at_bstar_for_claimed_c": "1.00000219886507583093403450291",
  "checks": {
    "critical_residual_below_1e_60": true,
    "g_second_derivative_negative": true,
    "crossing_above_claimed": true,
    "claimed_above_q1": true,
    "claimed_above_liu": true,
    "saturation_ratio_strictly_above_1": true
  },
  "all_ok": true
}