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

667 B · on GitHub

{
  "claim": "On every 2-atomic law supported on {b,1}, the iid + Liu-Example-4 mix with beta=1/5 has Gilmer ratio >= 1 whenever the mean is at most 0.38285.",
  "claimed_c": 0.38285,
  "claimed_beta": 0.2,
  "beats": {
    "name": "Liu 2023 Example-5 numerical constant",
    "value": 0.382709087918741,
    "arxiv": "2306.08824",
    "independently_recomputed": 0.382709087918735
  },
  "mesh_first_crossing_ex4_beta020": 0.38289680852720065,
  "mesh_min_ratio_at_claimed_c": 1.0000771402076711,
  "not_claimed": [
    "Frankl 1/2",
    "unconditional bound for every measure on [0,1]",
    "universe size 13",
    "|F| = 51"
  ],
  "replay": "compute/verify.py"
}