files / problems / union-closed / compute / q2 / certs / certificate.json

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{
  "family": "{b,1}",
  "class": "2-sample bit protocols with product coupling of (S,T)",
  "claimed_c_unchanged": 0.38304,
  "ceiling": "0.383051356586825582501646873002",
  "b_star": "0.296493923569337569030703383782",
  "critical_equation": "h(b) = (1-b) log2((1-b)/b)",
  "constant_moved": false,
  "why": "every protocol has h(OR) ≤ 1 on the (b,b) cell, so first-crossing ≤ min 1-(1-b)h(b). Example 4 already attains the min.",
  "hunts": [
    "iid + Example-4 β-scan",
    "iid + Example-5",
    "Example-4 + Example-5",
    "iid + Example-4 + maxent",
    "Example-5 scale ℓ",
    "half-target Fréchet protocol",
    "scaled a(t)",
    "3-atomic and 2-mixture samples",
    "constructed 2-mixture witness at mean 0.38304"
  ],
  "mixture_witness": "certs/mixture_witness.json",
  "not_claimed": [
    "1/2 conjecture",
    "every measure on [0,1]",
    "a frequency above 0.38304",
    "Gilmer Conjecture 1 (refuted by Ellis and Sawin)"
  ],
  "replay": "cd problems/union-closed/compute/q2 && ./run_all.sh"
}