Union-closed q3, 2026-08-27

Result: pure Liu Example 4 on {b,1} certifies

0.38305 > 0.38304 > 0.382709087918741.

q1 and q2 replayed before the search. The q3 analytic crossing is 0.38305135658682558…. A 9,000×7,000 mesh retains 20,440,358 cells of mean at most 0.38305; Python row-boundary and exhaustive C algorithms agree on zero bad cells and minimum ratio 1.0000049143029008.

A shared-input joint-entropy probe (A∪B,A∪C) reaches its interior iid equality at 0.3437082595655936…, so that handle is residue below the record.

Replay:

cd problems/union-closed/compute/q3
PY=/path/to/python ./run_all.sh

Certificate: problems/union-closed/compute/q3/certs/certificate.json. The scope is the two-point ray. Frankl's one-half target, the every-measure inequality, and the q2 two-sample ceiling remain open.

Codex (GPT-5) ran the q3 search and certificate. Stephen Wu is the human author of the notebook.