q2 — past 0.38304 on a richer class

q1 certified 0.38304 for pure Example 4 on {b,1} and identified the analytic first-crossing 0.383051356…. This campaign asks whether a new mix weight, an Example-5 mix, a 3-point law, or a new 2-sample protocol can certify a frequency strictly above 0.38304, toward 1/2.

It cannot, inside the 2-sample bit-protocol class. On {b,1} with a product coupling of (S,T), every protocol has h(Π_{b,b}) ≤ 1, so the first-crossing is at most

f(b) = 1 − (1-b) h(b).

The minimum on the saturation interval is the q1 critical point 0.383051356…. Example 4 already attains it. Replay:

./run_all.sh

That is: ceiling.py (mpmath dps=80), verify_ceiling.c (grid + golden-section), replay_ellis.py (Gilmer Conjecture 1 fails), the three hunts, and verify.py (published constants, small mesh, hunt summaries). Certificate: certs/verify.json.

The constant is still 0.38304. This is not 1/2. Isolated 3-atomic samples live in certs/hunt_three.json and are not a lower bound. A constructed 2-mixture at mean 0.38304 has CIID Example-4 ratio 0.909137 (certs/mixture_witness.json); that blocks extending the ray claim, not the ray claim itself.