Before the new prefix-variance calculation,8 November2026.
The previous turn supplied a sufficient averaged-variation target, not its
arithmetic proof. Attempt a stronger source-specific pair bound which could
give it by a standard martingale energy argument.

Candidate: every binary-prefix conditional variance of the ACTUAL whole-union
window count is at most5 times its unconditional mean, at mean>=10.
If true at the required application, a BMO energy estimate would give
E V^3<=6*(5mu)^3=750mu^3<900mu^3. Derive this implication independently;
do not import it from the observed root variance or an independent model.

Try to falsify the finite candidate at the record slope,height2,b12.
Deduplicate all feasible words. Use windows L=256,512,1024,2048,4096.
Common period cap2^23; one process120seconds. Scan every dyadic prefix
exactly, retaining its conditional variance and mean. If a violation occurs,
save the worst prefix, its child count histogram and enough information for
a direct integer Syracuse audit. Do not infer failure of H6 or EV^3<=900mu^3
from failure of this stronger candidate.

Independently recompute the source density by3-state phase-entry transfer,
using qF=q(initial)+sum new-entry densities. This does not enumerate words
and is credited to the existing feasible-phase interval/entry identities.
Keep small-mean rows explicitly; do not make a universal claim from a pass.
