The task completed here

The single new target selected by the plan is an explicit finite Hellinger certificate at one specified dimension and correlation. Theorem thm:finite completes that target for

It covers every Boolean function at this frozen instance, not merely a named coordinate and one selected comparison.

The all-dimensional soft-information and Hellinger statements are recorded separately below. They are not hypotheses of Theorem thm:finite. Completing one finite instance does not verify either general proof.

The finite calculation is elementary and is not represented as a new resolution of the original conjectures. Its contribution is a fully specified, reproducible certificate with explicit gaps and a clearly bounded dependency structure.