Global collision and pure-shuffle overhead audit

Exact statement

Exact enumeration checks 65,536 target-set families, 2,924 one-support policies with 28,856 signature intersections, and 3,905 pure-shuffle state-count vectors comprising 809,710 noninitial product states. All collision identities, matching boundaries, closed formulas, and clique-bound gaps agree.

StatusSource audit and independent complete-domain replay pass; strict-gap scope corrected

External reviewNo documented external or specialist review of these FPRD results is recorded.

Context

The audit separately tests the set identity, the support-matching intersection boundary, and the pure-shuffle finite-size count.

Proof or evidence

Direct multiplicity, collision excess, and inclusion–exclusion agree; nonempty one-support intersections are exactly matchings; the pure-shuffle formula and finite clique-bound gap agree state by state.

Global-overhead exact audit →

Verification notes

The source audit records 65,536 target-set families, 2,924 policies, 28,856 signature intersections, 3,905 size vectors, and 809,710 product states. An independent replay covers the target-set, size-vector, compatibility, and reduction domains and adds the single-block equality boundary; zero failures after correcting the prose scope.

Limitations

The computation is finite; arbitrary expression sizes and block counts come from the proofs.

Open work

Retain as implementation evidence; use the symbolic proofs for arbitrary sizes.