Diversity factorizes exact global collision overhead

Exact statement

Let $x$ be a maximum-degree participant, let $\mathcal A$ be the supports through $x$ , and let $\mathcal B$ be the $\gamma$ exceptional supports avoiding $x$ . Every compatible signature family is either a matching $N\subseteq\mathcal B$ , or $N\cup\{A\}$ for exactly one compatible $A\in\mathcal A$ . The target-set collision identity therefore gives an exact algorithm using $O(|\mathcal F|2^\gamma)$ target-intersection oracle calls, without enumerating the component product.

StatusSelf-contained proof; exact policy-valid target audit passes

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

Context

After choosing a participant that occurs in as many supports as possible, the remaining gamma supports form a valid exceptional kernel. A compatible family can use at most one support through the chosen participant, but FPRD-SH-T33 shows that this kernel need not be minimum.

Proof or evidence

Inclusion–exclusion splits uniquely into exceptional matchings and their one-hub extensions.

Diversity factorization theorem →

Verification notes

2,000 policy-valid target systems containing 24,636 useful states agree with direct collision excess.

Limitations

The complexity counts calls to a target-intersection oracle; the cost of representing and intersecting target sets is expression-dependent.
Equal conflict masks need not have equal target sets.
No external priority claim is made.

Open work

Test the factorization against an externally posed problem before extending the framework further.