Uniform-support stability and collision audit

Exact statement

Exact enumeration checks 1,082,432 support families in four complete small domains, all 182 maximal intersecting families at $(n,r)=(7,3)$ , and 640 deterministic larger policies. The EKR, Hilton–Milner, complementary-pair, spectral, and one-shot matching receipts all agree; the 175 maximum empty-core $(7,3)$ families are exactly the classical equality constructions.

StatusSource replay and independent boundary audit pass; T22/T23 hypotheses corrected

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

Context

The audit targets the phase boundary and equality structures rather than treating EKR as a black-box size inequality.

Proof or evidence

Complete-domain enumeration, maximal-clique enumeration, and independent matching counts agree with every stated boundary and receipt.

Uniform-support exact audit →

Verification notes

The source audit covers 1,082,432 complete-domain families, 182 maximal (7,3) intersecting families, 175 equality families, 640 larger policies, and 10,466 matching states. An independent audit adds the hostile (5,3), n=2r, and r=1 boundaries; zero failures after correcting the theorem hypotheses.

Limitations

The computation is finite; arbitrary-size conclusions come from the proofs and cited classical theorems.

Open work

Retain as implementation evidence; use the classical theorems and spectral proof for arbitrary parameters.