GATE D5
Uniform prime transfer, all p>182
What changed
The single prime p=191 becomes a theorem over primes: the k=13 tight interface is proper for EVERY prime p>182. The witness test reduces by CRT to a p-independent form, each representative gets a fixed s and an exact rational witness arc, and a lattice-point lemma supplies a witness for all p above threshold P0=78, so there are zero exceptional primes.
Evidence
check 1CRT-reduced witness formula validated exactly vs all 16,171 D4 witnesses (0 mismatch)
check 2Aggregate threshold P0=78, in-scope exceptional primes = none (183 > 78)
check 3Two independent verifiers ACCEPT, 18 of 18 corruption rejected, small-k matches exhaustive truth
Verification: double · I2 · 13 artifacts (reports, verifiers, corruption suites, manifest with SHA-256)