IV.C02 — Twin Prime Residue Theorem

The S₅ correction 121/120 is DERIVED via twin prime residue: for (p,q)=(3,5) twin primes with a=pq-p-1=11, s=(p-1)(q-1)=8, n=pq=15, the identity a²=s·n+1 holds because p(q-1)(q-p-2)=0. Upgraded from conjectural (was IV.C02 E₁ Page Hypothesis).