The verification machinery is sound on every axis we could test: (a) bit-for-bit agreement with an independent big-integer gcd implementation on all 1,113,775 pairs for n ≤ 300; (b) exact reproduction of every known exception from the literature; (c) the Sylvester–Schur invariant (some prime > i divides C(n,i)) verified on all ~2.5×10⁹ (n,i) rows with zero anomalies; (d) every Kummer digit-box mask bit re-derived from the independent Legendre valuation formula at n ∈ {65535, 65536, 65537, 70000, 99000, 100000} — chosen to bracket the 17-binary-digit boundary where a stack-corruption bug (fixed-size digit arrays) invalidated our first production run. The bug, fix, and re-verification are logged in the investigation trail; all published numbers come from the post-fix rerun.