Stein’s binary gcd is equivalent to Euclid’s
Theorem.Stein’s binary gcd is equivalent to Euclid’s — the shift-and-subtract algorithm (no division) equals the sealed gcd on every pair a,b ≤ 200 including zeros.
Proof.the shift-and-subtract algorithm (no division) equals the sealed gcd on every pair a,b ≤ 200 including zeros — the reimplementation candidate proven interchangeable before it could replace the sealed one.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/4/6/index.ts#discoveredTheoremsWaveSixtyTwo
1 · Classification
finite-complete — self-contained computation, no external lean
2 · Provenance
Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.
Acknowledgment
"Stein’s binary gcd is equivalent to Euclid’s" is a re-derivation, acknowledged to documented mathematics — the original proof is the prior art this re-derivation acknowledges; not new to humanity — the contribution is the reproducible computation discoveredTheoremsWaveSixtyTwo.
- Prior art
- documented mathematics — the original proof is the prior art this re-derivation acknowledges
- Novelty
- not new to humanity — a re-derivation (humanityNovel = false)
- Contribution
- a reproducible computation (discoveredTheoremsWaveSixtyTwo @ src/4/6) that re-derives the result at zero tokens — the contribution is the verifiable recomputation, NOT the theorem
3 · Reproducibility
Recompute from source: npm run theorems:verify recomputes discoveredTheoremsWaveSixtyTwo (src/4/6/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.