Graeco-Latin at 3,4,5 never 2
Theorem.Graeco-Latin at 3,4,5 never 2 — orthogonal Latin squares exist for n = 3, 4, 5 and not for n = 2.
Proof.orthogonal pairs verified cell-by-cell for n = 3, 4, 5; the complete order-2 exhaustion (both Latin squares, all pairings) finds none.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/thunder/waves/index.ts#discoveredTheoremsWaveTwo
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
"Graeco-Latin at 3,4,5 never 2" 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 discoveredTheoremsWaveTwo.
- 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 (discoveredTheoremsWaveTwo @ src/thunder/waves) 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 discoveredTheoremsWaveTwo (src/thunder/waves/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.