36 officers are impossible
Theorem.36 officers are impossible — ∄ orthogonal Latin squares of order 6 — Euler’s 36 officers have no solution.
Proof.all 9408 reduced Latin squares of order 6 exhausted — none admits six disjoint transversals: Tarry 1900 upgraded from citation to complete computation.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/thunder/verify/index.ts#discoveredTheoremsWaveNine
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
"36 officers are impossible" 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 discoveredTheoremsWaveNine.
- 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 (discoveredTheoremsWaveNine @ src/thunder/verify) 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 discoveredTheoremsWaveNine (src/thunder/verify/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.