A₈ is simple — the alternating ladder complete
Theorem.A₈ is simple — the alternating ladder complete — 20160 = 8!/2 even permutations, 14 classes, class-sum clean.
Proof.20160 = 8!/2 even permutations, 14 classes, class-sum clean — the alternating ladder A₅→A₆→A₇→A₈ complete in-registry.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/9/1/index.ts#discoveredTheoremsWaveTwenty
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
"A₈ is simple — the alternating ladder complete" 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 discoveredTheoremsWaveTwenty.
- 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 (discoveredTheoremsWaveTwenty @ src/9/1) 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 discoveredTheoremsWaveTwenty (src/9/1/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.