A₇ is simple
Theorem.A₇ is simple — |A₇| = 2520, classes {1,70,105,210,280,360,360,504,630} — no class-union containing 1 divides 2520.
Proof.all 2520 even permutations, classes {1,70,105,210,280,360,360,504,630} (7-cycle split by centralizer order), zero class-union divisors — the simplicity machine, third rung.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/thunder/verify/index.ts#discoveredTheoremsWaveTen
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
"A₇ is simple" 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 discoveredTheoremsWaveTen.
- 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 (discoveredTheoremsWaveTen @ 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 discoveredTheoremsWaveTen (src/thunder/verify/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.