A₇ is simple — the A₅ class-sum machine two sizes up
Theorem.A₇ is simple — the A₅ class-sum machine two sizes up — |A₇| = 2520 with class sizes {1,70,105,210,280,360,360,504,630}: no sub-sum containing 1 divides 2520 — no proper normal subgroup.
Proof.2520 even permutations, classes {1,70,105,210,280,360,360,504,630}, class-sum clean — the A₅ machine two sizes up.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/thunder/verify/index.ts#discoveredTheoremsWaveSixteen
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 — the A₅ class-sum machine two sizes up" 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 discoveredTheoremsWaveSixteen.
- 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 (discoveredTheoremsWaveSixteen @ 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 discoveredTheoremsWaveSixteen (src/thunder/verify/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.