STS(9) unique, |Aut| = 432
Theorem.STS(9) unique, |Aut| = 432 — 9!/840 = 432 = |AGL(2,3)| — the unique STS(9) and its automorphism group.
Proof.840 labeled systems counted; 9!/840 = 432 = |AGL(2,3)| = 9·48 by independent brute force — the project harmonic as an automorphism count, two routes as with Fano 168.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/thunder/verify/index.ts#discoveredTheoremsWaveSeven
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
"STS(9) unique, |Aut| = 432" 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 discoveredTheoremsWaveSeven.
- 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 (discoveredTheoremsWaveSeven @ 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 discoveredTheoremsWaveSeven (src/thunder/verify/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.