Fano unique, |Aut| = 168
Theorem.Fano unique, |Aut| = 168 — |Aut(Fano)| = |GL₃(𝔽₂)| = 168, and 30 = 7!/168 labeled S(2,3,7) systems.
Proof.exhaustive backtracking counts 30 labeled S(2,3,7) systems; |GL₃(𝔽₂)| = 168 by brute-force determinant count; 7!/30 = 168 — one orbit, two routes.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/thunder/waves/index.ts#discoveredTheoremsProvenWave
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
"Fano unique, |Aut| = 168" 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 discoveredTheoremsProvenWave.
- 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 (discoveredTheoremsProvenWave @ src/thunder/waves) 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 discoveredTheoremsProvenWave (src/thunder/waves/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.