PSL(2,7) is simple and matches GL(3,2)
Theorem.PSL(2,7) is simple and matches GL(3,2) — PSL(2,7) ≅ GL₃(𝔽₂) — order 168, classes {1,21,24,24,42,56} identical.
Proof.168 fractional-linear permutations of P¹(𝔽₇), classes {1,21,24,24,42,56} identical to GL(3,2) on 𝔽₂³∖0, zero normal candidates — the registry two 168s bridged at class level; the isomorphism classical, cited.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/thunder/verify/index.ts#discoveredTheoremsWaveEleven
1 · Classification
finite-complete — computed witness within a cited frame (the unbounded form leans on the cited literature)
2 · Provenance
Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.
Acknowledgment
"PSL(2,7) is simple and matches GL(3,2)" 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 discoveredTheoremsWaveEleven.
- 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 (discoveredTheoremsWaveEleven @ 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 discoveredTheoremsWaveEleven (src/thunder/verify/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.