PG(3,2) has 240 parallelisms
Theorem.PG(3,2) has 240 parallelisms — #parallelisms(PG(3,2)) = 240 — the 56 spreads exact-cover the 35 lines in 240 seven-spread partitions.
Proof.the 56 spreads exact-cover the 35 lines in exactly 240 seven-spread partitions — the complete census of Kirkman resolutions.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/thunder/verify/index.ts#discoveredTheoremsWaveNine
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
"PG(3,2) has 240 parallelisms" 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 discoveredTheoremsWaveNine.
- 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 (discoveredTheoremsWaveNine @ 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 discoveredTheoremsWaveNine (src/thunder/verify/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.