Bell numbers count set partitions
Theorem.Bell numbers count set partitions — B_{n+1} = Σ_{k=0}^{n} C(n,k)·B_k.
Proof.the Bell-triangle recurrence gives 1,1,2,5,15,52,203,877,4140 matching the RAW count of set partitions for every n ≤ 8 — two independent computations agreeing.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/9/1/index.ts#discoveredTheoremsWaveTwentyEight
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
"Bell numbers count set partitions" 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 discoveredTheoremsWaveTwentyEight.
- 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 (discoveredTheoremsWaveTwentyEight @ src/9/1) 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 discoveredTheoremsWaveTwentyEight (src/9/1/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.