Cayley n^(n−2) to n = 7
Theorem.Cayley n^(n−2) to n = 7 — the number of labelled trees on n vertices is n^{n−2}.
Proof.raw exhaustion over edge subsets with union-find counts 1,1,3,16,125,1296,16807 — independent of the Prüfer bijection; Cayley cited for all n.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/thunder/waves/index.ts#discoveredTheoremsWaveFour
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
"Cayley n^(n−2) to n = 7" 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 discoveredTheoremsWaveFour.
- 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 (discoveredTheoremsWaveFour @ 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 discoveredTheoremsWaveFour (src/thunder/waves/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.