divisor-count multiplicativity τ(2^a·3^b) = (a+1)(b+1)
Theorem.divisor-count multiplicativity τ(2^a·3^b) = (a+1)(b+1) — τ(mn)=τ(m)τ(n).
Proof.τ(mn)=τ(m)τ(n) for every coprime pair ≤ 200 with τ(p^k)=k+1 exact — wave 63’s 12-divisor count generalized to the lattice-size law.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/4/6/index.ts#discoveredTheoremsWaveSixtyFour
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
"divisor-count multiplicativity τ(2^a·3^b) = (a+1)(b+1)" 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 discoveredTheoremsWaveSixtyFour.
- 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 (discoveredTheoremsWaveSixtyFour @ src/4/6) 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 discoveredTheoremsWaveSixtyFour (src/4/6/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.