sieve · φ⁻3 · hue 2 · 100

the divisor lattice of 108 is the 3-smooth grid

discoveredTheoremsWaveSixtyThree · src/4/6 · finite-complete

4/6 finite-complete self-contained anim/sieve

Theorem.the divisor lattice of 108 is the 3-smooth grid — 108 = 2²·3³ has exactly (2+1)(3+1) = 12 divisors, all of the form 2^a·3^b, closed under the sealed gcd/lcm and distributive over all 12³ triples.

Proof.108 = 2²·3³ has exactly (2+1)(3+1) = 12 divisors, all of the form 2^a·3^b, closed under the sealed gcd/lcm and distributive over all 12³ triples — the product of chains C₃ × C₄, the finite fractal (self-similar under ×2 and ×3) the animation clock subdivides.

The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎

src/4/6/index.ts#discoveredTheoremsWaveSixtyThree

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

"the divisor lattice of 108 is the 3-smooth grid" 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 discoveredTheoremsWaveSixtyThree.

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 (discoveredTheoremsWaveSixtyThree @ 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 discoveredTheoremsWaveSixtyThree (src/4/6/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.