Gauss partitions the clock
Theorem.Gauss partitions the clock — Σ_{d|108} φ(d) = 108 instantiated at the hero cycle.
Proof.Σ_{d|108} φ(d) = 108 instantiated at the hero cycle — the 108 integer phases split by gcd class, each divisor clock owning exactly φ(d) primitive phases (compounds on wave fifty-four, computed on the sealed gcd).
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
"Gauss partitions the clock" 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.