Burnside counting witnessed on necklaces
Theorem.Burnside counting witnessed on necklaces — |X/G| = (1/|G|) Σ_{g∈G} |Fix(g)|.
Proof.(1/n)Σ k^gcd(i,n) equals brute canonical-rotation counting for all 24 (n,k) instances, n ≤ 8, k ≤ 3 — the orbit-counting lemma on the one-math gcd.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/thunder/verify/index.ts#discoveredTheoremsWaveEleven
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
"Burnside counting witnessed on necklaces" 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 discoveredTheoremsWaveEleven.
- 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 (discoveredTheoremsWaveEleven @ src/thunder/verify) 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 discoveredTheoremsWaveEleven (src/thunder/verify/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.