orbit-stabilizer theorem
Theorem.orbit-stabilizer theorem — |orbit(x)|·|stab(x)| = |G| for S₄ and A₄ acting on their points.
Proof.|orbit(x)|·|stab(x)| = |G| for S₄ and A₄ acting on their points — orbit size times stabilizer size recovers the whole group (the counting identity behind Burnside).
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/9/1/index.ts#discoveredTheoremsWaveThirtyFive
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
"orbit-stabilizer theorem" 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 discoveredTheoremsWaveThirtyFive.
- 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 (discoveredTheoremsWaveThirtyFive @ src/9/1) 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 discoveredTheoremsWaveThirtyFive (src/9/1/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.