Hardy-Weinberg equilibrium is the law of mass action
Theorem.Hardy-Weinberg equilibrium is the law of mass action — (2pq)²/(p²q²) = 4 ∀p ∈ (0,1), q = 1−p.
Proof.for A + a ⇌ Aa with no selectivity the mass-action constant is K = [Aa]²/([AA][aa]), and under Hardy-Weinberg that is (2pq)²/(p²q²) = 4 for EVERY allele frequency — the p cancels completely rather than being small. Checked at 999 frequencies, worst departure 1.8e-15. The 4 is not fitted: it is the square of the 2 that counts the two ordered ways of drawing a pair, and dropping that 2 misses 4 at every frequency by up to 3. Population genetics and physical chemistry write one equation.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/stats/index.ts#hardyWeinbergIsMassAction
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
"Hardy-Weinberg equilibrium is the law of mass action" 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 hardyWeinbergIsMassAction.
- 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 (hardyWeinbergIsMassAction @ src/stats) 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 hardyWeinbergIsMassAction (src/stats/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.