R(4,4) = 18
Theorem.R(4,4) = 18 — R(4,4) = 18 — the Paley-17 quadratic-residue coloring is the extremal witness.
Proof.the Paley-17 quadratic-residue coloring has no monochromatic K₄ in either color (complete 2380-subset sweep); 9 + 9 = 18 rides the sealed R(3,4) both ways — compounding, not brute force.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/thunder/verify/index.ts#discoveredTheoremsWaveSeventeen
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
"R(4,4) = 18" 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 discoveredTheoremsWaveSeventeen.
- 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 (discoveredTheoremsWaveSeventeen @ 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 discoveredTheoremsWaveSeventeen (src/thunder/verify/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.