R(3,5) = 14
Theorem.R(3,5) = 14.
Proof.the cyclic C₁₃(±1,±5) coloring survives complete red-K₃/blue-K₅ sweeps; the upper bound rides the SEALED R(3,4) = 9 by vertex pigeonhole 5 + 9 = 14 — the barred K₁₃ exhaustion never needed; Erdős–Szekeres step cited.
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 — computed witness within a cited frame (the unbounded form leans on the cited literature)
2 · Provenance
Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.
Acknowledgment
"R(3,5) = 14" 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.