van der Waerden W(2,3) = 9
Theorem.van der Waerden W(2,3) = 9 — W(2,3) = 9.
Proof.every 2-coloring of {1..9} forces a monochromatic 3-term progression (all 512 exhausted) and {1..8} has an escaping coloring — the exact threshold, both directions; van der Waerden cited for all r, k.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/9/1/index.ts#discoveredTheoremsWaveTwentyThree
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
"van der Waerden W(2,3) = 9" 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 discoveredTheoremsWaveTwentyThree.
- 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 (discoveredTheoremsWaveTwentyThree @ 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 discoveredTheoremsWaveTwentyThree (src/9/1/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.