R(3,3,3) ≤ 17
Theorem.R(3,3,3) ≤ 17 — R(3,3,3) ≤ 3·(R(3,3) − 1) + 2 = 17.
Proof.the recurrence 3(R(3,3)−1)+2 computed from the proven R(3,3) = 6; Greenwood–Gleason equality cited — a bound that EMERGED from a prior proof.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/thunder/waves/index.ts#provenTheoremsCompound
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(3,3,3) ≤ 17" 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 provenTheoremsCompound.
- 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 (provenTheoremsCompound @ src/thunder/waves) 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 provenTheoremsCompound (src/thunder/waves/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.