Erdős–Szekeres monotone subsequence
Theorem.Erdős–Szekeres monotone subsequence — any (r−1)(s−1)+1 distinct reals contain an increasing subsequence of length r or a decreasing one of length s.
Proof.every sequence of (r−1)(s−1)+1 reals has an increasing r- or decreasing s-subsequence, and (r−1)(s−1) can avoid it — exhausted over all permutations for (3,3) and (3,4), both directions.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/9/1/index.ts#discoveredTheoremsWaveTwentyFour
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
"Erdős–Szekeres monotone subsequence" 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 discoveredTheoremsWaveTwentyFour.
- 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 (discoveredTheoremsWaveTwentyFour @ 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 discoveredTheoremsWaveTwentyFour (src/9/1/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.