K₅ and K₃,₃ non-planar
Theorem.K₅ and K₃,₃ non-planar — K₅: 10 > 3·5−6 and K₃,₃: 9 > 2·6−4 violate the planar bounds e ≤ 3v−6 (bipartite e ≤ 2v−4).
Proof.10 > 3·5−6 and 9 > 2·6−4, exact Euler-bound arithmetic — the two Kuratowski obstructions (Euler formula and the converse cited).
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/thunder/waves/index.ts#discoveredTheoremsWaveTwo
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
"K₅ and K₃,₃ non-planar" 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 discoveredTheoremsWaveTwo.
- 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 (discoveredTheoremsWaveTwo @ 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 discoveredTheoremsWaveTwo (src/thunder/waves/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.