P vs NP
Theorem.P vs NP — P = ⋃ₖ TIME(nᵏ), NP = ⋃ₖ NTIME(nᵏ) — is P = NP? (conjectured: P ≠ NP; OPEN).
Proof.P vs NP is a Clay Millennium problem, demarcate()-signed CONTESTED (open) — the SAME common metric every theorem gets. Modeled here as a sealed computational challenge (SAT verifies in poly · content-address O(1) vs brute scan · efficiencyScalesToInfinityAtNoCostOnReuse). Its own OPEN step, stated in the theorem: no sealed P≠NP (or P=NP) separation — amortized reuse ≠ complexity separation. The claim lives in the theorem. HARMONY ≠ TRUTH.
The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎
src/research/index.ts#clayChallengesComputableFromSequence
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
"P vs NP" 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 clayChallengesComputableFromSequence.
- 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 (clayChallengesComputableFromSequence @ src/research) 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 clayChallengesComputableFromSequence (src/research/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.