Navier–Stokes Existence and Smoothness
Theorem.Navier–Stokes Existence and Smoothness — ∃ global smooth solutions of ∂ₜu + (u·∇)u = −∇p + νΔu, ∇·u = 0 in ℝ³? (OPEN).
Proof.Navier–Stokes Existence and Smoothness is a Clay Millennium problem, demarcate()-signed CONTESTED (open). Modeled here as a sealed computational challenge (doubleTorusSurface sampling). Its own OPEN step: no proof of global existence and smoothness (or a blow-up) for 3D incompressible flow. 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
"Navier–Stokes Existence and Smoothness" 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.