AI-Assisted Proofs Narrow Navier-Stokes Existence Gap by Three Specific Results

The team combined human-designed invariants with reinforcement learning to search for potential blow-up solutions in three-dimensional incompressible flow. They established tighter bounds on enstrophy growth and ruled out singularities under two new symmetry classes that had previously remained open. Sample size consisted of exhaustive computational enumeration over discretized initial data up to 2^14 grid points, with formal verification in Lean for one of the three results.

Contextually this sits between the 2000 Clay Prize formulation and the partial regularity theorems of Caffarelli-Kohn-Nirenberg. The work does not claim a full resolution but shifts the problem into a narrower regime where existing analytic techniques may now suffice. It also illustrates how AI search can be constrained by rigorous human lemmas rather than operating as an unconstrained black box.

Next steps require extending the symmetry exclusions to the full non-periodic case and securing independent verification of the Lean formalization. A complete solution remains distant, yet the methodology supplies a template that could be applied to other Millennium problems with similar local regularity questions.