A Deterministic Entropy Barrier Preventing Finite-Time Blowup in the 3D Navier-Stokes Equations

We prove that smooth solutions of the three-dimensional incompressible Navier-Stokesequations with finite enstrophy cannot develop finite-time singularities. The argument isdeterministic and relies on three components: (i) classical blowup necessity results(Beale-Kato-Majda, Constantin-Fefferman) implying asymptotic directional collapse ofvorticity; (ii) a coercive relationship between directional collapse and a local alignmententropy functional; and (iii) a viscous entropy barrier arising from angular diffusion ofvorticity directions. Together these yield a contradiction: blowup would require entropycollapse, while viscosity enforces a strict lower entropy bound. No probabilisticassumptions, discretization hypotheses, or symmetry restrictions are used.