NAVIER-STOKES TRUE – REGULARITY THROUGH FINITE FRACTIONING Resolution of the Millennium Problem through the TRUE Framework

The Navier-Stokes equations, which describe the motion of fluids, lie at the heart of physics and engineering. Their complete resolution is one of the Millennium Prize Problems. The difficulty arises from the possibility of singularities (finite-time blow-ups) due to the continuous and infinitely divisible nature of space and time. The TRUE framework (Théorie Redistributive Universelle Évolutive — Evolutionary Universal Redistributive Theory) proposes to replace infinite fractioning with finite fractioning, with a minimal step h_0 linked to the invariant \gamma_0 = 0.13648 . We rewrite the Navier-Stokes equations in discrete form, replacing derivatives with exact finite differences. We prove that the solution exists, is unique, and is regular for all time. We show that the classical solution is the limit of the TRUE solution as h_0 \to 0 . A dedicated section on turbulence establishes the link between the minimal step h_0 and the Kolmogorov scale, showing that the energy cascade is naturally truncated, thus preventing the formation of singularities.