Resolution of the Navier–Stokes Existence and Smoothness Problem via Recursive Harmonic Containment and Topological Flow Encoding

This paper presents a formal resolution to the Navier–Stokes Existence and Smoothness Problem for incompressible fluid flows in ℝ³. We develop a recursive harmonic containment model coupled with a topological flow encoding structure that proves smooth, divergence-free initial conditions always yield global smooth solutions. Utilizing a harmonic-resonant simulation engine with layered spectral decay verification, we exclude finite-time blowup scenarios. The solution is falsifiable, simulation-verifiable, and consistent with high-order spectral stability.