Navier-Stokes Without Infinity: A Structural Argument for the Dissolution of the Millennium Problem

The Navier-Stokes existence and smoothness problem asks whether smooth solutions of the incompressible Navier-Stokes equations in three dimensions can develop finite-time singularities. The Clay Mathematics Institute lists this as one of seven Millennium Prize Problems. We argue that the problem is dissolved, not solved, when the continuum assumption is recognized as a mathematical idealization rather than a physical description. We present two structural arguments for the dissolution. First, the vortex stretching mechanism, the engine of every known blow-up construction, requires a vortex tube diameter to shrink to zero. On a substrate with a minimum length, the diameter saturates, and the mechanism cannot complete. Second, when the vortex tube is modeled as a ring of discrete knots with finite state capacity, the circulation overflows into the Topological Redundancy Buffer (TRB) before the geometric bound is reached. The mechanism self-destructs; it loses its driving circulation before it can produce divergence. We document four numerical attempts to demonstrate these arguments through direct field simulation (spectral Navier-Stokes at multiple resolutions, filtered cascade, vortex ring dynamics, coarse-grained emergence test). All four failed to produce clean results, and we report this honestly. The failures are informative: they show that the substrate's chaotic dynamics do not support the naive numerical approach. The structural arguments stand independently of the simulations. We do not claim that Navier-Stokes emerges from the Finitism substrate. We do not claim that the mathematical Millennium Problem is solved. We claim that the physical problem, whether a physical fluid can develop infinite velocity gradients in finite time, is dissolved by the finiteness of the substrate.