Abstract We propose that the Navier-Stokes existence and smoothness problem, asking whether smooth solutions to the three-dimensional incompressible Navier-Stokes equations always exist globally, is resolved by the discrete structure of spacetime in Tick Graph Theory (TCC; Ploof 2026b). The Kolmogorov turbulent energy cascade, reinterpreted through Scale-Recursive Non-Uniform Domain Tiling (SRNUDT; Ploof 2026a, 2026c), is a remainder propagation process: organized laminar flow domains generate energy they cannot internally contain, which propagates as remainder to progressively smaller scales. In continuous spacetime, this cascade has no lower bound, permitting the mathematical singularities whose existence or non-existence constitutes the Millennium Prize problem. In TCC discrete spacetime, the cascade cannot propagate below the Planck-scale tick length (approximately 1. 616 x 10^-35 meters), providing a physical UV cutoff. We show that this cutoff implies global regularity: smooth solutions always exist in physical TCC spacetime because finite-time blowup requires remainder cascade to reach a mathematical singularity that the Planck floor structurally prevents. We further demonstrate that the Navier-Stokes mathematical singularity, when approached in the equations, corresponds physically not to a fluid pathology but to a gravitational phase transition, specifically a black hole formation event, at Planck-scale energy densities. The fluid singular regime and the general relativistic singular regime are the same physical phenomenon at different scales of description. TCC correction terms to the classical Navier-Stokes equations are of order (lP/L) ² and are negligible at all macroscopic scales, consistent with the empirical success of classical fluid dynamics. Testable predictions and the open mathematical formalization required are stated explicitly.
Bradley Ploof (Sun,) studied this question.