Structural Proof of the 3D Navier-Stokes Global Smoothness: A Mandatory Overlap Tax (MOT) Resolution

This paper provides a concise structural resolution to the 3D Navier-Stokes Global Smoothness problem by mapping fluid dynamics to the Mandatory Overlap Tax (MOT) framework. We define the non-linear inertial term (u • ∇u) as a Growth Surplus (S) and viscous dissipation (νΔu) as a Mandatory Overlap Tax (W). Building on the Universal Deficit Ratio (W = 2S) established in the my previous budgetary proofs of the Lonely Runner Conjecture(https://doi.org/10.5281/zenodo.18761522), we demonstrate that as the fluid moves toward smaller scales, the Tax (dissipation) scales quadratically while the Surplus (acceleration) scales only linearly. This creates a state of Strictly Dissipative Debt, where the fluid goes bankrupt and exhausts its kinetic energy before a velocity singularity (u --> ∞) can ever be funded. Consequently, the velocity field must remain Smooth and Globally Defined for all time, as the structural laws of the MOT framework forbid the existence of an infinite-density singularity.