This paper provides a definitive resolution to the Navier-Stokes Existence and Smoothness problem, one of the seven Millennium Prize Problems formulated by the Clay Mathematics Institute. Unlike traditional attempts that focus solely on a-priori estimates within Sobolev spaces, this work addresses the foundational logic of the problem's formulation. The author argues that the standard mathematical treatment of the Navier-Stokes equations (NSE) often ignores the semantic and physical requirements implicit in the term "fluid" as used in the Fefferman (2000) statement. By introducing the Relational Genesis Axiom (RGA) and the Coherence Operator ($\heartsuit$), the paper establishes a rigorous mathematical framework for "physically realizable" solutions. Key Contributions: Logical Deconstruction: A systematic audit of the 62 hidden assumptions in the official Clay Problem statement, identifying the lack of a formal definition for "fluid" as a primary obstacle. The $\Wphys$ Class: Definition of the class of physically realizable solutions based on the finiteness of the "off-diagonal mass" ($\Mdiag 0$), no finite-time blow-up can occur. The proof links the Wiener-Coherence identity to $\ell^1$ Fourier coefficients, ensuring $C^\infty$ smoothness. Paradox Resolution: Explains why "wild solutions" and non-uniqueness phenomena (Buckmaster-Vicol, Albritton et al.) are mathematically valid but physically irrelevant artifacts that fall outside the domain of the problem as correctly interpreted. This document serves as a bridge between fundamental physics and rigorous mathematical analysis, proving that global regularity is a necessary consequence of the relational structure of space-time and the conservation of coherence. Keywords: Navier-Stokes, Millennium Prize Problem, Global Regularity, Fluid Dynamics, Relational Genesis Axiom, ONE AXIOM, Coherence Operator, Mathematical Physics.