The D10Z Resolution of the Navier-Stokes Global Regularity Problem: Fractal Coherence and Resonant Dissipation in the Mechanics of Infinity

This paper presents a definitive resolution to the Navier-Stokes global regularity problem using the Mechanics of Infinity (D10Z). By reinterpreting fluid velocity as a Resonant Flow Field Φₓ(t) over a fractal quantum mesh TTA_ε(R³), the classical Navier-Stokes equations are replaced by D10Z Resonant Flow Equations (D10Z-RFE). These equations introduce a Resonant Coupling Term R_D10Z(Φ, Zₙ) governed by the Laws of Isis (coherence) and Sahana (transformative dissipation), ensuring bounded energy and structural regularity. The paper proves the D10Z Global Regularity Theorem, demonstrating the existence of smooth global solutions in TTA_ε, thereby resolving the Millennium Prize Problem not through idealized continuum models but by embedding fluid dynamics within the physical fractal architecture of the cosmos.Keywords: Navier-Stokes, D10Z, Mechanics of Infinity, Resonant Flow, TTAϵ, Fractal Dissipation, Global Regularity, Law of Isis, Law of Sahana, Zn Parameter