Global Regularity of Fractal Navier–Stokes Equations via the THZ Action and Disipation into the chi-Channel

The problem of existence and smoothness of solutions to the Navier–Stokes equations for incompressible fluid is treated not as an isolated mathematical question but as a consequence of a more fundamental physical paradigm. Within the Fractal Quantum Holographic Paradigm (FKGP 4.0) spacetime carries a fractal Hausdorff dimension D = 2.048, and classical differential equations are macroscopic approximations. Replacing the classical Laplacian with a fractional operator of order β = D − 1 = 1.048 provides dissipation sufficient for global regularity. Physically, this mechanism is interpreted as a drain of excess kinetic energy into the informational chi-channel whenever the fluid attempts to form a singularity. A Global Regularity Theorem is proved: for any initial data in H^β/2(R^3) the solution exists, is unique, and is smooth for all t > 0.