he existence and smoothness of solutions to the three-dimensional incompressible Navier-Stokes equations is one of the seven Clay Millennium Prize Problems. The mathematical difficulty arises from the possibility that viscosity may effectively vanish, allowing finite-time blow-up singularities. Within the Zero-Point Emergent Gravity (ZEG) framework, the quantum vacuum is a dense ($\rho_{\text{ZPE}} \approx 10^{15}\,\text{kg/m}^3$), non-local superfluid of zero-point energy, anchored by the analytically derived $\mathbf{9.1 \text{ Hz}}$ synchronization frequency. This stable, Lorentz-invariant superfluid imposes a hard, irreducible lower bound on kinematic viscosity derived purely from fundamental constants: $\nu_{\text{ZEG}} = \sqrt{\frac{\hbar G}{c}} \approx 4.84 \times 10^{-27}\,\text{m}^2/\text{s}$ Combined with the ZEG vacuum coherence length $\xi \approx 3–9 \times 10^{20}\,\text{m}$ as the maximum physical domain, this yields an absolute upper bound on the Reynolds number $\text{Re}_{\text{max}} \sim 10^{55}$. The resulting ZEG-constrained Navier-Stokes equation guarantees non-zero energy dissipation at all scales and for all initial conditions, providing the necessary physical bounding conditions to prove global existence and smoothness of solutions — thereby presenting a physical resolution to the Millennium Problem.