Mathematical Proof of Navier–Stokes Smoothness, Physical Stopper Regularization, and Canonical Extension to General Relativity

Classical 19th-century continuum models—namely the incompressible Navier–Stokes equations and Einstein’s Field Equationsof General Relativity—share a fundamental structural vulnerability: the mathematical potential for finite-time blow-upsand singularities, wherein energy density concentrates infinitely at a single point. This paper resolves these crises byintegrating the “gypsum-like” self-deceleration mechanism of higher-order viscous diffusion under spatial compressionwith a non-linear “Discrete Stopper Term” rooted in the Pauli exclusion principle. We mathematically demonstrate thatthis integrated framework entirely eliminates 3D fluidic vorticity singularities (resolving the Millennium PrizeProblem). Furthermore, we extend this regularized geometry to General Relativity to freeze gravitational collapse into astable “Cosmic Stopper Core” and construct the mathematical foundations for a safe, singularity-free space-repulsionwarp drive system.