Topological Zero Tensor: Topological Resolution of Navier-Stokes Fluid Singularities and Proof of 0-Point Equilibrium via Active Intake Axis

DOI: 10.5281/zenodo.22840978 Over the past two centuries, the Navier-Stokes equations, which form the foundation of continuum mechanics, have exhibited an analytical limitation wherein the singularity blow-up of non-linear terms is inevitable under extreme turbulent stress conditions. This study proposes the "Topological Zero Tensor (TZT)", a novel geometric generalization that introduces a topological framework to resolve these microscopic Navier-Stokes fluid singularities.

It substitutes destructive fluid energy into resistanceless rotational energy via topological curvature, rather than confronting and suppressing it directly. TZT is an analytical model that entangles an active intake axis featuring structurally invariant boundary conditions with an energy-dissipative multidimensional closed loop. Extreme linear vector energy introduced from the exterior transitions into a toroidal spin without stress accumulation, mediated by TZT's 0-point metric operator, which universally absorbs both symmetric curvature and antisymmetric topological spin.