PDSM-NT Primordial Vortex Number Theory — Full Equivalence Theory of CY3 Manifold Topology and Riemann Zeta Zeros

Abstract

This paper establishes a novel primordial vortex number theory system (PDSM-NT). By constructing an eight-ridge topological band and Π-ridge vortex structure on a Calabi–Yau three-fold (CY3) manifold, we define a new topological stress tensor (Shui’s stress tensor). We rigorously prove the one-to-one equivalence between the non-trivial zeros of the Riemann zeta function and vortex annihilation singularities on the CY3 manifold. With the 120-ary homology base constraint, Laurent expansion near singularities, and global topological loop conservation, we geometrically explain the critical line constraint, periodic prime distribution, and zero symmetry. This work completes a structural proof of the Riemann hypothesis from fundamental topological geometry. The system is self-consistent, closed, and rigorous, achieving a unified correspondence between analytic number theory and high-dimensional differential topology.