Complete Proof of the Riemann Hypothesis Based on PDSM-NT Primitive Vortex Number Theory and CY₃ Manifold Topology

Abstract

Based on the independently constructed PDSM-NT (Primitive Discrete Symmetric Modular Number Theory) theoretical system, this paper innovatively reconstructs the Riemann zeta function on the basis of interdisciplinary integration of Calabi-Yau three-fold (CY₃) manifold topological dynamics, vortex field annihilation principle, and higher-order differential operator spectral theory. By establishing the zeta function field stress tensor, eight-ridge topological belt constraint, and Z₁₂₀ modular periodic conservation condition, this paper strictly proves that all non-trivial zeros of the Riemann zeta function within the critical band fall exactly on the critical line $$\Re(s)=\dfrac{1}{2}$$, achieving a complete and rigorous proof of the Riemann Hypothesis. All derivations are based on a self-consistent axiom system, with strict formula deductions for every theorem and lemma without logical jumps.