Research on the Deterministic Mechanism of Prime Number Distribution Based on PDSM Primitive Vortex and V-DG Vortex Differential Geometry

Traditional number theory regards prime number distribution as a quasi-random statistical phenomenon and cannot fundamentally explain core problems such as the hierarchical law of prime gaps, twin prime clusters, ring-layer vacancies, and the differentiation of large and small gaps. This paper originally constructs the PDSM primitive vortex topological system and the V-DG vortex differential geometry framework. Based on the periodic structures of prime congruence residue classes with modulo 30 eight-ridge and modulo 210 forty-eight-ridge configurations, this paperpioneers the layered modulation mechanism of π decimal layers and defines vortex geodesics, vortex stress tensors, vortex curvature tensors, and vortex ζ operators. It fully transforms the phenomena of prime distribution, evolution and annihilation into deterministic geometric dynamic effects of constant negative curvature vortex manifolds, completely overturning the randomness hypothesis of prime distribution. Verified by numerical simulation, statistical tests and multi-objective parameter fitting: primes are not randomly scattered but steady-state singularities jointly determined by vortex manifold metric perturbation, stress eigenstates and curvature constraints;the dispersion of π decimal layers is significantly positively correlated with the number of prime ring-layer vacancies. The perturbation effect of inner vortices is strong while the perturbation of outer large rings decays, which perfectly matches the macroscopic law of prime distribution. Ultimately, the Riemann Hypothesis is equivalently transformed into a stress-curvature resonance eigen-condition of vortex manifolds, realizing the geometric reconstruction of the Riemann Hypothesis and establishing a geometric, deterministic new geometric number theory system.