Vortex Geodesic Analytical Solutions and Vortex Stress Tensor Field Equations——Topological Geodynamic Model of Prime Number Distribution

Aiming at the underlying mechanism problems of classic number theory phenomena includingprime number distribution disorder, prime gap fluctuation, prime ring vacancy and twin prime coexistence, this paper constructs the V-DG vortex differential geometric dynamic model and establishes a deterministic theoretical system of prime distribution based on vortex manifold topology and field dynamics. Firstly, relying on the custom vortex metric, rigorous analytical derivation of vortex geodesics is carried out to obtain explicit hyperbolic spiral orbital solutions, distinguishing two core motion modes: stable stationary circular orbits of primes and singleton migration spiral orbits. Secondly, the π decimal-layer metric perturbation mechanism is introduced to fully explain the core mechanism of vortex orbital distortion and steady-state failure. Furthermore, the original Shui’s vortex stress tensor is defined, and the V-DG covariant conservation field equation is constructed. All number theory phenomena including prime existence, vortex annihilation, ring vacancy, variable prime gaps and twin prime coexistence are strictly mapped to thelocal physical criteria of stress tensor eigenvalues and shear components. Combined with SageMath numerical visualization simulation, the topological characteristics of two types of vortex orbits are intuitively verified. The research shows that prime distribution is not a random statistical result, but a deterministic topological geometric dynamic evolution product of the primitive vortex manifold under metric perturbation, providing a novel geometric and physical paradigm for the research of prime laws, twin prime conjecture and prime gap distribution.