Topological Residual Theory; Gravitational Constant; Vacuum Permittivity; Helmholtz's Vortex Theorems; Dimensional Analysis; Grand Unified Theory

The Standard Model of modern physics contains dozens of free parameters that cannot be derived from first principles, among which the gravitational constant G and the vacuum permittivity ε₀ are regarded as independent fundamental constants. Based on the "Topological Residual Theory" (TRT), this paper establishes the "spatial right-handed cylindrical spiral motion at the speed of light" as the first postulate. By introducing Helmholtz's vortex theorems from fluid dynamics, we construct a physical picture of local topological energy equilibrium between gravity and electromagnetism. Furthermore, utilizing the spiral path ratio Ω (the inverse of the fine-structure constant) and the speed of light c, we propose a cross-dimensional constant absorption mechanism. Strict mathematical derivations demonstrate that G and ε₀ are not independent empirical parameters, but rather geometric residual projections of the same spatial spiral fluid at different topological levels, satisfying the exact algebraic relationship G = μ₀/Ω². This research provides a novel, pure geometric paradigm for the grand unification of macroscopic gravity and microscopic electromagnetism.