V64: Renormalization without Renormalization — Recovery of Natural Finiteness via the Dynamic Space Function Σ

Renormalization has long been regarded as an unavoidable but conceptually unsatisfactory procedure in quantum field theory, required to cancel divergent quantities arising from point-particle assumptions in a static vacuum. In this work, we demonstrate that these divergences are not fundamental, but rather artifacts of assuming a static background space. By introducing the space function Σ, originally developed in V60 as a dynamically generated spatial resolution, we show that self-energy terms become finite without subtraction or redefinition. Numerical simulations confirm smooth convergence of electron self-energy and reveal a universal invariant linking particle mass and spatial structure. Renormalization is thus reinterpreted as an emergent approximation of a deeper update-continuity principle. The Ward–Takahashi identity is preserved under Σ-regularization, demonstrating that gauge invariance and Lorentz covariance are maintained.