Geometric Regularization via Damping: Finite-Scale Transitions, Core Regularization, and the φ-Regime

This repository contains a paper-ready LaTeX manuscript describing a geometric damping framework applied to spherically symmetric spacetime metrics. The work distinguishes between exponential far-field damping and core regularization, clarifies their respective physical roles, and introduces a hybrid metric that remains smooth for all radii. A mathematically explicit definition of a “radical breakdown” of microscopic descriptions is provided, together with the introduction of a φ-dominated effective regime as an emergent, non-energetic structural layer. The approach is conservative in scope, avoids claims of energy generation, and is formulated to be testable against gravitational, lensing, and galactic-scale observations.