Non-Singular Cosmological Evolution via Functional Renormalization Group Flows and Categorical Descent

General Relativity predicts its own demise at singularities, where spacetime geodesics break down. This research proposes a framework to resolve these singularities by treating them not as mathematical endpoints, but as physical phase transitions governed by the Functional Renormalization Group (FRG). By formalizing a correspondence between the geometric flow of spacetime (Ricci flow) and the RG flow of quantum fields, I investigate the hypothesis that black hole interiors evolve into scale-invariant macroscopic subsystems. This project employs Category Theory (specifically descent data on fiber bundles) to ensure mathematical consistency across hierarchical scales. The ultimate objective is to derive coupled constraints on the variation of fundamental constants ($\alpha, G$), offering a falsifiable resolution to current tensions in precision cosmology such as the Hubble crisis.