Extreme Regimes of Geometric Renormalization and Horizon Structures in Theory Space

Extreme Regimes of Geometric Renormalization and Horizon Structures in Theory Space investigates high-gradient regions of the renormalization group (RG) flow within a geometric formulation of theory space. Without modifying beta functions, invariant dimension, or categorical structure, the paper analyzes extreme RG intensity as a structurally admissible regime of geometric renormalization. In these regions, the RG vector field acquires large norm while preserving smoothness and finite invariant dimension. The resulting quotient geometry produces boundary structures analogous to event horizons, interpreted as limits of theoretical accessibility rather than spacetime singularities. Entropic relaxation along gradient RG flow yields evaporation-like behavior without introducing new dynamics. The work demonstrates that black hole–like phenomena can emerge as extreme but structurally stable configurations within geometric renormalization, fully compatible with invariant dimension, scheme covariance, Fredholm structure, and categorical consistency.