Finite Black Holes and the Symbolic Universe: Resolving Singularity and Holographic Memory through KN Symmetry

This paper presents a unified treatment of gravitational finitude under KN symmetry, a ratio-preserving nonlinear transformation that replaces mathematical divergence with bounded structure. Applying KN regularization to black-hole collapse and information dynamics yields finite curvature, stable symbolic feedback loops, and a holographic correspondence that conserves information through bounded evolution. The framework demonstrates that apparent infinities—singularities, ultraviolet divergences, and unbounded spacetime scales—are artifacts of under-defined mathematics rather than physical reality. By integrating results from five prior open-science studies, this synthesis establishes a coherent model connecting curvature stabilization, modular feedback, and symbolic holography into a single finite description of the universe. The work suggests that physical law can be expressed entirely in bounded, reproducible form—without renormalization, extra dimensions, or mathematical infinities—offering a testable path toward a complete symbolic theory of gravity and information.