General Projection Geometry: Vacuum Hover Modified Ricci Flow, Black Hole Information Leakage and Testable Entropy Corrections

Abstract

This paper constructs the framework of General Projection Geometry (GPT) based on noncommutative topology to characterize spacetime dynamical evolution at the quantum gravity scale. We introduce the Mona three-phase topological dynamical operator and establish a vacuum ground-state system with dual fixed points of geometric dynamics and entropy thermodynamics. Subject to three sets of constraints: dynamical accumulation, topological stability and noncommutative torus quantization, the intrinsic topological modulus n=7 is uniquely determined. Free parameters are absent within the framework, and a mechanism for 22000-fold vacuum topological energy-level transition together with vacuum entanglement entropy breaking is naturally derived. We construct a noncommutative-classical projection map satisfying the low-energy correspondence principle. It is rigorously proven that black hole horizons act as topologically singular surfaces with irreversible projection, triggering boundary breaking of global vacuum states and outflow of entanglement residuals. The topological geometric origin of Hawking radiation is revealed from first principles. A testable, quantitatively distinguishable logarithmic correction formula for black hole entropy is presented. By virtue of the topological duality between vacuum phase transition and horizon information leakage, a global conservation closure is established, fundamentally resolving the black hole information paradox and forming a self-consistent, experimentally verifiable geometric system for quantum gravity.