Singularity Resolution to Galactic Rotation: Log-Corrected Quantum Gravity

Based on a unified non-perturbative quantum gravity framework, this paper systematically elaborates the cross-scale universality of the quantum gravitational correction term with a logarithmic term. At the microscopic scale of black holes, it dynamically resolves singularities through a repulsive potential while ensuring information conservation; at the macroscopic scale of galaxies, it sustains the flatness of rotation curves via additional gravity, eliminating the need for dark matter hypotheses or black hole spin fitting parameters. With quantum vortices (statistical average topological structures of microscopic particles) and nested AdS/CFT duality as the physical core, the framework derives a modified gravitational potential containing a logarithmic term: The logarithmic term lnr is the key to realizing the cross-scale "short-range repulsion and long-range attraction" effect. Double verification through black hole shadow observations (Sgr A*, M87*) and galactic rotation curve data (Milky Way, Andromeda Galaxy, NGC 2974) demonstrates that the framework achieves high observational consistency in both strong gravitational fields (black holes) and weak gravitational fields (galaxies). It for the first time realizes a unified description of gravity from the microscopic to the macroscopic scale, providing observable and reproducible empirical support for quantum gravity theory.