Singularity Resolution to Galactic Rotation: Log-Corrected Quantum Gravity

Based on a unified non-perturbative quantum gravity framework, this paper systematically elaborates on the cross-scale universality of the quantum gravitational correction term containing a logarithmic term. At the microscale of black hole singularities, it dynamically resolves the singularity through a repulsive potential and ensures information conservation; at the macroscale of black hole gravitational fields and galaxies, it maintains the high-speed revolution of stars and the flatness of rotation curves through additional gravity, eliminating the need for assumptions such as dark matter 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 with a logarithmic term: \( Φ(r)=-\frac{GM}{r}-\frac{kG_h M^2 (ln⁡r+1)}{r} \). Among them, the logarithmic term ln⁡r is the core of realizing the cross-scale effect of “repulsion at short distances and attraction at long distances”. Through predicting black hole shadows (Sgr A*, M87*) consistent with EHT observations without introducing additional free parameters (e.g., spin); calculating the “periastron” velocities of high-speed stars (S4714, S62) orbiting black holes; fitting galaxy rotation curve data (Milky Way, Andromeda Galaxy, NGC2974); and further analyzing the mathematical asymptotic behavior of dark matter halos, multiple cross-scale verifications (spanning nearly 30 orders of magnitude from black hole singularities to galaxies) prove that the framework has high consistency with observations in both strong gravitational fields (black holes) and weak gravitational fields (galaxies). It achieves the first unified description of gravity from the microscale to the macroscale, providing observable and reproducible empirical support for quantum gravity theory.