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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: 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 multiple cross-scale verifications—predicting black hole shadows (Sgr A*, M87*) consistent with EHT observations without introducing additional free parameters (e.g., spin), fitting galaxy rotation curve data (Milky Way, Andromeda Galaxy, NGC2974), and further analyzing the mathematical asymptotic behavior of dark matter halos (spanning nearly 30 orders of magnitude from black hole singularities to galaxies; spanning nearly 10 orders of magnitude from black hole shadows to galaxies)—it is proven that the framework has high consistency with observations in both strong gravitational fields (black holes) and weak gravitational fields (galaxies). This achieves the first unified description of gravity from the microcosmic to the macrocosmic scale, providing observable and reproducible empirical support for quantum gravity theory.