The Damascus Topology Model of Spacetime- A Fractal and Noncommutative Framework for Quantum Gravity and Entropic Expansion

The Damascus Topology Model (DTM) presents a novel framework for quantum gravity by replacing the canonical smooth pseudo-Riemannian manifold of General Relativity with a scale-dependent, fractional geometric topology.[1] By introducing the Damascus Topological Density Tensor and fractional scaling operators, the DTM naturally resolves ultraviolet divergences and embeds quantum non-locality—such as the Pancharatnam-Berry phase [2]—directly into the spacetime curvature. Crucially, the model yields a modified, fractional dispersion relation for gravitational waves. By applying this framework to the strain data of the GW150914 binary black hole merger [3], the DTM bounds the theoretical macroscopic phase shifts introduced by the underlying quantum-fractal micro-structure. This preprint provides the foundational master equations, details the fractional geometry, and establishes an empirical pathway to test macroscopic topological deviations using current gravitational-wave observatories.