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

This theoretical preprint introduces the Damascus Topology Model, a novel geometric framework that synthesizes Scale Relativity, Noncommutative Geometry, and Entropic Gravity to resolve both the singularity and dark energy paradoxes in standard cosmology. The model postulates that under extreme gravitational density (such as black hole interiors), spacetime undergoes spontaneous dimensional reduction to a 1+1D non-differentiable quantum fractal. Within this collapsed state, frame-dragging induces noncommutative topological folds—"temporal eddies"—that act as a quantum centrifuge, mechanically isolating matter and antimatter. By applying a hyperbolic scale limit to gravitational collapse, a(t) = \sqrt{\ell_P^2 + (k t)^2}, the model demonstrates that a zero-point singularity is avoided; collapse halts precisely at the fundamental Planck length (\ell_P). At this geometric limit, the perfect annihilation of the quarantined matter and antimatter generates a massive energy release that crystallizes directly into a macroscopic fractal Spin Network, negating the requirement for a primordial particle soup. Furthermore, the model proposes that subsequent cosmic acceleration is not driven by a "dark energy" fluid. Instead, expansion emerges as an entropic force—the thermodynamic necessity of the bounded fractal topology scaling outward to accommodate the forward flow of time. Ultimately, this framework provides a continuous, unified Action Principle that bridges black hole interior mechanics with early universe inflation.