The Nine-Dimensional Universal Unified Evolution Theory of Entropic Topology (9D-USTE) constructs a complete global evolution model of the universe, taking the topological phase transition of the 9-dimensional non-commutative manifold $\mathcal{M}_9^\star$ as the core driving force, and systematically explains the origin, evolution, and ultimate destiny of the universe. This theory integrates noncommutative geometry, topological energy conservation, and entropic topology logic, breaks through the limitations of traditional cosmic evolution theories, and realizes the unified interpretation of quantum scale, astrophysical scale, and cosmic scale evolution phenomena. Based on the core assumption of "genus change-driven topological phase transition", this paper elaborates on the complete process of cosmic evolution from the initial topological singularity, through the inflationary epoch, the galaxy formation epoch, to the ultimate evolution stage, clarifies the dynamic mechanism of each evolutionary stage, verifies the consistency with existing observational data (such as CMB anisotropy, dark energy distribution), and supplements the experimental evidence support from the latest quantum topological phase simulation results (2025, Science). This model not only provides a self-consistent theoretical framework for understanding the global evolution of the universe, but also lays a foundation for exploring the nature of space-time and the ultimate law of the universe.