Based on 9D-USTE v∞: Dark Matter and Dark Energy Topological Interaction Law -- A Falsifiable Physical Model for Cosmological Puzzles

Based on the Nine-Dimensional Universal Unified Evolution Theory of Entropic Topology (9D-USTE v∞), this paper establishes a rigorous, falsifiable physical model that unifies dark matter (DM), dark energy (DE), the Hubble tension, and the small-scale crisis of cold dark matter (CDM). Dark matter is identified as topological solitons with conserved Chern-Simons topological charge from 9D compactified space projection. Dark energy corresponds to residual topological pressure governed by the topological frustration index K*. A scale-invariant redshift evolution equation K* (z) is proposed, which quantitatively resolves the Hubble tension by cosmic topological maturation. A dynamically stabilized moduli mechanism introduces a topological fifth force 𝒻T that naturally solves the core-cusp problem via topological repulsion in high-gradient galactic regions. The model provides three smoking-gun observational signatures: step-like weak lensing distortion in the Bullet Cluster, topological CMB oscillations with a π/4 phase shift, and a characteristic stochastic gravitational wave background from cosmic strings generated by K* discontinuities. Preliminary fitting to the Milky Way rotation curve yields χ²/dof=1. 02, in excellent agreement with observations. All results are derived without additional free parameters or ad hoc assumptions, making 9D-USTE v∞ a self-contained unified framework for cosmic structure and evolution. A full N-body cosmological simulation based on K* (z) will be developed in future work.