This paper proposes a novel unified physical theory, the Xuan-Liang theory, which resolves three major challenges in modern physics through geometric-topological unification [3][5]: (1) Dark matter effects originate from velocity-curvature topological coupling; (2) Cosmic inflation and late-time accelerated expansion are unified via dynamic Euler characteristic evolution; (3) The black hole information paradox is resolved through holographic Xuan-Liang flux quantization. Compared to string theory (28+ parameters) and loop quantum gravity (complex discrete geometry), this theory requires only three fundamental constants to achieve mathematical simplicity (∼1/10 complexity) and experimental verifiability (explicit predictions for gravitational wave polarization modifications), providing a potential framework for next-generation physical paradigms.