The discrepancy between early-universe and late-universe measurements of the Hubble constant ($H_0$), known as the Hubble Tension, poses a significant challenge to the standard $\Lambda$CDM model. In this paper, we propose a resolution based on the Cosmic Relaxation Hypothesis, which treats the universe not as a static Hamiltonian system but as a non-autonomous dynamical system undergoing "computational aging." Governed by a logarithmic decay law $u_n \propto 1/\ln n$ (derived from number-theoretic constraints), fundamental physical parameters undergo an intrinsic drift. By mapping observational data to a relaxation parameter $\xi = 1/\ln(t/t_{Planck})$, we demonstrate that the apparently contradictory measurements from Planck ($z \approx 1100$), TRGB ($z \approx 0$, ancient stars), and SH0ES ($z \approx 0$, young stars) align precisely on a single dynamical trajectory $H(t) \propto 1/\ln t$. This unification resolves the tension without introducing exotic physics and predicts a "phantom-like" acceleration driven solely by system relaxation, ultimately leading to a "Computational Freeze" rather than a Big Rip.