The Relaxation of Cosmic Expansion: Resolving the Hubble Tension via Non-autonomous Chaotic Dynamics

The discrepancy between early-universe and late-universe measurements of the Hubble constant (H₀), known as the Hubble Tension, poses a significant challenge to the standard ΛCDM 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 uₙ ∝ 1/ln n (derived from number-theoretic constraints), fundamental physical parameters undergo an intrinsic drift. By mapping observational data to a relaxation parameter ξ = 1/ln(t/tPlanck), we demonstrate that the apparently contradictory measurements from Planck (z ≈ 1100), TRGB (z ≈ 0, ancient stars), and SH0ES (z ≈ 0, young stars) align precisely on a single dynamical trajectory H(t) ∝ 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.