A Conjecture of Matter:An Attemptive Derivation of the Hubble Constant from the Geometric Relaxation Framework

This paper attempts to extend the gravitational barrier and geometric relaxation framework to cosmological scales, deriving the Hubble constant H_0 from the geometric relaxation equation \\epsilon(t) = \\epsilon_0(1 - t/T) . The derivation yields H_0 = 1/T \\approx 71.4 km/s/Mpc. This value is in complete agreement with the Dark Energy Survey (DES) Year 3 cross-correlation analysis with CMB lensing, which reports H_0 = 71.5 \\pm 2.5 km/s/Mpc, and lies between the early-universe measurement (67.4) and the local-universe measurement (73.0). This paper does not claim that the derivation has proven the origin of the Hubble constant; it is presented only as a testable inference of the geometric relaxation framework. If this derivation holds, the nature of the Hubble tension would be reinterpreted: the difference between early-universe and local-universe measurements is not measurement error, but rather that the two sets of observations are modulated by different phases of the geometric relaxation process. Three falsifiability conditions for this attemptive derivation are provided. (Note on AI-Assisted Computation Certain mathematical derivations and physical calculations in this paper were performed by an AI tool (large language model) based on the theoretical framework and postulate system provided by the author. Specifically, the AI tool contributed to: formula derivation, equation solving, integral evaluation, series summation, and recalculation verification of established quantum mechanical results. All physical insights, core assumptions, logical premises, and the theoretical framework itself were independently developed by the author. The AI tool served solely as an auxiliary instrument for mathematical derivation and computational verification, comparable in role to symbolic computation software or numerical tools routinely employed by researchers. The author has reviewed every derived result for physical plausibility, consistency with known experimental data, and logical coherence, and assumes full responsibility for all conclusions. This statement is provided in the interest of academic transparency, while clearly distinguishing between the originality of ideas and the auxiliary role of computation.)