A Conjecture of Matter:Dark Matter in the Geometric Relaxation Framework—— An Exploratory Study

This paper tentatively applies the gravitational barrier and geometric relaxation framework to the dark matter problem. Rather than interpreting dark matter as an undiscovered particle, the framework reinterprets it as geometric strain gradient—the additional curvature effect produced by the gravitational field in regions of spacetime that have not yet fully relaxed. This exploratory study derives that, if dark matter is a manifestation of geometric strain gradient, its effective energy density should be on the order of \\rho_{\\text{DM}} = 1.0 \\times 10^{-9} J/m³, comparable to the dark energy density. This tentative interpretation requires no new particles or extra dimensions, and follows solely from the core equations of the geometric relaxation framework. It is explicitly stated that this interpretation is exploratory and non-deterministic—it does not constitute a claim that dark matter has been explained. Three explicit falsifiability conditions are provided; the fulfillment of any one would invalidate this exploratory interpretation. (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.)