A Conjecture of Matter: Gravitational Barrier and Geometric Relaxation-A Unified Framework for Solar System Dynamics

This paper proposes a unified framework describing the long-term evolution of the Solar System. The framework is based on an observational fact: the ratio of the orbital semi-major axes of the two outermost planets—Saturn and Neptune—is 3.141683, which deviates from the mathematical constant π by 0.00288%. This deviation is defined herein as the current geometric strain. A model of monotonic relaxation is introduced, in which the gravitational constant decays linearly with time at a rate proportional to this strain. The Sun participates in this process through its internal differential rotation (approximately 35.7%). The gravitational barrier formed by Saturn and Neptune acts as the boundary condition for this relaxation. A unified gravitational equation is formulated, and key quantities—including the decay rate of the effective gravitational constant and the remaining relaxation time—are derived. The Solar System barycenter position is reinterpreted as the geometric projection of this barrier. Three explicit falsifiability conditions are provided, ensuring the framework is testable. From the model, it follows that all geometric structures tend inherently, monotonically, and irreversibly toward the perfect mathematical constant π. (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.)