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 3.14196, which deviates from the mathematical constant π by 0.0117%. This deviation is defined herein as geometric strain, and it is proposed that this strain is monotonically decaying to zero. This process is termed geometric relaxation. The Sun, serving as the gravitational anchor of the system, participates in and drives this process through its internal strain (approximately 35.7%, as manifested by the differential rotation between its equatorial and polar regions). The gravitational barrier formed by Saturn and Neptune constitutes the boundary condition of geometric relaxation, constraining the orbital evolution of all bodies within the Solar System. The mathematical formulation of this framework is established, and key physical quantities—including the decay rate of the gravitational constant and the completion time of geometric relaxation—are derived. The position of the Solar System barycenter (approximately 1.508 × 10⁶ km from the solar center, as confirmed by high-precision astrometry) is reinterpreted within this framework as the geometric projection of the gravitational barrier. This paper invokes no extra-dimensional hypotheses, dark matter particle candidates, or quantum gravity schemes, but derives a cross-scale unified description solely from Solar System orbital geometry. Three explicit falsifiability conditions are provided, rendering the framework scientifically testable in the Popperian sense. (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.)