Phase-Manifold Interface Reflection (PMIR) in Solar-System Phase Coupling

This work introduces Phase-Manifold Interface Reflection (PMIR), a geometric framework for analyzing phase-based coupling observables in Solar System dynamics. Using publicly available JPL Development Ephemeris data, we construct centroid phase trajectories for grouped planetary subsystems and define a fixed-lag coupling observable between the inner and gas-giant subsystems. No numerical integration or force modeling is performed. With the coupling lag held fixed, the unwrapped phase difference evolves in piecewise-linear segments interrupted by localized curvature events. These events are quantified using a discrete second-difference operator serving as a curvature proxy. Conditioning this proxy on the Uranus–Neptune phase coordinates reveals a low-dimensional interface on the outer-state phase torus that gates when curvature events may occur. Crucially, curvature events do not coincide instantaneously with gate entry. Instead, event timing is shown to depend on the accumulated arc length traveled within the gated region of the outer-state manifold, rather than on elapsed time. This behavior is consistent with constrained, geodesic-like transport punctuated by reflection-like transitions at a phase-space interface. PMIR provides an effective geometric reduction of multi-scale gravitational dynamics in the chosen observable. While limited in scope, the framework demonstrates how emergent geometric structure can arise in classical celestial mechanics and motivates further investigation of interface-constrained transport in reduced phase spaces.