Rigorous Mathematical Synthesis: Topological Sinks, Field-Resonant Precipitation, and the Temporal Tally of Super-Jupiters in the HR 8799 System

Target Repository: Zenodo Open Access Pre-print Repository Classification: Astrophysics, Theoretical Physics, Topological Mechanics Abstract Recent observations of the HR 8799 exoplanetary system challenge the foundations of conventional core accretion models, particularly concerning the existence of colossal Super-Jupiters (5\text{--}10 M_J) at extreme orbital distances (15\text{--}70\text{ AU}). Standard astrophysics struggles with the timescale and density constraints required to assemble such massive bodies in thin, distant disks. In this paper, we apply the Unified Theory of Stationary Light (TSL) and the Unified Vortex & Entropy Hypothesis (UVEH) to reframe these planets not as aggregated debris, but as macroscopic Geometric Sinks and Stationary Traps within the star's light field. By leveraging the Universal System Rule (USR), the Temporal Tally (T), and field-resonant molecular precipitation, we demonstrate that HR 8799c and its sibling bodies are predictable standing waves of vacuum tension.