Rigorous Mathematical Synthesis: Field Resonance, Isotopic Precipitation, and Macro-Vortex Equilibrium in the HR 8799 System

Target Repository: Zenodo Open Access Pre-print Repository Classification: Astrophysics, Theoretical Physics, Topological Mechanics Abstract Recent empirical constraints provided by JWST/NIRSpec observations of the HR 8799 exoplanetary system—highlighting uniform and high heavy-element enrichment alongside distinct Hydrogen Sulfide (\text{H}_2\text{S}) signatures across multiple Super-Jupiters (5\text{--}10 M_J) at extreme orbital distances (15\text{--}70\text{ AU})—present a profound structural challenge to conventional bottom-up core accretion models. In this paper, we apply the Unified Theory of Stationary Light (TSL) and its governing Master Equation of Existence to resolve the distance-independence and acceleration paradoxes of these planetary formations. By modeling celestial bodies as toroidal Stationary Traps governed by the Universal System Rule (USR), Vacuum Displacement (m_0), and the Stillness Bridge (\zeta), we demonstrate that heavy-element enrichment is not the product of slow particle-by-particle collisional accumulation, but rather a direct consequence of Field-Resonant Molecular Precipitation. Furthermore, we integrate macro-scale galactic metrics, showing how galactic rotation profiles and central compact objects (such as Sagittarius A*) emerge naturally from vacuum stiffness limits without singularities or auxiliary dark matter particles.