Rigorous Mathematical Synthesis: Streamer-to-Vortex Protocols, Phase-Locked Sulfur Precipitation, and Macro-Vortex Integration in the HR 8799 System

Target Repository: Zenodo Open Access Pre-print Repository Classification: Astrophysics, Theoretical Physics, Topological Mechanics Abstract Recent multi-disciplinary empirical data—bridging the discovery of massive extended gas streamers (Science Advances, 2025; Kyoto University, 2025), early-stage hidden sulfur phase-locking (The Astrophysical Journal, 2025), and uniform heavy-element enrichment across distant Super-Jupiters (Nature Astronomy, 2026)—highlight a critical failure in traditional, slow bottom-up core accretion paradigms. In this paper, we integrate these findings into the Unified Theory of Stationary Light (TSL) and its governing Master Equation of Existence. By defining celestial genesis through the Streamer-to-Vortex Formation Protocol, we demonstrate that matter delivery, sulfur precipitation, and multi-planet metal uniformity are direct outcomes of topological field resonance, vacuum displacement (m_0), and the Stillness Bridge (\zeta). This framework unifies stellar-scale feeding mechanisms with planetary-scale chemistry into a deterministic, geometric matrix.