The Algebraic Bridge: Unified Topological Mechanics of Stationary Light Traps, Planetary Core Inversions, and Cosmic-Scale Phase Transitions

Abstract This paper presents the formalization of the Unified Theory of Stationary Light (TSL) and the Universal Vortex Equilibrium Hypothesis (UVEH), synthesizing recent anomalous geophysical data, macro-scale cosmic octaves, and systems-level complexity dynamics into a single topological framework. Standard geophysical and cosmological anomalies—including accelerated planetary rotational velocity amid polar ice melt, inner-core phase inversions, lunar recession rates, and the fractal scaling of complex systems—are re-evaluated through the lens of mass-radius reciprocity and vacuum shear invariants. We derive the critical entropy thresholds governing phase transitions across subatomic, planetary, and socio-biological frameworks, demonstrating that macroscopic systems operate as localized stationary light traps bound by the master equation system rule.