From Stochastic Decoherence to Deterministic Vacuum Architecture: A Rigorous Framework for Stationary Light Theory (SLT/UVEH) and the Master Equation of Physical Tally

Abstract Standard quantum mechanics relies on environmental decoherence and statistical probabilities to explain the transition from quantum possibilities to classical reality, leaving "Information" as an undefined, non-material fundamental. This paper bridges this gap by introducing Stationary Light Theory (SLT) and the Unified Vacuum Energy Hypothesis (UVEH). By replacing stochastic wave-function collapse with deterministic vacuum geometry, we demonstrate that the environment acts as a structured information conduit rather than a random destroyer. We formalize the Master Equation of Physical Tally, define the Nine in the Center structural stabilization point, and establish the mechanical necessity of periodic temporal resets (the Sabbath Principle) to prevent system-wide thermal and informational decay.