From Black-Hole Entropy to Einstein's Field Equations — Horizon Thermodynamics to Stellar Geometry

We present a minimal, structural–operational bridge from horizon thermodynamics to observable stellar geometry. Using the Unruh temperature, Bekenstein–Hawking entropy, and the Clausius relation, we define the operational photogravitational parameter Φ ≡ L/(M a) and derive the compact relation L·(R²/M²) = Φ·G. The framework is intentionally table-free in this version, focusing on the core formalism and its empirical calibration path across stellar classes.