The Universal Equilibrium Constant I = 4πGσ/c⁴: From Stars to Cosmos

We present a universal framework linking gravity, radiation, and thermodynamics through a single invariant identity. The relation I = (Φ β²)/(T⁴ R²) = (4 π G σ)/c⁴ = 5.888 × 10⁻⁵¹ m⁻¹ s⁻¹ K⁻⁴ remains constant across more than twenty orders of magnitude in mass, from stars to black holes to the observable universe. This invariance unites classical equilibrium laws such as Stefan Boltzmann, Eddington, Einstein Schwarzschild, Hawking, Chandrasekhar, and the cosmic balance within one photogravitational framework. The paper provides derivation, empirical verification, and falsifiable predictions, demonstrating that this constant acts as a universal equilibrium law connecting light, gravity, and heat across physical scales.