Boundary Closure in Radiative-Gravitational Systems

We identify and empirically validate a boundary-closure condition for stable radiative-gravitational systems. A scalar invariant, X = (L G M) / (g R^4 c^4 T^4), is formed solely from independently measured boundary observables (luminosity L, effective temperature T, surface gravity g, mass M, and radius R), with G and c included to place radiative and gravitational inputs on a common metrological footing. Using the Sun and two benchmark samples of detached eclipsing-binary components with geometry-based M and R and spectroscopic T and g, we find that X converges to a single value, X ≈ X_0 ≡ 4πσ/c^4, with a dispersion of 0.13% in the high-precision sample, consistent with measurement limits. In natural units (c=ħ=k_B=1, σ=π^2/60) this closure corresponds to the third-order Bose-Einstein integral, X_0 = π^3/15 ≃ 2.067. Scrambling boundary observables between systems destroys the closure, demonstrating that the result reflects a physical boundary constraint rather than a definitional identity. The closure is interpreted as a consequence of radiative decoupling: the surface where photon degrees of freedom detach from an optically thick interior and become defined as free-streaming radiation at the boundary.