We identify and empirically validate a boundary-closure condition governing stable radiative–gravitational systems. The analysis is based on a dimensionless scalar invariant, X = (L · G · M) / (g · R⁴ · c⁴ · T⁴), constructed exclusively from independently measured boundary observables: luminosity, effective temperature, surface gravity, mass, and radius. Using the Sun and two benchmark samples of detached eclipsing-binary components—where masses and radii are determined geometrically and temperatures and surface gravities spectroscopically—we find that the invariant converges to a single closed value set by fundamental constants, X = 4πσ / c⁴. When expressed in natural units (c = ħ = k_B = 1, σ = π² / 60), this becomes X = π³ / 15 ≈ 2.067, corresponding to the third-order Bose-Einstein integral. The dispersion of X is 0.13% in the high-precision benchmark sample, consistent with observational uncertainties. Random reassignment (scrambling) of boundary observables between systems destroys the closure, demonstrating that the convergence reflects a physical boundary constraint rather than a definitional identity. The closure is interpreted as a consequence of radiative decoupling: the surface at which photon degrees of freedom detach from an optically thick interior and become defined as free-streaming radiation at the boundary.