The Solar Photosphere Recovers the Stefan–Boltzmann Constant from Surface Observables

We construct a boundary description of a star using only quantities measured directly at the photosphere—luminosity , radius , and effective temperature —without introducing a radiation law a priori. From these observables we compute a geometric surface flux and examine its temperature scaling, yielding an empirical radiative coefficient determined entirely from measured data. Applied to the Sun, this boundary evaluation recovers a value coincident with the Stefan–Boltzmann constant within observational precision. The same computation, applied to an independent sample of 190 detached eclipsing-binary components, produces a narrow distribution centered on the same value. The result shows that the Stefan–Boltzmann scaling emerges directly from photospheric measurements at radiative boundaries, without prior assumption of the blackbody relation.