The Photospheric Origin of the Stefan-Boltzmann Constant: Empirical Recovery from Stellar Boundaries

We test whether the Stefan-Boltzmann constant emerges from photospheric observables alone: luminosity L, radius R, effective temperature Teff, with no assumed radiation law. We compute surface flux F as L divided by four pi R squared, then divide by T to the fourth. The result is sigma, purely from data. For the Sun, we get five point six seven zero three eight eight times ten to the minus eight watts per square metre kelvin to the minus four, ratio to sigma one point zero zero zero zero zero two. Across one hundred ninety detached eclipsing binaries, the mean is zero point nine nine six five plus minus zero point zero zero zero seven. This shows the constant is not a prior rule, but the direct outcome of the stellar boundary.