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

This paper tests whether the Stefan-Boltzmann constant emerges from photospheric observables alone: luminosity L, radius R, and effective temperature T_{\mathrm{eff}}, with no assumed radiation law. Surface flux F is computed as \frac{L}{4\pi R^2}, and then divided by T_{\mathrm{eff}}^4. The result is \sigma, derived purely from data. For the Sun, the computation yields 5.670388 \times 10^{-8} W m$^{-2}$ K$^{-4}$, with a ratio to \sigma of 1.000002. Across 190 detached eclipsing binaries, the mean ratio is 0.9965 \pm 0.0007. This shows the constant is not a prior rule, but the direct outcome of the stellar boundary.