Emergence of the Fine-Structure Constant from Topological Phase Fluctuations in a Spacetime Network

We derive the approximate value of the fine-structure constant alpha from the topology and statistical structure of a Planck-scale spacetime network within the Geometric Entropy Principle framework. Fermions are modeled as Möbius ribbon loops embedded in the network. The half-integer holonomy of the Möbius ribbon introduces a geometric factor 1/pi, while statistical phase fluctuations along the loop produce a suppression factor 1/sqrt(N). Together these yield alpha ~ 1/(pi sqrt(N)). The parameter N is derived from the microscopic GEP action via a Landau-Ginzburg analysis, giving N ~ 2000 and alpha^{-1} ~ 141 +/- 14, consistent with the observed value 137.036 within the theoretical uncertainty.