This paper explores a geometric approach to the infrared value of the inverse fine structure constant, α⁻¹. Working within the framework of stochastic coherence, we examine the natural consequences of phase quantization and Pontryagin duality, which suggest a compactified spatial topology of T³. In this setting, we evaluate the standard semiclassical expansion of the U(1) gauge field path integral. We find that the classical vacuum admittance is structurally consistent with the physical volume of the moduli space of flat connections (Vol(M)/Z₂ = 4π³), while the one-loop fluctuation determinants yield the discrete spectral corrections π² and π. The resulting additive structure, 4π³ + π² + π ≈ 137.036, closely approximates the experimental value without the introduction of free parameters. Rather than proposing a final theory, this work highlights a potential topological and structural origin for the electromagnetic coupling, offering a mathematically consistent perspective on the geometry of the vacuum.
ROHR ADRIAN LEONARDO (Tue,) studied this question.