Topological Derivation of the Fine Structure Constant from Stochastic Coherence: Phase Space Geometry on T³

We derive the infrared value of the inverse fine structure constant α⁻¹ = 4π³ + π² + π ≈ 137.036 within the stochastic coherence framework. Phase quantization compactifies momentum space to Z³; Pontryagin duality forces position space to T³ with period 2π. The classical vacuum admittance is the volume of the moduli space of flat U(1) connections modulo charge conjugation, Vol(M/Z₂) = 4π³, with unit normalization guaranteed by the triviality of the Ray–Singer analytic torsion on the flat torus. One-loop corrections from the linear and surface sectors of the integer lattice contribute π² (Euler–Basel) and π (Leibniz), respectively. Of these three terms, only π² admits dynamical modification under renormalization group flow: 4π³ is a topological invariant of the moduli space and π is a number-theoretic invariant (pole residue). The value g* = 4π³ + π ≈ 127.167 is therefore a fixed point of the RG flow, implying the absence of a Landau pole. The total running budget π² ≈ 9.870 exceeds the measured running of 8.100 at M_Z, and no existing measurement violates the fixed-point bound. One calibration parameter (the mode-energy scale) remains undetermined.