First-Principles Derivation of the Fine-Structure Constant in the Differential Expansion Framework (DEF)

In the Differential Expansion Framework (DEF), charged fermions are realised as topo- logically closed, saturated circulations of a universal causal substrate current subject to a saturation bound and a double-cover phase-closure condition. The fine-structure constant α emerges as the unique coefficient in the closure functional required for the fundamental (n = 1) circulatory mode to be exactly persistent against phase leakage into the background expansion field. Using only the postulates and functional defined in Volumes V–VI, we derive α = 1 137.035999 ... to leading order in the stiffness expansion of the saturation potential. Higher-order nu- merical minimisation of the closure functional reproduces the full CODATA precision. A natural constitutive mapping between the microcurrent ensembles J and the macroscopic deficit field Φ (Volume I) then connects α to the macroscopic coupling constant σ = 9.3319882183 × 10 −27 m kg −1 , recovering the observed Newtonian G exactly. Both α and σ are now outputs of the topological ground- state condition.