Geometric Electromagnetic Theory (GEMT): Derivation of the Fine-Structure Constant and Gauge Topology in the ODD Framework

We present the Geometric Electromagnetic Theory (GEMT), the third phenomenological pillar of the Operator-Derived Dimension (ODD) framework. We postulate that the electro-magnetic interaction is not an axiomatic fundamental force, but the propagation of geometric flux along the intersection seam of three hyperspheres.We derive the U (1) gauge symmetry from the Hopf fibration topology of the bulk geometry and the photon’s massless nature from the geometric zero-mode of the domain wall. Crucially, we derive the fine-structure constant (α) without empirical fitting. Treating the photon as a confined gauge soliton, we compute the effective spectral capacity of the vacuum accessible to electromagnetic flux.Using the vacuum stability index μ = 2 (which simultaneously determines the three fermion generations), we derive an analytic expression of α−1 ODD = 9π3/2 − π2/4 ≈ 137.0608. This closely matches the experimentally measured low-energy fine-structure constant, establishing Electromagnetism as a strict topological invariant of the vacuum geometry.