We construct a finite-support geometric framework in which electromagnetic coupling arises as the affine projection of an admissible interface geometry. The underlying structure is defined by a local admissibility partition on sign-chains of an ordering field, yielding a spectrum with eigenvalues \(\lambda _{\textrm{adm}}\) and \(\lambda _{\textrm{res}} = 1 - \lambda _{\textrm{adm}}\) . For the electromagnetic channel, this spectrum is fixed by admissibility to \(\lambda _{\textrm{adm}} = 2/3\) and \(\lambda _{\textrm{res}} = 1/3\) . We show that the electromagnetic interface has intrinsic Hausdorff dimension \(D_H^{\textrm{EM}} = 1 + \lambda _{\textrm{res}} = 4/3\) , and that the low-energy coupling is the Hausdorff density of this interface under inverse-power smoothing at the Thomson scale: \(\begin{aligned} \alpha (\mu _0) = \frac{1}{4\pi }\,\mu _0^{-1/3}\,\mathcal {H}^{4/3}\!\left( \mathcal {L}_\infty ^{\textrm{EM}}\right) . \end{aligned}\) The scale evolution of the coupling follows from the same admissibility spectrum: \(\begin{aligned} \frac{d\alpha }{d\ln \mu } = \frac{\alpha ^2}{2\pi }\,\lambda _{\textrm{adm}}\sum _f Q_f^2, \end{aligned}\) with \(\lambda _{\textrm{adm}} = 2/3\) for the electromagnetic channel. Both the geometric scaling and the coupling structure are determined by a single admissibility partition. Conventional electromagnetic expressions arise as affine readouts of this finite-support geometry.
