This paper develops a constraint-based formulation of electromagnetic coupling within the framework of Unified Recursion Theory (URT). Rather than introducing forces, fields, or dynamical propagation mechanisms, electromagnetic interaction is expressed as a structural deformation of admissibility geometry through charge-class-dependent modifications of the informational stiffness field (σ). Charge is defined as a symmetry-class label on admissible recursion states that determines how systems deform the admissibility structure of other systems within a shared environment. Coupling arises as mutual deformation of the admissibility threshold (σ_threshold), evaluated locally at each admissible recursion event. No propagation mechanism is introduced; consistency across events is enforced by charge-class invariance and admissibility constraints. In the dense-event limit, discrete admissibility updates approximate a continuous representation that is consistent with classical electromagnetic behavior. This compatibility is not a derivation of Maxwell’s equations, but a structural consistency condition. Imposing finite-speed causal structure in this limit yields a propagation scaling condition that constrains the curvature-to-stiffness mapping G(R). This constraint defines a two-regime requirement on G(R): an interior regime consistent with finite propagation scaling and a boundary regime characterized by admissibility saturation. Together with four previously established constraints, this result provides the fifth anchor necessary for full closure of the curvature-to-stiffness mapping. The paper preserves canonical URT operator discipline throughout: no new operators are introduced, λ remains diagnostic, and the Oscillation Recursion Mirror (ORM) remains a binary, event-local admissibility evaluator. Electromagnetic interaction is thus recast as a structural property of admissibility geometry rather than a dynamical field phenomenon.