This paper develops a structural framework linking quantum and relativistic relations through representation covariance and electromagnetic coupling geometry. By requiring physical energy to remain invariant under transformation between linear cycle-counting and angular phase representations of periodic processes, the relation between Planck’s constant and the reduced Planck constant naturally emerges. The electromagnetic vacuum then provides a second structural boundary through its constitutive parameters, fixing the propagation speed of electromagnetic signals. Together, these boundaries determine the intrinsic Compton scale of massive particles. Requiring invariant internal phase accumulation leads directly to the Minkowski spacetime interval and the relativistic energy–momentum dispersion relation. The work also reformulates Lorentz kinematics in wavelength form, expressing relativistic dilation through ratios between intrinsic and motion-induced wavelengths. The framework reproduces standard quantum and relativistic relations in vacuum while proposing a falsifiable prediction: under controlled modifications of effective electromagnetic coupling geometry, a small deviation from representation consistency may arise. This provides a potential experimental test of the structural principles developed in the paper.