Electromagnetism as Phase Geometry in the Zero Field (𝕆)

Electromagnetism is extraordinarily well described by Maxwell’s equations and, in quantum theory, by gauge symmetry—yet the physical picture can feel fragmented: potentials seem “optional,” while phase appears to be the truly decisive quantity (as in interference and the Aharonov–Bohm effect). This preprint proposes a compact R-theory interpretation in which a coherent substrate, the zero field \mathbb{O}, underlies physical phenomena and electromagnetism is the geometry of phase-consistency within that substrate. Electric charge is modeled as topological phase winding; the gauge potential A_\mu is treated as a connection required for consistent local phase descriptions; and the electromagnetic field tensor F_{\mu\nu} appears as the curvature of that connection. From this mapping, the homogeneous Maxwell equations follow as a geometric identity, while a minimal action principle yields the inhomogeneous equations and charge conservation. The paper’s aim is deliberately modest: it does not claim to replace Maxwell/QED, but to provide a unified and intuitive phase-geometric reading, and to outline conservative experimental search directions for potential coherence-dependent deviations in ultra-coherent systems (e.g., superconducting cavities or flux-quantization geometries).