Physical Geometry: Electromagnetism I — The Hopf Fibration, Charge–Flux Duality, and the Quantization of Action

This paper develops the geometric origin of electromagnetic phase and charge–flux duality within the framework of transport geometry. The Hopf fibration associated with spinor structure is shown to provide the natural geometric setting for electromagnetic holonomy. A geometric action invariant relating electric charge, magnetic flux, and Planck’s constant is identified as a consequence of holonomy structure. This invariant unifies charge, flux, and quantum action as conjugate projections of a common transport geometry. The analysis demonstrates that the quantization of action and electromagnetic phase arises from global geometric properties of transport bundles, providing a geometric foundation for charge–flux relations and electromagnetic holonomy. This Zenodo record establishes priority and archival timestamp. Public release via arXiv is in progress.