Defining Electromagnetic Fields from Continuity and Divergence-Free Structure

We clarify the conceptual bridge between a field-only ontology of electromagnetic energy flow and the usual electric and magnetic field variables. We show rigorously that a single scalar energy density does not define propagation, but that the relation between scalar configurations at different times, constrained by continuity, forces the introduction of directional transport. We prove a reconstruction result: given an energy density u and an energy flux S satisfying |S|