Electromagnetism from a Self-Referential Geometric Axiom: Three Independent Derivations and Empirical Consequences

Electromagnetism is derived—not assumed—from a single self-referential geometric axiom: the spacetime metric is determined by the total stress-energy, and dynamics must be invariant under local phase relabeling. From this, Maxwell’s theory follows uniquely. I give three independent, convergent derivations: (1) Noether localization of a global phase symmetry; (2) a constraint route where enforcing pointwise charge conservation introduces a gauge potential and its curvature; and (3) a discrete holonomy (Wilson plaquette) construction whose continuum limit reproduces the standard field theory. Consistency with gravity is explicit via the Bianchi identity and covariant stress-energy conservation. A radion that rescales the gauge kinetic term cures the Coulomb singularity while keeping the photon massless, and predicts specific hydrogen level shifts that bound a short-distance core scale. No extra dimensions, no hand-waving—one axiom, three derivations, testable consequences.