Electromagnetism as Unbound Phase Closure Maxwell, Gauge Theory, and the PSOC4(3) Disclosure

A coherence-closure interpretation of electromagnetism as U(1) phase made physically transmissible through SO(3) orientation. Electromagnetism is commonly described as a classical field theory, a relativistic tensor theory, or a quantum gauge interaction mediated by photons. Each description is operationally successful, yet none fully explains why electromagnetic theory possesses its characteristic architecture: phase invariance, charge coupling, electric divergence, magnetic circulation, transverse propagation, polarization, and photon exchange. This paper proposes that electromagnetism may be interpreted as the unbound phase limit of PSOC4(3), the four-generator phase-spatial closure structure: PSOC4(3) = U(1)θ ⊕ SO(3)J In this interpretation, U(1)θ supplies the phase-gauge relation of electromagnetism, while SO(3)J supplies the orientational disclosure required for field direction, rotation, polarization, angular momentum, and propagation geometry. Electromagnetism is therefore not merely U(1) phase symmetry, nor merely a spatial field. It is U(1) phase coherence made physically transmissible through SO(3) orientation. Maxwell’s equations are preserved as the classical field law of this disclosure. Relativistic electromagnetism is preserved as the tensor unification of electric and magnetic projections. Quantum electrodynamics is preserved as the quantum exchange theory between charged matter and the electromagnetic field. PSOC4(3) does not replace these theories; it discloses their closure ontology. The central thesis is that light is unbound phase coherence, matter is bound phase coherence curvature, and electromagnetic interaction is the exchange relation between the unbound and bound regimes of phase. Electromagnetism is therefore the bridge-domain between propagation and closure, field and particle, light and matter.