U(1) as Curvature-Phase Residue in PSOC4(3)

This paper reconstructs the electromagnetic U(1) sector within the PSOC4(3) closure framework. In standard physics, U(1) functions as the gauge symmetry associated with electromagnetism and charge conservation. Here, we propose a deeper ontological interpretation: U(1) is the conserved curvature-phase residue preserved when the 3.141D coherence-curvature equilibrium resolves into 3.000D spatial closure. The residual 0.141D-type aperture is not treated as a literal spatial dimension or fixed energy unit, but as the structural source-band through which electromagnetic phenomena become possible. On this basis, the electromagnetic field tensor Fmu nu is interpreted as the bivectorial organization of directed and circulatory curvature, corresponding to the electric and magnetic field components. Electromagnetic duality becomes the internal self-rotation of this U(1) residue under the Hodge dual operation. Photon emission is then described as the quantized null release of curvature-phase during closure transitions, with E = hν representing the energy of a specific emitted closure quantum rather than the structural residue itself. Charge is interpreted as localized anchoring of U(1) residue, current as its transport, and radiation as its unanchored propagation. This framework preserves the standard formal role of U(1), Maxwellian field structure, electromagnetic duality, and photon quantization while offering a unified explanation for why electromagnetism is phasegoverned, long-range, dual, and radiational. In this reconstruction, electromagnetism is the visible expression of unclosed curvature preserved by spatial closure.