Gauge Fields as Closure Constraints - Charge, Symmetry, Coupling, and Interaction in Atomic Continuum Ontology

Paper 5 interpreted quantum fields as structured excitation domains within Atomic Continuum Ontology and particles as localized reclosure residues of field-mode excitations. This sixth paper extends the sequence from fields and particles to gauge structure, charge, coupling, and interaction. The central thesis is that gauge symmetries are closure constraints governing admissible field transformations. A gauge transformation does not merely express mathematical redundancy; in ACO translation, it expresses the requirement that a field may transform while preserving closure admissibility. Charge is interpreted as a coupling residue of gauge-closure constraint. Gauge fields arise as closure mediators required to preserve admissible local transformation. The covariant derivative becomes the formal expression of closure-covariant change. Interaction is then interpreted not primarily as object collision, but as field reconfiguration under shared gauge closure. Electromagnetism provides the clearest worked example: U(1) gauge symmetry becomes phase-charge closure, charge becomes phasecoupling residue, and the electromagnetic potential A_mu becomes the closure mediator preserving local phase admissibility. The paper concludes by presenting a gauge ladder from U(1) through SU(2) and SU(3), preparing later work on weak transaction closure and color confinement closure.