The Withdrawn Structure: Enabling Conditions, Diagnostic Seams, and the Ontology of the Aharonov-Bohm Effect

The Aharonov-Bohm effect has generated a sixty-year debate between two interpretive camps: one holding that electromagnetic potentials are physically real, the other that electromagnetic fields act non-locally. This paper argues that the debate is structurally analogous to the paradigmatic seams identified across ten cases in the philosophy of physics and mathematics, where a framework generates phenomena it cannot accommodate because its enabling conditions have been excluded from its ontology. The enabling condition of electromagnetism, on the analysis presented here, is neither the potential nor the field but the connection on the electromagnetic fibre bundle, a relational structure from which both potential and field are derived as partial, regime-dependent articulations. The potential is the connection expressed in coordinates (hence non-unique). The field is the connection's curvature (hence informationally incomplete: it loses the holonomy). The Aharonov-Bohm effect is the diagnostic seam where this incompleteness forces itself into experimental visibility. The connection's withdrawal from local determination, manifested as gauge freedom, is not a defect of the formalism but the formal signature of an enabling condition that must remain operative but non-thematic for the framework to function. This diagnosis dissolves the binary between the two camps by identifying their shared presupposition: that the fundamental entity must be a locally determined quantity. It does not propose new physics. It applies a structural diagnostic, developed and tested across independent domains, to an experimentally confirmed quantum phenomenon whose interpretation remains contested.