Conserved Currents on Multiply Connected Domains: Covering-Space Constraints in Quantum and Gravitational Dynamics

The relationship between quantum mechanics and general relativity is typically pursued via quantizing the spacetime metric or modifying the Standard Model. This paper proposes an alternative structural approach: treating both frameworks as local differential theories whose admissible global solutions are restricted by the geometry of their domains. The Schrödinger equation, expressed in Madelung form, makes this explicit: probability is conserved, and the resulting current must route around regions where the wavefunction is zero. This same structure of current routing around obstructions explains double-slit interference, Bell correlations, gravitational lensing, and the geometric role of phase in coherent evolution. Here, "phase" is used in its geometric sense as a connection on the space of states, while "density" is the conserved quantity whose zeros define the topological obstructions. The incompatibility therefore dissolves not by quantizing gravity or modifying quantum mechanics, but by recognizing their common structure. This paper initiates a series (Unitary Scale Theory, UST) examining scale-independent consequences of covering-space constraints on conserved currents. Version history v1 (January 2026): Initial publication. v2c (February 2026): Title refined to clearly reflect scope. Holonomy language updated throughout for consistency with covering-space / lift-projection framework developed in subsequent papers in the series. No changes to mathematical content or results.