Junction from Phase Curvature to Spatial Curvature: A Fiber-Geometric Formulation

Abstract Standard quantum mechanics represents global phase with a single U(1) structure and typically treats phase transport as geometrically trivial unless additional external structure is introduced. In multi-carrier phase algebras, however, closed phase evolution can exhibit intrinsic holonomy, implying a nontrivial internal connection and curvature on the phase fiber. This article isolates the geometric junction at which internal (phase-fiber) curvature becomes operationally accessible as an effective curvature on the base manifold governing spatial transport. The mechanism is formulated in connection-theoretic terms: an internal transport law induces an effective base-level connection acting on multi-component amplitudes, whose curvature controls measurable departures from flat propagation. We highlight three observable channels—loop-dependent phase transport, interferometric shifts, and semiclassical deflections—through which internal holonomy can be tested without assuming a curved metric a priori. The resulting framework provides a compact geometric interpretation of how spatial curvature may emerge as a projection of internal phase holonomy, and it delineates the conditions under which this projection becomes experimentally distinguishable.