Gauge freedom forces transport; transport path-dependence forces curvature. This paper derives a discrete connection-like transport rule as a bookkeeping necessity once second-tier correction admits coboundary (gauge) freedom. Using only refinement stability over a composition index semigroup, it introduces transport operators acting on the second-tier Abelian accumulator and defines a holonomy residue as the normalized mismatch between two refinement orders. The resulting curvature witness is framed as an obstruction to refinement-order independence in gauge comparison, without assuming manifolds, limits, derivatives, Lie theory as primitives, or any physical field postulates.