Defect Cartan Gravity III: Multivalued Defects, Conserved Cartan Currents, and Network Signatures

We construct the defect sector that feeds the cosmological and weak-field phenomenologyof Defect Cartan Gravity. Multivalued Stueckelberg label fields ΦA define distributionaltwo-forms ΣA = ddΦA supported on codimension-2 worldsheets. We interpret ΣA asPoincar´e duals of defect worldsheets and build explicit Cartan source currents τ defI and σ def I J that couple to the coframe and spin connection. We show how these currents arisefrom a diffeomorphism- and Lorentz-invariant worldsheet action and therefore satisfy thecovariant conservation identities required by the Bianchi identities. We then coarse-grain toa network description using a velocity-one-scale closure (ξ(t), v(t)), derive ρdef (t) and wdef (t),and provide a practical parameterization for defect anisotropic stress Πdef (k, t) that entersgravitational slip in Paper II.