Global admissibility constraints for coupled sectors in the Quantized Dimensional Ledger

This paper develops a coupled-sector version of the Quantized Dimensional Ledger (QDL) framework. In QDL, physical constructions are represented as integer vectors in a ledger lattice and judged by structural admissibility rather than by dimensional homogeneity alone. Earlier stages of the programme developed admissibility-preserving maps, closure classes, operator exclusions, interaction architecture, and matter representation selection. The present paper asks whether a full physical theory—decomposed into gravitational, gauge, matter, measurement, and interface sectors—can be subjected to one common admissibility law. A global ledger map and admissibility operator are introduced for coupled theories, together with an obstruction-space formulation in the quotient Λ/K/KΛ/K. The main structural result is a coupled-sector compatibility theorem: a coupled theory is globally admissible if and only if the obstruction classes of its constituent sectors sum to zero. This yields a precise interface criterion showing that sector-wise admissibility of the primary sectors is necessary but not sufficient; the interface sector must carry vanishing residual obstruction. Two explicit lattice-level witnesses illustrate the result. In the first, four individually admissible sectors assemble into a globally admissible coupled action. In the second, the same primary sectors are paired with a closure-defective interface and the total action leaves the admissible kernel. The paper does not claim a dynamical unification of the Standard Model and gravity. Its claim is narrower and structural: QDL admits a mathematically explicit compatibility test for coupled representational sectors, providing a pre-dynamical constraint on admissible theory assembly. The paper thereby marks the coupled-sector stage of the broader QDL Unified Admissibility Theory programme.