Audited Operational Realisability: A Closure-Completion Reflection for Carriers with Audit Data

Many mathematical frameworks come with audit data alongside their main objects: source ledgers, route registries, residual budgets, status annotations, nonclaim boundaries, and meta-audit records. Audited Operational Realisability (AOR) is the meta-theory of typed carriers that close as audit systems within a declared scope. A PreSB carrier is a typed carrier together with this audit data; it is an AOR carrier when every declared audit obligation is discharged inside the scope. We show that every PreSB carrier admits a canonical completion into the full subcategory of AOR carriers via a reflection obtained as a monotone Knaster--Tarski saturation on the complete lattice of AOR-extending operations. The reflection is developed in four parts: the closure-completion construction and its universal property; the eight-stratum decomposition of the structural defect; the thirteen-type residual atlas, with reciprocal local and global mismatch types, its discharge cascades, and cascade-stable AOR; and refinement chains with asymptotic statuses, yielding the hierarchy RefStableAOR subset CascadeStableAOR subset AOR. The development is meta-theoretic and carries no PDE-specific worked example; concrete AOR-instance applications belong to consumer manuscripts that cite this meta-theory at paper level. Two scope disclosures apply. The cascade-confluence theorem uses Newman’s lemma as a classical body input after proving the local diamond property and the well-founded discharge relation; Appendix D records the corresponding formal companion row as partial. The hierarchy is exhibited via named witness carriers and their typed obstruction markers; full predicate-level non-membership proofs at every level remain framework future work.