Certified End-to-End Graph-Induced Surrogate Compression for Black-Box Local Intervention

In expensive graph intervention, the search domain is often not designed by the optimizer. A cheap graph heuristic or learned front end proposes a shortlist, and a black-box optimizer then spends simulator calls inside that domain. This fixed-domain view hides the central risk: the shortlist may be simple enough to compress, or it may be missing the edits that matter. Returning to the full library exposes this risk but destroys the simulator-call budget. We formulate the missing layer as auditable post-screening: the system returns not only a deployment, but also queried interactions, surrogate fit, omitted-candidate risk, and a deploy / expand / enrich / fallback recommendation. Local footprints induce a shortlist interaction graph; clique queries and Möbius inversion recover a graph-induced surrogate whose query complexity is controlled by local overlap and bag load rather than ambient library size. Outside, joint, and sparse-clique certificates turn residual shortlist risk into one-sided measurable quantities. The practical system is pairwise, with general-order theory as the structural query template; on moderate real tasks and localized large graphs, it reaches high-call greedy references in the main giant-connected-component (GCC) rows using up to about 70% fewer simulator calls, while the same run records shortlist credibility, certificate evidence, and next-call repair decisions under the charged budget.