Retrieval-augmented generation (RAG) is hard to monitor in production: exhaustive relevance labels do not exist for non-stationary multi-million-passage corpora that re-index in real time. As a result, retrieval quality is generally understudied and often deprioritised in favour of generation-oriented metrics. In this work, we propose auditing retrieval coverage by probing for evidence of missing documents rather than enumerating every relevant one. Our method Re:CAP (REtrieval Coverage Audit by iterative Probing) is a reference-free audit loop applied to a deployed RAG pipeline’s initial answer and retrieved context: it identifies the topics already covered, generates probing questions for plausibly missing topics, retrieves candidate documents, and applies an LLM-as-judge to retain only those that introduce previously-unretrieved information. On four public benchmarks, Re:CAP recovers 9–29% of gold labels that flat BM25 top-500 cannot reach, rising to 48% on TREC-COVID. On MuSiQue Re:CAP beats flat hybrid top-500 by +12.9 pp on recall at less than half the document budget. An ensemble BM25, dense, and hybrid baseline (top-500 each) still leaves out 21.2% of gold docs on TREC-COVID that Re:CAP recovers; human annotators judge that 78.9% of those structurally distinct documents add new information to the baseline answer (Fleiss κ = 0.79, n = 123), and 73.9% on live production traffic (n = 180). End-to-end recall is reproducible to within ±1% across three independent runs, making Re:CAP a stable instrument for periodic retrieval audits.

This paper proposes a method for the joint optimization of constraint weights and symbol activations within the Gradient Symbolic Computation (GSC) framework. The set of grammars representable in GSC is proven to be a subset of those representable with lexically-scaled faithfulness constraints. This fact is then used to recast the problem of learning constraint weights and symbol activations in GSC as a quadratically-constrained version of learning lexically-scaled faithfulness grammars. This results in an optimization problem that can be solved using Sequential Quadratic Programming.