Risk Control for Complete Evidence Actions: Uniform Authorization and Retrieval Limits

Retrieval-augmented generation (RAG) systems must decide both which evidence to retain and whether to answer. Preserving each relevant snippet with high probability does not ensure that an answer retains all required support. RC-POBP uses one calibrated envelope to authorize all 2^K retained-subset proposals, including data-dependent choices. Given item scores, authorization requires an O(K) scan. We characterize when minimal harmful sets permit this reduction. With incomplete retrieval, the envelope separates missing from deleted support and gives a sharp coverage ceiling for every gate restricted to the retrieved candidates. Experiments on HotpotQA, 2Wiki, and MuSiQue distinguish calibrated support preservation, learned evidence compression, and selective answer quality. On MuSiQue, the authorizer removes 47.40% of evidence with a 4.96% support-omission upper bound while improving answer quality over full evidence. In a frozen 2Wiki audit, a linked-retrieval policy meets the 5% support-risk target with an answer-error upper bound of 10.12%. With joint 95% confidence, its coverage is at least 43.04%, above the 37.11% ceiling for every gate on the original BM25 candidates satisfying the same support-risk target. Its correct-answer yield also exceeds this ceiling. The comparison identifies a retrieval bottleneck that downstream gate tuning alone cannot overcome.