Claim-Level Grounding Verification with Conformal Risk Control for Retrieval-Augmented Generation in Regulated Domains

Retrieval-augmented generation (RAG) is now used in legal, clinical and compliance work, where an unsupported sentence is a liability, yet existing hallucination detectors score a response as a whole, give no control over the rate at which ungrounded statements slip through, and leave nothing a reviewer can audit. This paper proposes CGV-RC, a claim-level grounding verification overlay with conformal risk control. A response is decomposed into atomic claims; each claim triggers a claim-conditioned re-retrieval and is scored by claim-level entailment, a numeric and entity consistency check and a provenance check. A logistic model fitted on a calibration split fuses the three, and a split-conformal threshold bounds the claim-level false-negative rate by a chosen tolerance. Three propositions, on the fusion-gain ceiling, the finite-sample conformal miss rate and response-level risk, are derived and validated numerically. Because no public corpus labels the four hallucination types that matter in regulated work, the study uses a synthetic generative model with type-specific detector blind spots calibrated from published ranges, so results characterise the method under stated assumptions rather than measure a deployed system. Across three simulated domains CGV-RC reaches a mean AUROC of 0.887 against 0.681 for passage-level NLI and 0.663 for five-sample self-consistency at about 7 percent of the latter's cost. The gate holds the target miss rate within finite-sample error, but a 1 percent tolerance leaves only 22 percent of grounded claims unreviewed, and extrinsic claims remain the hardest class.