Do LLM Recommenders Know When They're Hallucinating? Auditing Confidence Calibration in Catalog Faithfulness

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arXiv:2608.10008v1 Announce Type: cross Abstract: LLM recommenders for top-$K$ item suggestion regularly emit titles outside the target catalog. Prior audits measure this as a binary out-of-domain rate; none ask whether the model knew it was hallucinating. We jointly audit hallucination rate (OOD@10) and verbalized-confidence calibration (ECE, Brier, reliability) for four zero-shot LLM recommenders from four independent vendors (Mistral Large, Llama-3.3-70B, GPT-OSS-120B, Claude Sonnet 4.6), not grounded or fine-tuned systems, across three catalogs (MovieLens-25M, Amazon Reviews 2023 Toys, Yelp Open Dataset), stratified by item popularity. Hallucination is catalog-dependent (0--0.2\% on MovieLens, 4.5--8.3\% on Amazon, 2.2--8.4\% on Yelp), but verbalized confidence is materially miscalibrated even when hallucination is zero (ECE up to 0.223 on MovieLens despite 0\% OOD). All four LLMs are systematically \emph{under}-confident across all twelve cells, verbalizing a mean of 67--86 on items they recommend with 92--100\% accuracy. This is the opposite of the over-confidence usually emphasized in LLM-hallucination work. The under-confidence is best read as an \emph{elicitation mismatch}: ``Just Ask'' elicits a generic recommendation-quality rating, not a catalog-membership probability. A conformal abstention threshold over verbalized confidence reduces hallucination by at most 0.7\,pp across $\alpha \in \{.05, .10, .15, .20\}$, at 4--21\,pp of coverage cost: the under-confident channel cannot separate correct items from hallucinations, so the threshold mostly removes correct …

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