Semantic Caches for LLM Web Services Leave Their Error Budget Unspent

Web services built on large language models (LLMs) receive many paraphrases of earlier queries, which a semantic cache answers from stored responses. A reused answer can be wrong, so wrong answers must stay below a share $δ$ of the queries. Existing caches reuse above a fixed similarity threshold or, like vCache, learn a per-entry rule that bounds each query's error by $δ$. However, fixed thresholds break the budget on new streams, and per-entry rules need labels on every entry before reusing it. We find an unspent error budget, as vCache realizes only 12-55% of $δ$ on three public query streams. Surplus spends this budget where reuse is most likely correct. It ranks queries by a risk score shared across paraphrase clusters and opens risk bins as far as an audited error estimate allows. Free labels from every LLM call and a ledger of realized errors keep this threshold safe under drift. On five streams, including ORCAS search queries, Surplus holds $δ$ in every test cell, which no baseline does. On the shuffled streams it serves 40% more hits than vCache, and its pooled hit rate beats the best baseline holding $δ$ in each cell by 4.10 points. In a vLLM testbed it cuts the mean latency by 31.59% at the highest load, against 23.67% for vCache.