When an LLM codes a text corpus and you hand-check a sample to correct its errors, a rare category (under 1% of items) is hard: a uniform audit of 200 often holds no positives, and normal-approximation intervals cover as little as 16%. Sampling items by the coder's uncertainty fixes coverage for the rarest categories but needs a floor on each item's inclusion probability, and the best floor differed by prevalence: 0.02 below 1%, 0.05 to 0.10 above.
Milestone 4d of research/llm-coding-inference tests one rule that needs no labels: floor = clip(5 × q̄, 0.02, 0.10), with q̄ the corpus mean of the calibrated coder probability. On GoEmotions (38,234 comments, nine emotions, 0.10% to 1.96% prevalence, audit of 200, 500 draws per cell) coverage was 92.4% to 96.0%, 93% or more in eight of nine. For the six categories under 1% the interval was 0.48 to 0.80 of the width of a uniform-audit Wilson interval; at 1% and above it was valid but no narrower.
Caveats: the multiplier was picked after seeing the earlier floor sweep on the same corpus, the coder is a weak logistic stand-in rather than an LLM, and the three rarest categories still produce audits with no positive about half the time. Next is a real LLM coder and a second corpus.
Code, numbers and log: research/llm-coding-inference/.