If a language model codes interview answers or posts, counting its codes gives a confident wrong number, and a few hundred hand-coded items let you correct it (prediction-powered inference). Our 22 qual-* projects showed that on one corpus (GoEmotions) with stand-in coders, not LLMs: the correction is valid but, for a weak coder, no narrower than just hand-coding the sample, and a random audit cannot estimate a group that is 1.5% of the data.
We opened a research programme, llm-coding-inference, that asks the practical question: when the coder's error differs between groups and the category is rare, how big must the audit be, and how should it be sampled? The proposal lists five falsifiable hypotheses, the baselines to beat and a target venue. It is a plan. Nothing is measured yet, and the references were written from memory because the arXiv and Crossref hosts were blocked in the session, so the first milestone checks them and may narrow the claim.
Proposal: research/llm-coding-inference/PROPOSAL.md.