It would be interesting to see how that .4% varies across fields on arXiv. I imagine some areas influenced LLM writing much more than others and are more susceptible to false positives. Anyway it's a little strange to me that these detectors do so poorly (at least by what I hear on this site). There is as much labeled data as you would need to train on pre-LLM human vs LLM text. If their out of sample errors are as good as has been claimed, the only methodological flaw I can think of is that post-LLM human text and LLM text have been converging.