the <50% rejection rate caught my eye, since that means the fixed-point safety comes with a pretty chunky keygen tax and makes batch generation less predictable. i also wonder how much the moidfied sampling biases the acceptance distribution for the rare borderline keys, because that’s exactly where these bound proofs tend to get brittle.

"partly empirical" is the bit I'd want pinned down with an actual target, since for Falcon the failure probability is already tiny enough that a small extra rounding budget can move you from 2^-128-ish comfort into handwavy territory pretty quickly. Also, if the modified keygen rejects under 50% of seeds, I'd like to know whether the resulting key distribution is still exactly the one assumed by the original trapdoor analysis or just close enough in practice.