I know next to nothing about hashing and Fourier transforms and the like, but my laypersons guess is this is technically true, since if the user makes no attempt to edit the output it could be authored in such a way to give a signature that gives away its author.

But if the user simply sends the output through an intermediary (perhaps local, low resource) LLM, or makes edits themselves, then it will be highly unlikely to be considered authored by ChatGPT by OpenAI’s forensics checks

It’s probably very much not in OpenAI’s interest to use such a system, since it could unnecessarily displease users.