Given f(prompt, model) -> text is there some h(model, text) -> [0,1) which tells you if the the text was generated by the model? Crucially, could you publish h without publishing the model?

It’s a bit like public key cryptography — if generating text is using sign() to sign a prompt with your model then is there a publicly available verify() that verifies the output came from the model but which doesn’t leak the private model itself?

What sort of things exist like this (other than private, API models recording all text they’ve generated)?