The only way this works is to use the same exact model and weights right? So that you can replay the text generation as it would have been originally done, and compare output?
And then what, if there is no match do you need to retry with all other known models that could have been used?
Or are models sufficiently similar that they are interchangeable for this type of watermark?
And what if a competing or open source model was used? I can't see how the watermark would work.
And if you have access to a non-watermarked output? How can you prove they are not simply using another key? How can you be sure the text is not watermarked? From the explanations, you can't.