There's a difference between reproducing a signature in an encyclopedia or in some way that makes it clear that you are recording the thing as it is.
Putting a signature on a work is forgery and in most jurisdictions charged as fraud.
If you produce an artwork in the style of someone and then clone the signature of someone who produces art in that style, there is a reasonable case for fraud.
Yeah, the references to copyright/trademark in this thread are confusing to me. I feel like there are much more straightforward legal arguments against falsely claiming artwork is by a famous artist.
For starters people pay for ChatGPT accounts used to generate these things. Secondly people use ChatGPT to generate stuff they put up on social media slop accounts to earn money. You'd probably build a case by finding a collection of these to justify discovery for more and build your fraud case based on that kind of thing where people are generating and publishing work with your signature on it for money. That's both a criminal and civil case.
Putting a signature on a work is forgery and in most jurisdictions charged as fraud.
If you produce an artwork in the style of someone and then clone the signature of someone who produces art in that style, there is a reasonable case for fraud.