This is not a great method in a world with closed models and highly diverse open models and samplers. It’s intellectually appealing for sure! But it will always be at best a probabilistic method, and that’s if you have the llm weights at hand.
What makes it not a good method? Of course if a model's weights are publicly available, you can't compel anyone using it to add fingerprinting at the sampler stage or later. But I would be shocked if OpenAI was not doing something like this, since it would be so easy and couldn't hurt them, but could help them if they don't want to train on outputs they generated. (Although they could also record hashes of their outputs or something similar as well – I would be surprised if they don't.)
