The model doesn't know what its training data is, nor does it know what sequences of tokens appeared verbatim in there, so this kind of thing doesn't work.

It's mind boggling if you think about the fact they're essential "just" statistical models

It really contextualizes the old wisdom of Pythagoras that everything can be represented as numbers / math is the ultimate truth

That might be somewhat ungenerous unless you have more detail to provide.

I know that at least some LLM products explicitly check output for similarity to training data to prevent direct reproduction.

Would it really be infeasible to take a sample and do a search over an indexed training set? Maybe a bloom filter can be adapted