Am I misreading that paper? They define hallucinations as anything other than the correct answer and prove that there are infinitely many questions an LLM can't answer correctly, but that's true of any architecture- there are infinitely many problems a team of geniuses with supercomputers can't answer. If an LLM can be made to reliably say "I don't know" when it doesn't, hallucinations are solved- they contend that this doesn't matter because you can keep drawing from your pile of infinite unanswerable questions and the LLM will either never answer or will make something up. Seems like a technically true result that isn't usefully true.