Can large language models know what they know?

I did not want to ask only whether an LLM can know. That question can be postponed indefinitely by arguing over belief. So this paper asks the more annoying, second-order question: if there is knowledge anywhere in the system, can the system tell when it has it?

Sosa's aptness supplies the standard. Mechanistic interpretability might supply the evidence. Neither move makes the answer simple, which is part of the point.