An ability to answer questions with a train of thought showing how the answer was derived, or the self-awareness to recognize you do not have the ability to answer the question and declare as much. More than half the time I've used LLMs they will simply make answers up, and when I point out the answer is wrong it simply regurgitates another incorrect answer ad nauseum (regularly cycling through answers I've already pointed out are incorrect).

Rather than give you a technical answer - if I ever feel like an LLM can recognize its limitations rather than make something up, I would say it understands. In my experience LLMs are just algorithmic bullshitters. I would consider a function that just returns "I do not understand" to be an improvement, since most of the time I get confidently incorrect answers instead.

Yes, I read Anthropic's paper from a few days ago. I remain unimpressed until talking to an LLM isn't a profoundly frustrating experience.