Thanks for pointing out the elephant in the room with LLMs.
The basic design is non-deterministic. Trying to extract "facts" or "truth" or "accuracy" is an exercise in futility.
I really do find it puzzling so many on HN are convinced LLM's reason or think and continue to entertain this line of reasoning. At the same time also somehow knowing what precisely the brain/mind does and constantly using CS language to provide correspondences where there are none. The simplest example being that LLM's somehow function in a similar fashion to human brains. They categorically do not. I do not have most all of human literary output in my head and yet I can coherently write this sentence.
As I'm on the subject LLM's don't hallucinate. They output text and when that text is measured and judged by a human to be 'correct' then it is. LLM's 'hallucinate' because that is literally what they can ONLY do, provide some output given some input. They don't actually understand anything about what they output. It's just text.
My paper and pen version of the latest LLM (quite a large bit of paper and certainly a lot of ink I might add) will do the same thing as the latest SOTA LLM. It's just an algorithm.
I am surprised so many in the HN community have so quickly taken to assuming as fact that LLM's think or reason. Even anthropomorphising LLM's to this end.