> I think you misunderstand the language others are using. "Hallucination" doesn't refer to an "error" in the sense that crashing is an error, it refers to a situation in the problem class above, which is compatible with it working correctly every time.

I do not misunderstand, I think maybe you do. You think there is a proper next word selection based on logic or meaning and there for the model selected the wrong one - it hallucinated.

I am saying the model has no concept if anything other than the probability of select a token which is not based in any logic so it is working properly- it only works on numbers.

It is random chance that it is ever correct, not that it is correct often and messed up this one time.