My personal definition of hallucination (which I thought was widespread) is when a model states a fact about the world that is entirely made up - "the James Webb telescope took the first photograph of an exoplanet" for example.

I just got pointed to this new paper: https://arxiv.org/abs/2508.01781 - "A comprehensive taxonomy of hallucinations in Large Language Models" - which has a definition in the introduction which matches my mental model:

"This phenomenon describes the generation of content that, while often plausible and coherent, is factually incorrect, inconsistent, or entirely fabricated."

The paper then follows up with a formal definition;

"inconsistency between a computable LLM, denoted as h, and a computable ground truth function, f"