“In this paper, we formalize the problem and show that it is impossible to eliminate hallucination in LLMs.”
Xu, Jain and Kankanhalli use learning theory to show an LLM cannot learn every computable function. Use one as a general problem solver and it will make things up. Every vendor promising a hallucination fix in the next release is selling a mitigation and calling it a cure. The math says the bug ships with the product.