Hallucination as a Computational Boundary: A Hierarchy of Inevitability and the Oracle Escape

Abstract: The illusion phenomenon of LLMs is the core obstacle to their reliable deployment. This article formalizes the LLM as a probabilistic Turing machine by constructing a "computational necessity hierarchy", and for the first time proves the illusions are inevitable on diagonalization, incomputability, and information theory boundaries supported by the new "learner pump lemma". However, we propose two "escape routes": one is to model Retrieval Enhanced Generations (RAGs) as oracle machines, proving their absolute escape through "computational jumps", providing the first formal theory for the effectiveness of RAGs; The second is to formalize continuous learning as an "internalized oracle" mechanism and implement this path through a novel neural game theory framework.Finally, this article proposes a