Language Model Hallucinations: An Impossibility Theorem and Its Architectural Consequences

Language-model specialization of the projection-insufficiency framework. Establishes hallucination as a structural failure class — delayed constraint failure (DCF) — necessarily arising in any bounded-context autoregressive generator, and characterizes which common mitigation strategies satisfy the resulting constraint requirement and on which constraint sub-class. Abstract We establish a structural account of hallucination in autoregressive language models: no system that selects tokens solely by bounded-context next-token prediction can guarantee globally consistent outputs across all prompts whose correctness depends on constraints extending beyond the context window. We formalize language generation as a…