Large language models hallucinate as a structural property of what they are — computable systems generating output over a domain that exceeds computability. No amount of training data, scale, or internal verification can eliminate the failure. Byzantine Hallucination Consensus adapts Lamport's 1982 fault-tolerance framework for a model its authors never imagined: every attention head a potential traitor, every token a probabilistic vote, consensus approached asymptotically rather than crossed at a fixed threshold. The book builds the framework chapter by chapter as a live investigation, stress-tests it against the existing multi-agent literature, and maps where it breaks down. For engineers who build the systems that have to survive the lies they cannot prevent.