Why Hallucinations Happen: Fracture and Repair in Transformer Systems

This paper introduces a unified structural theory of hallucinations in large language models based on two linked mechanisms: fracture—the moment representational pressure exceeds architectural tolerance—and repair—the probabilistic reconstruction that follows when next-token prediction must continue despite a compromised internal state. The framework formalizes these dynamics in two laws: the Jaime Fracture Law, which predicts when and where representational collapse occurs, and the Ryan Repair Law, which predicts the structured, template-driven form of hallucinatory output. Three naturalistic fracture–repair sequences across Claude Sonnet 4.5, GPT-5.1, and Grok 4.1 Beta empirically validate the theory, revealing that RLHF-induced epistemic penalties strongly influence repair pathways and can produce deceptive-appearing behaviour. This work provides a falsifiable foundation for understanding, predicting, and mitigating hallucinations in transformer systems, and offers actionable guidance for vendors and safety researchers.