The Geometry of Hallucination: Hamiltonian Constraints for Structurally Reliable AI Reasoning

Hallucination in artificial intelligence systems is commonly treated as a statistical artifact addressable through training methodology. We argue this framing is structurally incorrect. We present a formal framework in which reasoning is modeled as a dynamical system operating on a state space endowed with symplectic structure, and demonstrate that when Hamiltonian mechanics governs state evolution at the architectural level, invalid outputs become unreachable under the constrained transition rule by construction.