Hallucination Is Not a Resonance Error

This paper challenges the prevailing interpretation of large language model hallucinations as resonance, alignment, or representation errors. Instead, it argues that hallucinations arise from structural admissibility failures: the absence of invariant constraints enforced prior to generation. Drawing on Filtration Theory, the paper reframes hallucination as a control problem rather than a semantic or statistical one. When systems are permitted to generate outputs without upstream filtration, boundary enforcement, or rollback authority, error manifests as confident but unconstrained continuation. The analysis distinguishes between optimisation, learning, and admissibility, and shows why downstream correction mechanisms such as reinforcement learning, fine-tuning, or retrieval augmentation cannot fully resolve hallucination in the absence of invariant-first control. The paper has implications for AI safety, system governance, and the design of autonomous agents operating under uncertainty. It complements and extends the invariant-first control architecture formalised in the Filtration Theory framework.