This paper reframes hallucination in large language models (LLMs) as a stochastic dynamical state rather than a binary error event. Because LLMs generate outputs under non-zero conditional entropy (H(Y|X) > 0), complete elimination of hallucination is theoretically impossible. We introduce Risk-Gated Contractive Control (RGCC-X⁺), a control-theoretic middleware architecture that enforces adaptive contraction on hallucination dynamics based on measurable epistemic risk signals.RGCC-X⁺ integrates multi-sample semantic variance, predictive–evidence gap detection, entropy-based uncertainty estimation, and evidence-consistency verification into a unified risk function. This risk signal modulates contraction strength dynamically, yielding provable boundedness under Lyapunov stability analysis. We further derive an entropy-constrained lower bound demonstrating that hallucination cannot fall below an irreducible floor determined by conditional entropy.Rather than claiming elimination, the framework provides a principled mechanism for asymptotically approaching the entropy-imposed minimum while preventing long-horizon epistemic drift. Preliminary results show directional improvements consistent with theoretical predictions. This work shifts hallucination mitigation from heuristic correction toward provably stable epistemic regulation.
Alim ul haq khan (Mon,) studied this question.