Risk-Gated Contractive Control for Hallucination Suppression in Large Language Models: A Stability-Theoretic Approach Toward the Entropy-Constrained Error Floor

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.