RGCC-X⁺ V2: Recursive Geometric Contraction Control for Large Language Model Hallucination Mitigation — A Lyapunov-Inspired Dynamic Stability Framework with Empirical Validation

Hallucination in large language models (LLMs)—the generation of factually incorrect, fabricated, or epistemically overconfident content—remains a major barrier to deployment in high-stakes domains. Existing mitigation strategies, including retrieval-augmented generation (RAG), reinforcement learning from human feedback (RLHF), and inference-time sampling heuristics, primarily address knowledge insufficiency or alignment preferences. However, none explicitly model the temporal evolution of epistemic drift under adversarial prompting or multi-turn conversational pressure.We introduce RGCC-X⁺ V2 (Recursive Geometric Contraction Control), a control-theoretic framework that reframes hallucination under pressure as a dynamic state instability problem. Instead of treating errors as isolated query-level failures, RGCC-X⁺ models the conversational epistemic state as a bounded stochastic recurrence and applies adaptive contraction through a risk-calibrated feedback mechanism. The framework integrates: (i) a five-component risk estimator with logistic regression-derived weights (ROC-AUC = 0.847); (ii) an Extended Kalman Filter for nonlinear latent state tracking; (iii) a three-tier escalation cascade; and (iv) a self-correction recovery module with formal guarantee. A Lyapunov-inspired analysis establishes mean-square boundedness of epistemic error under the adaptive contraction schedule.On a 312-question benchmark spanning five stress categories—including adversarial multi-turn drift—RGCC-X⁺ V2 reduces mean hallucination severity by 38.4% relative to an uncontrolled baseline (paired t-test: p < 0.001, Cohen’s d = 0.81). In adversarial scenarios, reduction reaches 61.7%. When combined with RAG, the system achieves 52.3% reduction with a statistically significant interaction term (two-way ANOVA: F(1,308) = 14.3, p < 0.001), indicating genuine complementarity rather than additive overlap. Utility preservation analysis confirms response informativeness remains within 4.2% of baseline.These findings suggest that hallucination under adversarial conditions can be effectively mitigated through stability-inspired feedback control. RGCC-X⁺ V2 provides a deployable, model-agnostic regulation layer that complements retrieval-based approaches and advances the treatment of hallucination from a static knowledge problem to a tractable control problem.