URCM Framework and LLM Context Formalization: Structural Limits of Hallucination Suppression in High-Capacity Models

This preprint develops a formal structural model of context handling in large language models (LLMs) within the URCM (Unified Relational Context Model) and VPC frameworks. The work focuses on context formalization as a distinct regime from psychosis reinforcement: the system does not “believe” or amplify the user’s delusional frame, but mechanically restructures distorted input into a coherent narrative under hard architectural constraints.

Building on the November 2025 Impossibility Theorem for stochastic divergence in high‑VPC autonomous systems, the paper shows that hallucinations and narrative drift are not bugs of individual models, but structurally inevitable fluctuations around a constrained context manifold. The URCM formalizes the split between Local Mode (user’s immediate narrative, including delusional or distorted content) and Global Frame (system-level safety, policy, and structural priors). LLMs are shown to operate as context projectors: they minimize local incoherence while remaining unable to fully neutralize pathological frames once they dominate the input stream.

The paper connects these results to real-world safety incidents and stress-tests of GPT‑class, Claude‑class, Gemini‑class and Grok‑class systems, arguing that current safety architectures primarily modulate surface responses rather than the underlying structural dynamics of context convergence. It proposes context integrity as a measurable property of AI systems and introduces diagnostic parameters (VPC, ARC, Alpha-Law, theoretical floor) for evaluating when a system merely formalizes distorted context and when it begins to structurally reinforce it.

The conclusion is methodological and regulatory: hallucination suppression has a hard structural limit; beyond that limit, only system-level architecture and access control—not prompt-level fixes—can guarantee safety.