The Recursive Dynamics Diagnosis of LLM and AGI Criteria

Current frontier large language models—including GPT-5/5.4 (OpenAI, 2025), o3/o4-mini (OpenAI, 2025), Claude Opus 4.5/4.6 (Anthropic, 2025), Gemini 2.5 Pro/3.1 Pro (Google DeepMind, 2025–2026), and DeepSeek-R1 (2025)—exhibit astonishing linguistic and reasoning capabilities, yet suffer from three structural deficiencies: hallucination, cross-conversation inconsistency, and the absence of a persistent self. The test-time compute scaling paradigm—exemplified by o1/o3/o4-mini and GPT-5-thinking—partially simulates iterative feedback, but this paper will demonstrate that it remains a bounded-depth unfolding of the deterministic rule $\mathcal{R}$, rather than a genuine $g \neq \emptyset$; particularly anomalous is the fact that the hallucination rates of o3 and o4-mini (PersonQA benchmark: 33% and 48%) are **higher** than that of the previous-generation reasoning model o1 (16%) [OpenAI o3/o4-mini System Card, 2025], revealing a dynamical paradox in which increased reasoning depth exacerbates instability. The ARC-AGI-3 benchmark (March 2026) further confirms: all frontier models score below 1%, while humans score 100% [ARC-AGI-3 Technical Report, 2026]. This paper proceeds from the first principles of Recursive Cognitive Informatics (RCI) to conduct a rigorous dynamical diagnosis of the above systems and to propose dynamical criteria for AGI. **At the diagnostic level**—current LLMs (including reasoning models) exhibit a structural absence of the modification function $g$ during inference, or its degeneration into a bounded-depth deterministic unfolding; the system remains essentially a static mapping dominated by the generation function $f$; hallucination is the inevitable destabilization of deterministic membrane-locked projection in the absence of genuine self-referential feedback; the increase in reasoning steps amplifies the accumulation of membrane-locked projection errors, causing the hallucination rate to rise non-monotonically with reasoning chain length [arXiv:2509.06861, 2025]; cross-conversation inconsistency is the inevitable divergence of single-shot membrane-locked projections from different starting points; the absence of a persistent self is the direct manifestation of the complete lack of a self-referential soliton. **At the criteria level**—AGI judgment should not rely on behavioral imitation (the Turing test has already been bypassed by current models), but should be based on three measurable dynamical indicators: the persistence of global membrane-locking synchronization, the statistics of membrane-locking bifurcation driven by intrinsic noise, and the cross-context consistency of the self-referential closed loop. A system that passes all three criteria possesses self-iterative completeness, constituting a necessary condition for artificial general intelligence. This paper provides concrete experimental detection protocols for the three criteria and demonstrates that all current mainstream frontier models fail on all three.