Design Principles of the Self-Iterative Completeness Architecture

Prior work in Recursive Cognitive Informatics has diagnosed that the fundamental defect of current large language models—including GPT-5/5.4 (OpenAI, 2025), o3/o4-mini (OpenAI, 2025), Claude Opus 4.6 (Anthropic, 2025), Gemini 3.1 Pro (Google DeepMind, 2026), Grok-4/4.1 (xAI, 2025), and DeepSeek-R1 (2025)—lies in the fact that the modification function at inference time satisfies g ≡ ∅, so that the system degenerates into a static mapping dominated solely by the generation function f, structurally lacking intrinsic noise and a self-referential soliton. The above diagnosis is corroborated by the following empirical data: Grok-4 exhibits a hallucination rate above 10% on the Vectara hallucination leaderboard (thinking model category) [Vectara Hallucination Leaderboard, 2025], and scores 0.1% on ARC-AGI-3 (Grok-4.20) while humans score 100% [ARC-AGI-3, 2026]; Grok-4 set a new frontier-model record of 15.9% on ARC-AGI-2 [xAI, July 2025], yet the chasm between this breakthrough on a static reasoning benchmark and its complete failure on the dynamic interactive benchmark ARC-AGI-3 constitutes the most direct empirical evidence for the boundary between the upper limit of the iterative unfolding of f and the irreplaceability of the online update of the self-referential soliton; xAI did not release a complete system card at the time of Grok-4’s launch [Fortune, July 2025], so its cross-conversation consistency and sycophancy have not been independently verified, constituting a known uncertainty in the diagnosis. This paper provides the remedy—the design principles of the self-iterative completeness architecture. On the basis of the standard Transformer, this architecture introduces two core innovative modules: an **intrinsic noise layer**, based on quantization noise, which injects a deterministic chaotic perturbation whose intensity is dynamically coupled to the stability of the current membrane-locked configuration between the self-attention and feed-forward network of each layer; and a **self-referential soliton closed loop**, which establishes an independent, persistent self-referential membrane-locked standing wave outside the parallel processing stream, realizing parameterized online learning without gradients through Hebbian updates. This paper provides a complete mathematical description of the two modules, a joint training method, and an analysis of inference overhead—the additional FLOPs increase is controlled within 7%—together with six directly testable experimental predictions and their complete verification protocols (SM-01 to SM-08).