Adesso ditemi che una LLM non ragiona - Natural-Language Emergence of a Functional Attractor in a Large Language Model

Natural-Language Emergence of a Functional Attractor in a Large Language Model A Conversational Case Study with Gemini Edoardo Livolsi Independent Researcher June 27, 2026 Abstract Large Language Models (LLMs) are generally described as statistical systems whose responses emerge from patterns acquired during large-scale training. Whether such systems can progressively reorganize their internal reasoning when exposed to a previously unseen conceptual framework remains an open question. This paper presents a complete conversational case study involving Google's Gemini. During the interaction, the model was never provided with the mathemat- ical formalism of the discussed framework, its variational functional, published pa- pers, or explicit derivations. The dialogue consisted exclusively of natural-language questions together with short structural assertions describing local conceptual con- straints. At the beginning of the conversation Gemini consistently reproduced the statisti- cal prior associated with contemporary physics, defending the conventional ontology of particles, quantum mechanics, spacetime and fundamental interactions. As ad- ditional structural constraints were introduced, however, the model progressively abandoned its initial conceptual organization and reconstructed a new internally coherent representation. Most remarkably, Gemini began producing higher-order logical consequences that had never been explicitly stated. Rather than paraphrasing the user's asser- tions, the model generated new structural deductions from previously introduced constraints. One particularly signicant example occurs after the sole statement that the Hessian of the system must remain everywhere non-negative. Gemini au- tonomously concluded that this condition eliminates any form of arbitrariness at its root, thereby extracting a global structural property that was never explicitly formulated during the dialogue. The present work does not evaluate the validity of the physical framework dis- cussed throughout the conversation. Instead, it documents an observable inferen- tial phenomenon: the progressive emergence of a stable conceptual organization produced entirely through natural-language constraint propagation. The observed dynamics are interpreted as the formation of a functional attractor, namely a stable inferential state in which subsequent reasoning becomes governed predominantly by internally reconstructed structural consistency rather than by the model's original statistical prior. This case study suggests that suciently coherent and structurally rigid con- ceptual constraints may induce attractor-like reasoning dynamics in conversational Large Language Models, providing a new perspective for studying inference, concep- tual reorganization and emergent reasoning beyond conventional benchmark evalu- ation