Intuition emerges in Maximum Caliber models at criticality

Whether large predictive models merely parrot their training data or produce genuine insight lacks a physical explanation. This work reports a primitive form of intuition that emerges as a metastable phase of learning that critically balances next-token prediction against future path-entropy. The intuition mechanism is discovered via mind-tuning, the minimal principle that imposes Maximum Caliber in predictive models with a control temperature-like parameter $\lambda$. Training on random walks in deterministic mazes reveals a rich phase diagram: imitation (low $\lambda$), rule-breaking hallucination (high $\lambda$), and a fragile in-between window exhibiting strong protocol-dependence (hysteresis) and multistability, where models spontaneously discover novel goal-directed strategies. These results are captured by an effective low-dimensional theory and frame intuition as an emergent property at the critical balance between memorizing what is and wondering what could be.