World Model Science: Self-Organized Criticality, Weak Chaos, and Metastable Belief Dynamics in Long-Horizon LLM Agents

Long-horizon LLM agents must maintain task state across extended sequences of observations, actions, tool calls, and intermediate beliefs. We study these trajectories through three dynamical views: self-organized criticality, weak chaos, and metastable belief dynamics. Our framework aligns agent-implied states with benchmark-grounded states and measures stress accumulation, error avalanches, temporal dependence, local--global mismatch, bounded divergence, belief-basin transitions, and finite-size scaling under explicit null models. Across 22 experiments spanning controlled puzzles, tool use, embodied tasks, multi-hop retrieval, general-assistant reasoning, and Game of Life, we find that locally valid actions can persist after global state fidelity fails, stress can trigger abrupt collapse, error sequences exhibit long memory, dependency depth changes the propagation regime, and larger horizons support larger avalanches. At the same time, divergence remains bounded, belief states show metastable rather than fully chaotic behavior, and stronger claims of universal power laws, critical points, or shared intervention optima are not supported. These results suggest a science of agent world models based on trajectory-level dynamical diagnostics rather than terminal reward alone.