This work investigates a minimal compatibility-based model of interacting agents. The main result is that local agreement reliably produces reorganization, but does not generically lead to global consensus. I study a system in which agents interact only if their states are sufficiently similar. The model exhibits a clear transition from disordered to partially ordered configurations. However, full global stabilization appears only under specific structural conditions. I systematically test the robustness of this transition under the followig condition: – rule variation – constrained topology (1D, 2D, small-world networks) – heterogeneity (agent-dependent parameters) – additional compatibility dimensions (orientation) Across all configurations, the reorganization threshold persists, but global consensus is often suppressed. Instead of a single unified state, the system stabilizes into multiple coherent domains. These results show that compatibility alone is not sufficient to produce global order. Structural constraints—such as connectivity, variability, and dimensional conditions—play a decisive role in determining whether global coherence emerges. This provides a minimal and testable framework for studying the separation between local agreement and global stability in complex systems. Methodological support and analytical assistance were provided with the help of GPT-5 (ChatGPT, OpenAI).
Adam (Adanio19) Wygrabek (Tue,) studied this question.