Coexistence Compatibility as a Constraint on Realizability in Complex Systems

This preprint introduces a minimal framework for analyzing complex systems under coexistence constraints. While traditional approaches focus on local feasibility (stability, energy, structural validity), this work shows that such properties are not sufficient to guarantee global realizability when multiple states must coexist. We define an incompatibility functional I(C) capturing interaction-induced constraints and introduce the Congruity Index of States (ICS) as a quantitative measure of configuration quality. Through a toy model, a multi-agent simulation and analogies with concurrent systems and physical computing, the work shows that system capacity is often limited by the growth of incompatibility rather than by local constraints alone. The framework suggests that many scalability limits observed in AI, distributed computing and physical systems can be interpreted as manifestations of compatibility constraints under coexistence.