Conditions for Social Structure Formation: A Minimal Dynamical Framework for Cross-Individual Stable Structure Emergence

This paper proposes a minimal dynamical framework for explaining how stable social structures emerge. Conventional social theories often define society as a collection of individuals, institutions, or shared norms. Such approaches describe social organization but do not explain a more fundamental question: why stable supra-individual structures arise and persist. The framework proposed here argues that social structure is not reducible to individual aggregation. Instead, stable social organization emerges when sustained interactions among individuals generate persistent shared structures whose maintenance no longer depends on any single participant. Three minimal formation conditions are proposed: sustained interaction density, stable shared structural accumulation, and independent structural maintenance. The framework further derives consequences including structural inertia, path dependence, stability constraints, fragmentation dynamics, and long-term structural stabilization under sustained interaction. The framework attempts to explain why institutions persist, why collective norms stabilize, why social fragmentation emerges, and why historical structures constrain future social evolution. Potential applications include cognitive science, artificial intelligence, multi-agent systems, computational social science, complex systems, and large-scale structure formation research.