The Zhu-Liang Theorem of Recursive Nested Functions: Reconstructing Self-Organization and Complex Systems

Self-organization and complex systems are core research areas in systems science, yet traditional theories struggle to provide a unified explanation for fundamental features such as emergence, adaptation, and hierarchy. Based on the Zhu-Liang Theorem of Recursive Nested Functions, this paper incorporates complex systems into the cognitive category $\Cog$, demonstrating that the recursive element structure of a system corresponds to its intrinsic hierarchy, the self-organization process is the interaction and projection of recursive elements at different layers, and emergence arises from the irreducible contribution of deep recursive elements to shallow layers. The layer complementarity principle reveals why complex systems exhibit regularities at finite scales and provides a recursive ontological foundation for the relationship between the whole and parts in systems science. This reconstruction not only unifies diverse phenomena in complex systems but also reveals a deep resonance with the philosophical wisdom of ``one flower, one world.''