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This paper aims at providing a rigorous definition of self-organization, one of the most desired properties for dynamic systems, such as peer-to-peer systems, sensor networks, cooperative robotics, or ad-hoc networks. We propose a framework in order to prove the self-organization of dynamic systems with respect to generic criteria (e.g., similarity, load balancing, geographical neighborhood, battery level) that can be composed in order to construct more complex criteria. We illustrate our theory with a case study that consists in proving the self-organization of CAN, a representative peer-to-peer system.