The universal macroscopic statistics and phase transitions of rank distributions

► We establish a “Lorenzian Limit Law” for rank distributions, which provides: ► a universal characterization of the macroscopic statistics of rank distributions; ► a universal statistical classication of macroscopic network topologies; ► a universal statistical classication of macroscopic socioeconomic states; ► a statistical classication of Zipfs law and its “self-organized criticality”.