This paper presents a complexity science informed theory to describe how organizing forms emerge and foster innovation. The theory explores the bidirectional linkages between fine-grained interactions among human beings in a complex adaptive system and the emergent coarse-grained properties that characterize qualitatively distinct and yet stable organizing forms in social systems. By exploiting a mathematical foundation that has been successfully employed in analogous cases in the natural sciences, it opens the door to a rigorous theory of performance and adaptation in human systems by relating changing local rules of interaction to qualitative changes in emerging organizing forms. This process is mediated by evolving models of the system in the environment developed and shared among individuals. Finally, the paper explores whether this model can be used canonically and does so in the context of axiomatic hurdles that must be overcome if a practical mathematical theory of human organizing is to be realized.