Formalizing Shi in Complex Systems: The Field-Shi Framework of Flow, Structure, and Transformation

<div> This paper proposes a minimal formalization framework (Field-Shi Framework) for describing complex socio-technical systems, reconstructing the relation between action and structure from a "flow-prior" perspective. Different from the traditional modeling approaches centered on resources, power, or probability, this paper defines "Shi" as the relational condition between action and structure, that is, the ability of the structure to amplify, suppress, or deflect actions, and further expresses the original driving force of the system as the Shi flow (S) in multilayer networks. On this basis, the structure (Field, F) is re-understood as the compressed representation of the long-term stable pattern of the Shi flow, rather than an a priori analytical starting point.&nbsp; </div> <div> <br> </div> <div> To achieve minimal formalization, this paper introduces the FS Matrix as a local structural slice to describe the multi-field structural environment faced by actors at a specific moment. Meanwhile, the framework depicts the core mechanisms of system dynamics, including the redistribution, generation, and dissipation of the Shi flow, as well as the processes of structure generation, deformation, and phase transition, and explains the system evolution at different time scales through a layered fast-slow structure. In addition, this paper proposes the dual perspectives of the actor and the observer, unifying the local decision-making environment and the overall Shi flow evolution in the same analytical system. </div> <div> <br> </div> <div> &nbsp;At the theoretical level, the FS framework distinguishes two fundamentally different strategic problems: one is the optimal action selection within the existing structure (within-matrix optimization), and the other is to change the system structure through actions under structural constraints (matrix transformation). This division connects the traditional decision theory and the structural evolution theory, providing a unified grammar for strategic judgment in complex systems. At the application level, this paper further defines the role of artificial intelligence in this framework, pointing out that AI is more suitable for Shi flow sensing and structural recognition, while rule generation and institutional rewriting still need to be undertaken by humans.&nbsp; </div> <div> <br> </div> <div> Overall, this paper does not attempt to construct a closed prediction model, but proposes a "grammar of complex systems" that enables the consistent expression of the relations among the Shi flow, structure, and action, thus providing a transferable theoretical basis for complex system analysis, strategic decision-making, and institutional design. </div>