The Foundations of Order VI: The Scale-Rigidity Law: The Structural Driver of Institutional Evolution

Why do larger organizations invariably develop more rigid institutions? Classical theories appeal to the consolidation of power, cultural tradition, or path dependence---all attributing rigidity to factors external to the institution itself. This article advances an alternative proposition: scale is itself an independent driver of institutional rigidity. Institutions are pre-written scripts for cooperation, enabling individuals who do not know one another to coordinate without renegotiating roles and procedures for every interaction. When scale is small, the script can be thin and adjust on the fly. But when cooperation expands from a few dozen individuals to millions, coordination costs rise at a rate far exceeding linear growth, and standardized scripts transform from an option into a necessity. It is not that managers prefer rigidity; it is that large-scale cooperation, mathematically, does not permit flexibility. This article proposes the scale-rigidity law: organizational scale and institutional rigidity maintain a stable positive correlation on the regression line. We test this law through isomorphic verification across three scales---firms, states, and digital platforms---demonstrating its cross-scale universality. We further engage in dialogue with Weber's theory of bureaucracy, organizational ecology's concept of structural inertia, and North's theory of institutional change, clarifying the complementary position of our framework: existing theories have explained the form of rigidity and the mechanisms that lock it in; this article supplements them by explaining why rigidity initially arises. The continuous reinforcement of institutional rigidity leads to the self-locking of the institution itself, creating the structural conditions for the growth of outlier orders---providing the logical premise for the succeeding article, ``Outlier Orders.'' Four testable predictions are derived to anchor the causal effect of the scale-rigidity law through dual pathways in both virtual and real worlds.