Structural Ruptures in World-System Transitions: A Formal Account of Historical Change

Many pivotal historical transformations appear discontinuous: existing institutional and economic structures cease to be valid, and a new structural regime emerges. In this work, we propose a formal framework for analyzing these transitions using the Theory of Non-Derivability and Admissibility (TNA) and the concept of Structural Rupture. A world-system is modeled as a configuration space governed by a structural constraint operator S that defines the domain of admissible states. We introduce the Bresciano Metric to quantify the structural distance between the system's current state and its admissibility boundary. We demonstrate that major historical shifts—such as the collapse of medieval fortifications or the emergence of the Atlantic economy—constitute non-derivable structural transitions S S'. This formalization explains the inherent unpredictability of systemic change: the rupture invalidates the very structural conditions that defined prior admissibility. The framework provides a unified formal language to model long-term structural change across historical and complex systems.