The Curvature Constraint: Universal Bounds on Recursive Adaptation in Complex Systems

Across complex adaptive systems; biological, economic, technological, and ecological; a recurring constraint emerges in the rate at which systems can update without losing coherence. This paper introduces the Curvature Constraint, a derived principle identifying a bounded rate of recursive systemic adaptation typically centered around a 2% annualized curvature band. Rather than an arbitrary metric, this range arises from the structural interplay between entropy leakage, feedback response, memory retention, and symbolic assimilation. Using the Spectrum of Possibility and Recursive Choice (SPARC) framework, I formalize curvature as the rate of directional change in a system’s coherence over time. I demonstrate that exceeding this band destabilizes feedback loops, while slower rates result in stagnation or loss of adaptivity. Drawing on empirical observations from growth economics, cognitive science, urban infrastructure, and evolutionary biology, I show that this attractor is not a policy convenience but a structural necessity. The Curvature Constraint serves as both a descriptive insight and a prescriptive boundary for forecasting, governance, and technological development, providing a minimal universal constraint on sustainable systemic transformation.