Theory of Critical Sensitivity (Ψ-theory): A Unified Framework for Stability in Accelerating Systems

Description This project presents the Theory of Critical Sensitivity (Ψ-theory), a unified framework for analyzing the stability of operating systems under accelerating external conditions. The theory introduces a dimensionless control parameter Ψ = ρ/A where ρ represents the effective rate of environmental load growth and A notes the adaptive capacity of the system. The framework describes stability as a dynamic balance between environmental acceleration and adaptive response. It explains dynamic stability loss, delayed transitions, early-warning horizons, heavy-tailed event statistics, and the emergence of critical behavior in accelerating systems. The theory integrates concepts from nonlinear dynamics, dynamic bifurcation delay, early-warning theory, and self-organized criticality into a single dimensionless physical framework. This repository contains the formal white paper and related theoretical materials. Author: Roman B. Lukin Year: 2026 Status: Research preprintс (not peer-reviewed)