The Principle of Critical Sensitivity A First-Principles Analysis of Stability, Adaptation, and Collapse

Description The Principle of Critical Sensitivity: A First-Principles Analysis of Stability, Adaptation, and Collapse develops a domain-independent analytical framework for studying stability transitions in adaptive systems. Starting from minimal mathematical assumptions, the manuscript derives the concepts of stability classes, critical boundaries, adaptive margins, and critical sensitivity without assuming any specific physical model. Rather than proposing a new physical theory, the work formulates a general analytical framework that separates universal mathematical structure from domain-specific observables and identifies several open mathematical problems concerning the existence and representation of universal critical sensitivity measures.