What question did this study set out to answer?

This research aims to develop a general analytical framework to study stability and adaptation in various systems.

July 19, 2026Open Access

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

Key Points

This research aims to develop a general analytical framework to study stability and adaptation in various systems.
Derived concepts of stability classes, critical boundaries, adaptive margins, and critical sensitivity from minimal mathematical assumptions.
Formulated a domain-independent framework vs. specific physical models.
Identified open mathematical problems related to universal critical sensitivity measures.
Outlined definitions of stability classes and critical boundaries relevant to adaptive systems.
Clarified the mathematical relationship between stability and adaptation in various contexts.
Proposed a framework with potential implications for studying stability transitions across different domains.

Abstract

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.

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