The Universal Principle of Stability: Coherence and Tolerance as the Structural Basis of Stable Systems

This paper proposes a universal structural principle of stability applicable across dynamic systems in multiple scientific domains. The principle states that a system remains stable when the coherence between successive states remains within a bounded tolerance domain. Formally, stability can be expressed as: ∀i: Γ (xᵢ, x₈+₁) ∈ T where xᵢ represents successive system states, Γ (xᵢ, x₈+₁) measures the coherence between these states, and T denotes the tolerance domain within which coherence must remain for stability to persist. The paper develops a domain-independent conceptual framework linking stability with structural coherence under change. It further argues that several established stability concepts — including Lyapunov stability, attractor stability, biological homeostasis, engineering control stability, ecological resilience, and thermodynamic stability — can be interpreted as domain-specific instantiations of this structural condition. The work builds upon the broader theoretical framework introduced in *The Principle of Preserved Coherence Under Change* and connects stability to the emergence of identity as the observational recognition of preserved coherence across change.