A General Binding Threshold

Across physical, biological, and cognitive systems, many configurations dissolve unless actively restored. Certain configurations, however, persist by maintaining their own structure despite ongoing disruption. This paper proposes a general threshold condition for persistence, expressed as: τ_self⁻¹ ≥ κ Γ_disruption Here, τ_self⁻¹ represents the rate of internal restoration, Γ_disruption represents the rate of environmentally driven disruption, and κ is a boundary-dependent geometric coefficient. When restoration exceeds disruption under this relational condition, a system begins to draw its next configuration primarily from its own prior state. This marks the onset of a self-stabilizing interior. The threshold formulation is illustrated across lipid vesicles, morphogenetic repair, phoneme attractors, and recurrent neural circuits. These examples differ in material, mechanism, and scale, yet each demonstrates how self-preserving identity can emerge when internal restorative dynamics outrun disruption. This motivates the view that persistence and identity formation can be structurally modeled through a shared restoration–disruption threshold across domains.