The Saturation Field: Universal Threshold Dynamics in Driven Dissipative Systems A Stochastic Rupture Framework Extension

We propose that a broad class of natural and social phenomena — spanning quantum physics, astrophysics, atmospheric science, biology, materials science, and human behaviour — shares a common dynamical topology described by the saturation field equation ∂tχ = S − Γχ − αχ2 , where χ = local state/maximum system capacity is a dimensionless saturation field, S is external forcing, Γ is linear dissipation, and α captures nonlinear self-saturation. We identify fifteen instances across eight domains, classify them into three dynamical routes to threshold (forced, self-organised critical, and spatial), and show that near any threshold the universal critical scaling Ψ ∼ (ε) β holds with β = 1/2, where ε measures distance from threshold. The Stochastic Rupture (SR) framework 1 provides the physically anchored instance in which the parameters are derived from first principles via the Bekenstein information bound; all other instances presented here represent empirical realisations of the same topological structure. We articulate falsifiable predictions and delineate clearly what the framework explains and what it does not