Structural Necessity of Boundary-Mediated Gradient Scaling

Abstract We establish a conditional structural theorem governing persistent localized growth under sustained exterior gradients. Rather than deriving scaling within a specific transport equation, we identify boundary mediation and persistence as structural constraints that reduce asymptotic exponent freedom independently of microscopic dynamics. We prove that, under explicitly stated assumptions, persistent boundary-mediated systems admit a dominant asymptotic boundary dimension and necessarily obey dMdt = C M^ (df +) /d, C>0, where df denotes the asymptotic boundary dimension and the transport scaling exponent. The result identifies a mechanism-defined universality structure within the restricted class of persistent, localized, gradient-driven systems. The theorem is conditional, falsifiable, and does not assert universal growth across arbitrary systems