Structural Origins of Exponential Persistence IV (SOEP)

Structural Origins of Exponential Persistence IV (SOEP) establishes the universality structure of persistence scaling under coarse-graining and renormalization. Building on the structural inevitability (SOEP I), spectral dimensional reduction (SOEP II), and analytic asymptotics (SOEP III), this work introduces a persistence renormalization operator acting on survival distributions and proves that exponential persistence forms a stable fixed point under broad structural perturbations. Local contraction, entropy decay, and homogenization mechanisms are analyzed to characterize the basin of attraction of the exponential class. Alternative universality classes—including power-law and stretched exponential persistence—are identified through structural phase boundaries determined by noise tails and memory effects. The results establish persistence universality as a structural phenomenon in open dynamical systems. Related resourcesAdditional preprints, theoretical frameworks, and ongoing work by the author are available at:https://murad-ahmadov.github.io/