Structural Origins of Exponential Persistence II (SOEP)

Structural Origins of Exponential Persistence II (SOEP) establishes the spectral mechanism underlying persistence dynamics in open metastable systems. Building on the structural axioms introduced in SOEP I, the work proves that persistence observables evolve on a finite-dimensional slow spectral manifold generated by isolated eigenmodes of the effective Dirichlet generator. Under metastable separation of timescales, a finite cluster of slow eigenvalues governs survival probabilities, quasi-stationary behavior, and escape rates, yielding spectral dimensional reduction of persistence dynamics. These results provide the mathematical bridge between structural inevitability and analytic persistence asymptotics, forming the spectral foundation of the SOEP universality program. Related resourcesAdditional preprints, theoretical frameworks, and ongoing work by the author are available at:https://murad-ahmadov.github.io/