Generalized Impedance Kernels in Finite-Capacity Reservoirs: A Hysteresis Flow Framework

CORRIGENDUM -- Note regarding Version 1: Previous iterations of this framework proposed a linear friction constraint. Subsequent dimensional analysis has confirmed that this linear scalar approximation is physically incoherent regarding unit homogeneity and leads to singularity artifacts (negative capacity) in high-density boundary layers. This paper resents the corrected Generalized Impedance Kernel framework. We demonstrate that flow retardation is not a linear scalar function, but an integral of the topological interference density. Simulations confirm that the linear approximation (V1) induces destabilizing oscillations, whereas the Kernel-based approach guarantees asymptotic stability.