Structural dichotomy and mass criticality in indirect chemotaxis cascades: fourth-order ellipticity versus Volterra memorytranslating…

arXiv:2605.30438v1 Announce Type: new Abstract: We investigate the structural and operator-theoretic foundations of indirect signal-generation mechanisms in Keller--Segel-type chemotaxis models. By analyzing a physically motivated multi-stage signaling cascade, we establish a precise mathematical dichotomy between instantaneous equilibration and transient kinetic memory. Specifically, we prove that the fully equilibrating parabolic--elliptic--elliptic (PES) cascade reduces to a static fourth-or