We characterize integral bordisms of (nonlinear) PDEs by means of geometric Green kernels and prove that these are invariant for the classic limit of statistical sets of formally integrable PDEs. Such geometric characterization of green kernels is related to the geometric approach of canonical quantization of (nonlinear) PDEs, previously introduced by us [3,4,5,6]. Some applications are given where particle fields on curved space-times having physical or unphysical masses, (i.e., bradions, luxons and massive neutrinos) are canonically quantized respecting microscopic causality.