Graph-space well-posedness for diffusion equations with degenerate instantaneous diffusion

What the math gives to ML

The paper provides a constructive way to represent completely monotone memory as a continuum of exponentially decaying internal states, together with an energy pairing in which the physical-to-memory and memory-to-physical couplings cancel exactly. The important transferable asset is a contraction and dissipativity guarantee that does not require the instantaneous operator to be coercive, so recurrent dynamics remain stable even when direct state damping is absent. This suggests a structure-preserving state-space neural layer whose decay rates and coupling matrices can be learned while retaining a certificate based on a nonnegative memory measure and adjoint coupling.