Corollary: Continuous-time storage threshold

The generator

has propagator ${\mathcal{P}}_{e^{-\kappa t}}$. For $\kappa >0$, strict ideal separation survives exactly for

For $\kappa =0$, it survives at every finite delay.

Proof. The identity component is fixed and the traceless component decays as $e^{-\kappa t}$. Apply (eq:delaythreshold).