Proposition: Bounded addition to an admitted baseline

Under Assumption ass:baseline, adding $\lambda {\mathcal{G}}_{r_{\mathrm{c}}}$ gives a unique strongly continuous CPTP bounded-perturbation propagator.

Proof. Interleave the baseline propagator with Poisson-distributed jumps of rate $\lambda q_{r_{\mathrm{c}}}$, applying $\mathcal{J}$ at each jump. The sum over ordered jump times converges in trace norm, with factorial bounds, and is CPTP. It solves the bounded variation-of-constants equation. Picard iteration with bound $2\lambda q_{r_{\mathrm{c}}}$ proves uniqueness.