Scaling reparametrization conjecture for identifiable path/cycle models

Let $\mathcal{M}=(G,In,Out,V)$ be a linear compartmental model. Suppose either that $G$ is strongly input-output connected and $|Out|=1$, or that $G$ is strongly connected and $|In|=1$. Scaling reparametrization conjecture. An identifiable scaling reparametrization exists if and only if $\mathcal{M}=(G,In,Out,V)$ is an identifiable path/cycle model. This conjecture aims to generalize necessary and sufficient conditions previously obtained for identifiable scaling reparametrizations in a special single-input/single-output setting; its resolution is left as future work.