Dimension-preserving leak-removal conjecture for output connectable compartmental models

Let $\mathcal{M}=(G,In,Out,V)$ represent a linear compartmental model. Assume that $G$ is output connectable and $|Out|=1$. Assume the dimension of the image of the coefficient map is $k$. Let $\widetilde{\mathcal{M}}=(G,In,Out,L)$ be the corresponding model, where $In \cup Out \subseteq L$. Dimension-preserving leak-removal conjecture. The dimension of the image of the coefficient map of $\widetilde{\mathcal{M}}$ is also $k$. In other words, this property of being dimension-preserving is conjectured to apply to all output connectable models; the paper proves it in a special case.