Unidentifiability conjecture for the mammillary model with input 2 and output 3

Let $n\geq 5$. Let $\mathcal M=(G,\textit{In},\textit{Out},\textit{Leak})$ be an $n$-compartment mammillary model with $\textit{In}=\{2\}$, $\textit{Out}=\{3\}$, and $\textit{Leak}=\varnothing$. A parameter is unidentifiable if it cannot be recovered from the coefficient map. Unidentifiability conjecture. The parameters

$$k_{12},\quad k_{21},\quad k_{13},\quad k_{31},\quad k_{41},\dots,k_{n1}$$

are unidentifiable. This conjecture completes the identifiability classification suggested by Proposition 2.3; the parameters $k_{14},\dots,k_{1n}$ are generically locally identifiable, while the stated unidentifiability of the remaining parameters is not established here.