Identifiability conjecture for Fin and Wing submodels of cycle graphs

For $n\geq 3$, let $G$ be a graph obtained from the $n$-compartment cycle graph by adding one or more incoming edges or one or more outgoing edges. Let $In=Out=\{1\}$ and $Leak=\emptyset$.

Fin-and-Wing submodel conjecture. The linear compartmental model $(G,In,Out,Leak)$ is generically locally identifiable.

The coefficient maps for these submodels are complicated, so the paper does not analyze their Jacobians completely. It proves identifiability for certain families of added edges and conjectures the broader statement for models with more than one or two incoming or outgoing edges.