Quantum maxflow/mincut conjecture for tensor-network maps

Let $N$ be a $v$-valent graph with $k$ input cut edges and $l$ output cut edges, with the incoming edges at each vertex locally ordered. For a $v$-index tensor $W$ on a vector space $V$, let $\theta_{N,W}:V^{\otimes k}\to V^{\otimes l}$ be the linear map obtained by placing a copy of $W$ at every vertex according to the local edge ordering and contracting along internal edges. Quantum maxflow/mincut conjecture. The map $\theta_{N,W}$ is injective for generic $W$ if and only if $N$ admits $k$ edge-disjoint paths from the input to the output. Moreover, its image is generic with respect to any fixed basis of $V$: if $h\leq l-k$ basis vectors $\vec b$ are inserted into $h$ output slots not lying on the $k$ edge-disjoint paths, then the resulting map $\theta_{N,W,\vec b}:V^{\otimes k}\to V^{\otimes(l-h)}$ is also injective for generic $W$. This proposed quantum analogue of maxflow/mincut concerns injectivity and genericity of tensor-network maps; the supplied context gives no evidence that it has been resolved.