The bridge-graph quantum max-flow conjecture below the cut threshold

Let $w$ be a positive integer and let $(a,b)$ and $(a',b')$ lie in $\mathbf{U}_w\cup\mathbf{V}_w\cup\mathbf{W}_w$, with $ab'\leq a'b$. Consider the corresponding bridge graph with bond dimension $w$. Bridge-graph threshold conjecture. Its quantum max-flow equals its quantum min-cut and is $ab'$:

$$\operatorname{QMaxFlow}=\operatorname{QMinCut}=ab'.$$

This is the conjectural case singled out among the regions not covered by the paper's proved results. The inequality selects the smaller of the two evident cut values, and the claim is presented as open.