Farber's diameter conjecture for higher associahedra

Let $k$ and $n$ be positive integers with $n=2k$. For a bipartite $(k,2k)$-plabic graph $G$, let $G^{\operatorname{op}}$ be the graph obtained from $G$ by a $180^\circ$ rotation followed by changing the colors of all vertices. The Farber diameter conjecture. The diameter of the higher associahedron $\Upsigma_{\mathcal{A},k-1}$ equals

$$\frac12 k(k-1)^2.$$

More generally, the minimal number of square moves needed to connect $G$ with $G^{\operatorname{op}}$ equals

$$\frac12 k(k-1)^2.$$

This conjecture concerns the maximal square-move distance between regular plabic graphs and extends the corresponding diameter question for the ordinary associahedron. Its status is not resolved in the supplied source.