Rotation invariance conjecture for Newton–Okounkov bodies of plabic graphs

Let $G$ be a plabic graph, and let $rG$ denote any rotation of $G$. Its associated Newton–Okounkov body is denoted by $\Delta_G$. Rotation invariance conjecture. All rotations of a plabic graph give the same Newton–Okounkov body up to unimodular equivalence. This conjecture contrasts with the possibility that reflections can produce Newton–Okounkov bodies that are not unimodular equivalent to the original one. The source does not provide evidence resolving the conjecture.