Hamiltonian invariance conjecture for Plücker-torus potentials

Let $d4c$ be a Plücker sequence of type $(k,n)$, and let $L_\mathfrak{s}\subset\operatorname{Gr}(k,n)$ be its associated Plücker torus. The Laurent polynomial $W_\mathfrak{s}$ is defined on the algebraic torus $H_1(L_\mathfrak{s};\mathbb{Z})\otimes\mathbb{C}^\times$. Hamiltonian invariance conjecture. The Laurent polynomial $W_\mathfrak{s}$ is an invariant of the Hamiltonian isotopy class of the Lagrangian torus $L_\mathfrak{s}$. This asserts that the potential depends only on the Hamiltonian isotopy class, rather than on the chosen Plücker sequence or auxiliary construction.