Gross–Manturov–Tucker's interpolating partial-duality polynomial conjecture

Let $G$ be a ribbon graph, and let $~^{\partial}{\mathscr{E}}^{*}_{G}(z)$ denote its partial-$*$ polynomial. A polynomial is odd or even when all terms with nonzero coefficients have, respectively, odd or even degree, and it is interpolating when its support is an integer interval of consecutive integers. Gross–Manturov–Tucker's conjecture. If the partial-$*$ polynomial $~^{\partial}{\mathscr{E}}^{*}_{G}(z)$ is neither an odd nor an even polynomial, then it is interpolating. This conjecture concerns the coefficient-support behavior of partial-duality polynomials; the supplied text gives no resolution, so its status remains open.