The factorial specialization conjecture for Grassmannian quantum series

Let $G(k,n)$ be the Grassmannian, let $P(k,n)$ be its Gorenstein toric degeneration, and let $A_{G(k,n)}(q)$ denote the special solution to the quantum ${\cal D}$-module determined by the small quantum cohomology of $G(k,n)$. Let $A_{P(k,n)}(q,\tilde{q})$ be the associated $GKZ$-hypergeometric series. Factorial specialization conjecture. In the case of Grassmannians, $A_{G(k,n)}(q)$ can be obtained by the natural specialization of the toric series at $\tilde{q}={\bf 1}$, namely

$$A_{G(k,n)}(q)=A_{P(k,n)}(q,{\bf 1}).$$

This identifies the Grassmannian quantum solution with a specialization of the hypergeometric series for its Gorenstein toric degeneration and would provide the computational input for the factorial method of obtaining instanton numbers of Calabi–Yau complete intersections. The source gives no resolution of the conjecture.