The Seidel-element and Jacobian-generator conjecture for compact toric manifolds

Let $X$ be a compact toric manifold, not necessarily semi-Fano. Let $QH^*(X,\omega_q)$ denote its small quantum cohomology, let $W_q^{\mathrm{LF}}$ be the Landau–Ginzburg potential, and let $S^{\circ}_l$ be the normalized Seidel elements. The monomials $Z_l$ are the generators associated with the toric divisors in the Jacobian ring $\operatorname{Jac}(W_q^{\mathrm{LF}})$.

Seidel-element and Jacobian-generator conjecture. The isomorphism

$$QH^*(X,\omega_q)\overset{\simeq}{\longrightarrow}\operatorname{Jac}(W_q^{\mathrm{LF}})$$

maps each normalized Seidel element $S^{\circ}_l$ to the corresponding generator $Z_l$.

This extends the theorem established in the semi-Fano case to arbitrary compact toric manifolds. In the non-semi-Fano case, the potential is generally a Laurent series over the Novikov ring rather than a Laurent polynomial, but the monomials $Z_l$ are still defined. The source gives no resolution of the conjecture.