The Gamma Conjecture for local mirror symmetry

Let $X$ be the noncompact toric variety considered in the paper, with K-groups $K(X)$ and $K^c(X)$ paired by

$$\langle F,S\rangle=\int_X\operatorname{ch}(S)\operatorname{ch}(F)\operatorname{Todd}_X.$$

Choose bases $\{F_1,\ldots,F_d\}$ of $K(X)$ and $\{S_1,\ldots,S_d\}$ of $K^c(X)$ satisfying $\langle F_i,S_j\rangle=\delta_{ij}$. Let $w$ be the cohomology-valued hypergeometric series defined in the paper, let $\operatorname{ch}(F_k)$ be the corresponding basis of $H_c^{\mathrm{even}}(X)$, and let $mir(S_k)$ denote the mirror of $S_k$ under homological mirror symmetry. The Gamma Conjecture for local mirror symmetry. The expansion of $w$ satisfies

$$w\left(t_1,\ldots,t_{p-n},\frac{[\widetilde D_{n+1}]}{2\pi\sqrt{-1}},\ldots,\frac{[\widetilde D_p]}{2\pi\sqrt{-1}}\right)=\left(\frac{1}{2\pi\sqrt{-1}}\right)^{n+1}\sum_{k=1}^d\left(\left(\int_{mir(S_k)}\Omega_{Y^t}\right)\operatorname{ch}(F_k)\right),$$

where $\Omega_{Y^t}$ is the holomorphic form on the mirror. Equivalently, for every mirror pair $(E,mir(E))$, the central charges match:

$$Z_t(E)=C_t(mir(E)).$$

This is the local-mirror-symmetry form of the Gamma conjecture: the hypergeometric-series expression for the central charge on the coherent-sheaf side should agree with the oscillatory period on the mirror side. The supplied text does not state whether this conjecture has been resolved.