Aganagic--Vafa and Aganagic--Klemm--Vafa mirror conjecture for disk amplitudes

Let $W_H$ be the B-model prepotential obtained by integrating $\log y/q_0$ with respect to $q_0$, and write

$$W_H=f(q_1,\ldots,q_k)\log q_0+W_{H,\mathrm{inst}}(x,q_1,\ldots,q_k),$$

where $W_{H,\mathrm{inst}}$ is the instanton part. Let $W^{\mathcal{X},(\mathcal{L},f)}(x,q_1,\ldots,q_k)$ be the pullback, under the open--closed mirror map, of the disk potential $F_{0,1}^{\mathcal{X},(\mathcal{L},f)}(Q,X)$, assembled from its sectors with the character factors specified in the source. Aganagic--Vafa--Aganagic--Klemm--Vafa mirror conjecture. One has

$$W^{\mathcal{X},(\mathcal{L},f)}(x,q_1,\ldots,q_k)=W_{H,\mathrm{inst}}(x,q_1,\ldots,q_k).$$

The conjecture identifies the open A-model disk potential with the instanton part of the B-model superpotential after the open--closed mirror transformation. The supplied context gives no evidence that it has been resolved.