The mirror conjecture for projective bundles

Let $X$ be a smooth projective variety and let $V=\bigoplus_{i=0}^n L_i$ be a direct sum of line bundles, where $L_i$, $i=1,\ldots,n$, are nef and $-K_X-c_1(V)$ is ample. Let $J_{\mathbb P(V)}$ be the generating function of the quantum $\mathcal D$-module of $\mathbb P(V)$, and let $I_{\mathbb P(V)}$ be the twisted hypergeometric series defined using the twisting factors from the preceding construction. The mirror conjecture for projective bundles. Under these hypotheses,

$$J_{\mathbb P(V)}=I_{\mathbb P(V)}.$$

This identifies the quantum $\mathcal D$-module generator of the projective bundle with the explicitly constructed twisted hypergeometric series. The statement is presented as a proposal in the paper; no resolution is supplied in the given text.