Mirror conjecture for the extended GLSM in the positive phase

Consider the extended GLSM in the positive phase $\zeta>0$, with GLSM $I$-function $I^+_w(q,z)$ and GLSM small $J$-function $J^+_w(Q,z)$. Let $I^{\mathrm{CY}}_0(q,z)$ and $I^{\mathrm{CY}}_1(q)$ be the corresponding quintic Calabi–Yau periods. Positive-phase extended GLSM mirror conjecture. Under the mirror map

$$\log Q=\frac{I^{\mathrm{CY}}_1(q)}{I^{\mathrm{CY}}_0(q)},$$

one has

$$J^+_w(Q,z)=\frac{I^+_w(q,z)}{I^{\mathrm{CY}}_0(q,z)}.$$

This is the positive-phase mirror statement for the extended GLSM; the relevant GLSM small $J$-function was yet to be defined in the source, and no resolution is given.