Mirror-family conjecture for affine partial minimal models

Let $U\subset Y$ be a smooth affine partial minimal model with smooth boundary $E$, let $V$ be the mirror fibre, and let $\theta_E$ be the corresponding theta function. Let $F$ be a general fibre of $\theta_E$, let $A_V$ be the canonical mirror algebra, let $A_{C_Y}$ be the subalgebra associated to the relevant cone, and let $I_E$ be the ideal generated by the zero tropical locus of $\theta_E$. Mirror-family conjecture for affine partial minimal models. The general fibre $F$ of $\theta_E$ is log Calabi–Yau; $E$ is one fibre of the canonical mirror family for $F$; and $U\subset Y$ and $(Y,E)$ are fibres of

$$\operatorname{Spec}(A_V)\to\operatorname{Spec}(A_{C_Y})$$

and of the corresponding family over $Z(I_E)$.

The conjecture would extend the canonical mirror construction from affine log Calabi–Yau varieties to the general-fibre geometry arising from a partial minimal model. The supplied text gives no evidence of resolution.