Cox ring conjecture for universal torsors of log Calabi–Yau pairs

Let $U'\subset Y'$ be an snc minimal model of an affine log Calabi–Yau variety with maximal boundary, let $Y\to Y'$ be the universal torsor, and let $U\subset Y$ be its restriction. Let $V$ be a fibre of the canonical mirror to $U$, let $C_Y\subset\operatorname{Sk}(V)$ be the cone defined by the tropicalization of the sum of the boundary theta functions, and let

$$\operatorname{Cox}(Y')=\bigoplus_{L\in\operatorname{Pic}(Y')}H^0(Y',L).$$

For $L\in\operatorname{Pic}(Y')$, write $P_L=p^{-1}(L)$. Cox ring conjecture. $\operatorname{Spec}(\operatorname{Cox}(Y'))$ is one fibre of

$$\operatorname{Spec}(A_{C_Y})\to\operatorname{Spec}(R_V).$$

In particular, $C_Y$ parameterizes a canonical theta-function basis for $\operatorname{Cox}(Y')$, and the integer points $P_L(\mathbb Z)$ parameterize a canonical theta-function basis for $H^0(Y',L)$. This would recover canonical bases simultaneously for the Cox ring and each graded section space. The supplied text gives no evidence of resolution.