Symmetry conjecture for tropical theta pairings

Let $U$ and $V$ be affine log Calabi–Yau varieties with maximal boundary, and let $\operatorname{Sk}(U)$ and $\operatorname{Sk}(V)$ be their skeleta. For $u\in\operatorname{Sk}(U)$ and $v\in\operatorname{Sk}(V)$, consider the two tropical theta pairings $\theta_v^{\mathrm{trop}}(u)$ and $\theta_u^{\mathrm{trop}}(v)$. Symmetry conjecture. The two pairings are equal:

$$\theta_v^{\mathrm{trop}}(u)=\theta_u^{\mathrm{trop}}(v).$$

This conjecture asserts compatibility between the two mirror constructions and is used in the source to identify which theta functions are regular on a partial minimal model. The supplied text gives no evidence of resolution.