Positivity conjecture for tropical slab functions

Let $X$ satisfy the generic condition assumed in the construction. For a primitive relative class $\gamma$, let $l_{\gamma}$ be an affine line labeled by $\gamma$, let $u\in l_{\gamma}\setminus\bigcup_{d\in\mathbb{N}}W'_{d\gamma}$, and let $f_{\gamma}(u)$ be the power series obtained as the inverse limit of the wall-crossing functions. Positivity conjecture. The coefficients of $f_{\gamma}(u)$ are always positive. This conjecture is motivated by the Gross–Siebert program; the supplied text gives no resolution status.