Cha's simplicial-polytope conjecture for arbor h-polynomials

Let $E$ be an $n$-element set and let $\tau$ be an arbor on $E$. Its $h$-polynomial is $h(\tau,t)=\sum_{i=0}^n h_i(\tau)t^i$, where $h_i(\tau)$ counts the lattice points of the arbor polytope $\mathcal Q_\tau$ having $i$ nonzero coordinates. Cha's simplicial-polytope conjecture. The polynomial $h(\tau,t)$ is equal to the $h$-polynomial of an $n$-dimensional simplicial polytope for every arbor $\tau$ on $E$. In particular, $h(\tau,t)$ is palindromic and unimodal. This is attributed to Cha (2025); its resolution is not specified in the source.