The real-rootedness conjecture for arbor Ehrhart polynomials

Let $t$ be an arbor and let $Q_t$ be its associated lattice polytope. Denote by $E_t(u)$ the Ehrhart polynomial of $Q_t$, which counts lattice points in the dilates $uQ_t$ for nonnegative integers $u$.

The real-rootedness conjecture for arbor Ehrhart polynomials. For any arbor $t$, all roots of $E_t(u)$ are negative real numbers in the interval $[-1,0]$, excluding $0$.

This is a proposed root-location property for the Ehrhart polynomials of the polytopes $Q_t$; the source gives no proof or resolution.