4 problems

The Ehrhart–Zeta duality conjecture. For every linear arbor $t$,

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 $0$.

The arbor polytope h-vector realization conjecture. For every arbor $t$, there exists a simple polytope $\Phi_t$ such that

The h-vector reversal conjecture. For every linear arbor $t$, the $h$-vectors of $t$ and $\operatorname{Rev}(t)$ are equal.