Postnikov–Stanley conjecture on the roots of truncated affine Weyl arrangement polynomials

Let $\Phi$ be an irreducible root system with Coxeter number $h$, and let $V$ be its ambient vector space. For integers $a\leq b$, define the truncated affine Weyl arrangement

$$\mathcal{A}_{\Phi}^{[a,b]}=\{H_{\alpha,k}\mid \alpha\in\Phi^+,\ k\in\mathbb{Z},\ a\leq k\leq b\},$$

where $H_{\alpha,k}=\{x\in V\mid (\alpha,x)=k\}$, and write $\chi(\mathcal{A}_{\Phi}^{[a,b]},t)$ for its characteristic polynomial. Postnikov–Stanley conjecture. If $a,b\in\mathbb{Z}$ satisfy $a\leq 1\leq b$ and $1\leq a+b$, then every root $z\in\mathbb{C}$ of

$$\chi(\mathcal{A}_{\Phi}^{[a,b]},t)=0$$

has real part

$$\operatorname{Re}z=\frac{(b-a+1)h}{2}.$$

This extends the Linial-arrangement case $[a,b]=[1,n]$, asserting that the characteristic polynomial has all its roots on a common vertical line in the complex plane. The supplied text states the conjecture but gives no information about whether it has been resolved.