Real-part conjecture for unbalanced truncated affine arrangements

Let $R$ be an irreducible root system in $\mathbb{R}^n$, and let $a$ and $b$ be integers with $a+b\geq 2$. Define the truncated $R$-affine arrangement ${\cal A}^{ab}(R)$ by the hyperplanes

$$\langle \alpha,x\rangle=-a+1,-a+2,\dots,b-1,$$

where $\alpha$ ranges over the positive roots of $R$. In the unbalanced case $a\neq b$, write ${\cal A}={\cal A}^{ab}(R)$, let $h({\cal A})$ be its number of hyperplanes, and let $\chi_{\cal A}(q)$ be its characteristic polynomial. Real-part conjecture. All roots of $\chi_{\cal A}(q)$ have real part equal to $h({\cal A})/n$. This extends the root-location phenomenon established for the type $A_{n-1}$ arrangements to other irreducible root systems; the source reports considerable supporting evidence, while the general unbalanced case remains open.