Soulé's zeta-function order-of-vanishing conjecture

Let $X$ be a scheme of finite type over $\mathbb{Z}$, let $d=\dim X$, and assume that higher Chow groups $CH^r(X,i)$ are defined for such schemes, have finite ranks, and satisfy $CH^r(X,i)\otimes\mathbb{Q}=0$ for $i\gg0$. Soulé's zeta-function order-of-vanishing conjecture.

$$-\operatorname{ord}_{s=d-r}\zeta_X(s)=\sum_i(-1)^i\operatorname{rk}(CH^r(X,i)).$$

This is Bloch's reformulation of Soulé's conjecture on the order of vanishing of the zeta function. The source gives the stated hypotheses but does not provide a resolution status.