Ziegler's critical-arrangement restriction conjecture

Let ${\mathcal{A}}$ be a hyperplane arrangement, and for an integer $k$ call it $k$-critical when

$$\Omega^1({\mathcal{A}})_{-k}\neq0$$

and

$$\Omega^1({\mathcal{A}}\setminus\{H\})_{-k}=0$$

for every $H\in{\mathcal{A}}$. Here $|{\mathcal{A}}|$ denotes the number of hyperplanes and ${\mathcal{A}}^H$ the restriction to $H$. Ziegler's critical-arrangement restriction conjecture. If ${\mathcal{A}}$ is $k$-critical, then there exists some $H\in{\mathcal{A}}$ such that

$$|{\mathcal{A}}|-|{\mathcal{A}}^H|=k.$$

The claim is motivated by the inequality $|{\mathcal{A}}|-|{\mathcal{A}}^H|\geq k$ for every $H$ when ${\mathcal{A}}$ is $k$-critical. The source does not state a resolution.