Ziegler's generic restriction conjecture for logarithmic forms

Let ${\mathcal{A}}'$ be an essential and free arrangement in $V={\mathbb{K}}^\ell$ with $\ell\geq 4$. Let $X$ be a generic subspace with $\dim X>2$, and define the restriction

$${\mathcal{A}}'\cap X:=\{H\cap X\mid H\in{\mathcal{A}}'\setminus{\mathcal{A}}'_X\}.$$

Here, $X$ is generic if it is $(\ell-\operatorname{codim}X)$-generic with respect to ${\mathcal{A}}'$, meaning that

$$\operatorname{codim}_V(X\cap Y)=\operatorname{codim}X+\operatorname{codim}Y$$

for every relevant intersection subspace $Y$ of ${\mathcal{A}}'$. Write $\Omega^1({\mathcal{A}}')$ for the module of logarithmic $1$-forms and $\operatorname{res}_H$ for the restriction map. Ziegler's generic restriction conjecture. The map

$$\operatorname{res}_H\colon\Omega^1({\mathcal{A}}')\longrightarrow\Omega^1({\mathcal{A}}'\cap X)$$

is surjective, and the minimal numbers of generators of $\Omega^1({\mathcal{A}}')$ and $\Omega^1({\mathcal{A}}'\cap X)$ are equal. This conjecture concerns how logarithmic forms behave under generic cuts of free arrangements; Ziegler stated that it would imply that such a generic cut is never free. Its resolution is not supplied in the source.