The non-square grid conjecture on the weak Lefschetz property

Let $X$ be an $a\times b$ grid, with $b>a\ge 2$. For any integer $d\ge a$, set $I=\Lambda_{X,d}$ and $A=R/I$.

Non-square grid conjecture. The Artinian algebra $A$ fails to have the weak Lefschetz property.

This conjecture asks whether every remaining non-square grid case fails the weak Lefschetz property. The supplied text gives no resolution, so the conjecture remains open.