Migliore, Miró-Roig and Nagel's weak Lefschetz conjecture for an odd-dimensional complete intersection

Let $K$ be a field of characteristic $0$, let $n\geq4$, and let $R=K[x_1,\dots,x_{2n+1}]$. Let $\ell\in R$ be a general linear form and set

$$I=\langle x_1^d,\dots,x_{2n+1}^d,\ell^d\rangle.$$

Migliore, Miró-Roig and Nagel's conjecture. The ring $R/I$ fails the Weak Lefschetz property if and only if $d>1$. Furthermore, if $n=3$, then $R/I$ fails the Weak Lefschetz property when $d=3$. The source presents this as an open conjecture arising from examples of failure of the Weak Lefschetz property.