Gray-operad conjecture for semistrict n-categories

Let $G_n$ be an $n$-operad, and let \text{\cal P}_k(G_n) denote its $k$-th slice. A semistrict $n$-category is a category presented as an algebra for an operad.

Gray-operad conjecture. There is a unique contractible $n$-operad $G_n$ such that, for every $k$ with $0\leq k\leq n-1$, \text{\cal P}_k(G_n) is the free $k$-fold monoid operad. A semistrict $n$-category is an algebra for this operad.

The claim is motivated by the identification of strict $2$-categories with the proposed semistrict notion in dimension $2$ and Gray-categories in dimension $3$. The text describes the statement as a conjecture and gives no resolution.