Koszulity parity conjecture for totally associative n-ary operads

Let ${t\mathcal{A}ss}^n_d$ be the operad for degree-$d$ totally associative $n$-algebras. The Koszul property is considered for arbitrary arity $n$ and degree $d$. Koszulity parity conjecture. The operad ${t\mathcal{A}ss}^n_d$ is Koszul if and only if $d$ is even. The claim is motivated by the observation that Koszulity depends only on the parity of $d$; its general validity is not established in the source.