Koszulity parity conjecture for partially associative n-ary operads

Let ${p\mathcal{A}ss}^n_d$ be the operad for degree-$d$ partially associative $n$-ary algebras. The Koszul duality isomorphisms identify ${p\mathcal{A}ss}^n_d$ with the Koszul dual counterpart of ${t\mathcal{A}ss}^n_{-d+n-2}$, so Koszulity is expected to depend on the parity of $n-d$. Koszulity parity conjecture. The operad ${p\mathcal{A}ss}^n_d$ is Koszul if and only if $n \equiv d \pmod{2}$. This is presented as an equivalent reformulation of the preceding conjecture; the source does not establish it in general.