Gap-length conjecture for minimal models of partially associative n-ary operads

Let ${p\mathcal{A}ss}^n_d$ be the operad for degree-$d$ partially associative $n$-ary algebras, in the non-Koszul parity case $n \not\equiv d \pmod{2}$. A gap in a minimal model means a consecutive range of arities in which no generators occur. Gap-length conjecture. The minimal model of ${p\mathcal{A}ss}^n_d$ has a gap of length $n-1$. Computations for small values of $n$ suggest that the gap grows linearly with $n$, but the source reports computational limitations and does not prove the general assertion.