Nonvanishing leading-term conjecture for the elliptic graph-complex classes

For $n\geq0$, let $t_{2n}$ be the loop-free graph with $2n+2$ vertices described in the source, and let $\delta_{2n}\in\mathfrak{r}^{\mathrm{non-fr}}_{(1)}$ be Enriquez's derivation. Under the stated isomorphism between the graph-complex cohomology and the non-framed Grothendieck–Teichmüller Lie algebra, the leading-term conjecture. The element $\delta_{2n}$ corresponds to a graph cohomology class every representative of which has a nonzero coefficient of $t_{2n}$. The source constructs closed nonexact classes with these tree parts and proposes this correspondence; no resolution is stated.