Master relation for the classes $\Xi^m_{g,n}$

For $g\geq0$ and $m,n\geq1$ with $2g-2+n+m>0$, let $\Xi^m_{g,n}$ be the Laurent polynomial in $u$ with coefficients in the tautological ring of $\overline{\mathcal{M}}_{g,n+m}$ obtained by summing the classes $\Xi(T)$ over the relevant pre-stable rooted trees, and write $(\Xi^m_{g,n})_d$ for its coefficient in tautological degree $d$. Master relation. One has

$$\Xi^m_{g,n}\in R^*(\overline{\mathcal{M}}_{g,n+m})\otimes_{\mathbb{Q}}\mathbb{Q}[u].$$

Equivalently, for every $d\geq2g-1+m$,

$$(\Xi^m_{g,n})_d=0.$$

This is the asserted vanishing relation for the tree-sum class; the source supplies no resolution evidence, so its status remains open.