The symmetric theta conjecture for decorated trees

Let $\beta$ be a weak composition, let $\mathsf{RTT}_0(\beta)=\bigcup_{\alpha\vDash_0\lvert\beta\rvert}\mathsf{RTT}_0(\alpha,\beta)$, and let $\operatorname{oldXi}$ be the symmetric-function operator defined in the paper. Write $\mathsf{inv}(T)$ and $\alpha(T)$ for the inversion statistic and associated composition of $T$. The symmetric theta conjecture.

$$\left.\operatorname{oldXi}e_\beta\right\rvert_{t=1}=\sum_{T\in\mathsf{RTT}_0(\beta)}q^{\mathsf{inv}(T)}x^{\alpha(T)}.$$

This is the $q$-enumerative tree formula conjectured in the cited work and is presented here as a conjecture; the supplied text gives no resolution status.