D'Adderio–Iraci–Vanden Wyngaerd Theta conjecture at $t=0$ for the $(1,2)$-bosonic-fermionic coinvariant ring

Let $R_n^{(1,2)}$ be the $(1,2)$-bosonic-fermionic coinvariant ring, and let $\operatorname{Frob}(R_n^{(1,2)};q;u,v)$ denote its multigraded Frobenius series. The notation $\Theta_{e_k}$, $\Theta_{e_\ell}$, $\nabla$, and $e_m$ has the same symmetric-function meaning as in the Theta conjecture, and $|_{t=0}$ denotes specialization at $t=0$. Theta conjecture at $t=0$. For all $n \geq 1$,

$$\operatorname{Frob}(R_n^{(1,2)}; q;u,v) = \sum_{ k + \ell < n} u^k v^\ell\left(\Theta_{e_k}\Theta_{e_\ell}\nabla e_{n-k-\ell}\right)|_{t=0}.$$

This is the $t=0$ specialization of the preceding Theta conjecture and is used in the paper to derive evidence and formulas for the $(1,3)$-bosonic-fermionic coinvariant ring. Its resolution is not specified in the source.