t=0 specialization of the Theta conjecture

Establish that, for every integer n≥1, the multigraded Frobenius series of the one-boson, two-fermion coinvariant ring R_n^{(1,2)} satisfies \[\Frob(R_n^{(1,2)};q;u,v)=\sum_{k+\ell<n}u^kv^\ell\left(\Theta_{e_k}\Theta_{e_\ell}\nabla e_{n-k-\ell}\right)\big|_{t=0}.\]

Background

This is the t=0 specialization of the preceding Theta conjecture. It gives a proposed formula for the q,u,v-graded Frobenius series of R_n^{(1,2)}.

The paper cites a conditional theorem stating that, if this specialization is true, then all hook-character multiplicities of R_n^{(1,2)} have an explicit q-binomial formula. The specialization remains an assumption in the paper and is not established there.