Singular ramified irregular vertex operator conjecture

Let $p,q$ be positive integers, let

$$c=13-6\left(t+\frac{1}{t}\right),\qquad \Delta_{p,q}=\frac{(pt-q)^2-(t-1)^2}{4t},$$

and let $\chi_{p,q}$ be the singular vector of level $pq$ in $M_{\Delta_{p,q}}$. A ramified irregular vertex operator is called singular when it annihilates this vector. Singular ramified vertex-operator conjecture. For every positive integers $p,q$, a singular ramified irregular vertex operator $\Phi^{\Delta_{p,q}}_{\Lambda,\Lambda}(\alpha,\beta,c_{\emptyset};z)$ exists; its parameters $\alpha$, $\beta_1,\ldots,\beta_{2r-1}$ and $c_{\emptyset}^{(m)}$ are polynomials in $c$, $\Lambda_r,\ldots,\Lambda_{2r-1}$ and $\Lambda_{2r-1}^{-1}$, and there are $pq$ such parameter sets counted with multiplicity. The source does not report a proof or disproof.