Annulus Liouville CFT boundary three-point bootstrap conjecture

Let $Q$, $\beta$, $\mu$, $\mu_\partial$, $P$, $q$, $G$, $U_{\rm FZZ}$, $\eta$, and $H$ be the quantities in the annulus Liouville CFT bootstrap formula. For $\mu\;\geqslant\; 0$, $\mu_\partial>0$, and $\beta\in(0,Q)$, the boundary three-point constant $H^{\mu_\partial,\mu_\partial,\mu_\partial}_{Q+iP,\beta,Q-iP}$ is related to the bulk-boundary expression by an absolute constant $C$ through

$$\int_{\mathbb{R}^{+}}G(Q+iP,\beta)U_{\rm FZZ}(Q-iP)\frac{q^{\frac{P^2}{2}}}{\eta(q^2)}\,dP =C\int_{\mathbb{R}^{+}}H^{\mu_\partial,\mu_\partial,\mu_\partial}_{Q+iP,\beta,Q-iP}\frac{q^{\frac{P^2}{2}}}{\eta(q^2)}\,dP.$$

This is a proposed annulus conformal bootstrap identity in Liouville CFT; the source gives no evidence that it has been proved or refuted.