Open Virasoro conjecture for the full open partition function

Let $F^c$ and $F^o$ be the closed and open descendent generating series, and define the full partition function by

$$\mathsf{Z}=\exp(F^c+F^o).$$

Let $L_n$ be the differential operators in $u$ and the variables $t_i$, and define, for $n\geq -1$,

$$\mathcal{L}_n=L_n+u^n s\frac{\partial^{n+1}}{\partial s^{n+1}}+\frac{3n+3}{4}u^n\frac{\partial^n}{\partial s^n}.$$

Open Virasoro conjecture. The operators $\mathcal{L}_n$ annihilate the full partition function:

$$\forall n\geq -1,\qquad \mathcal{L}_n\mathsf{Z}=0.$$

These constraints extend the closed Virasoro constraints to the open theory and are intended to determine the open descendent invariants. The supplied text gives no resolution evidence.