The universal Psi constraint for Hodge integrals with lambda insertions

Let $X$ be a smooth projective variety, and let $\Psi_{g,n}$ denote the universal expression for Hodge integrals with one $\lambda_{g-1}$ or $\lambda_g$ insertion defined in the source. Universal Psi constraint. For every smooth projective variety $X$,

$$\Psi_{g,n}\equiv 0$$

for all $g\geq 0$ and $n\geq -1$. This conjectural constraint is motivated by the Virasoro conjecture for Gromov–Witten invariants and is proposed as a universal relation; its resolution is not stated in the source.