The $1$-parameter semigroup $\psi^{t}$ decreases the filtration on stalks of points which do not belong to $L_{1}\cap L_{2}$. More precisely,

$$\psi^{t}(\underline{Hom}_{p}^{alg}(E_{1},E_{2})^{s})\subset\underline{Hom}_{\psi^{t}(p)}^{alg}(E_{1},E_{2})^{s-\int_{0}^{t}\mu},$$

where $p\in P(L_{1},L_{2})$ is an arbitrary point.