\widetilde{\zeta}^* T_{{\overline{{\mathcal}M}_{0,r}({X,e})}} @>>> \widetilde{\zeta}_\Pi^* T_{{\overline{{\mathcal}M}_{0,r}({X,e})}} @>>> 0 \end{CD}$$ In the corresponding long exact sequence of cohomology, $H^0$ of the first and third terms vanishes. Therefore 