Fibration stability implies adiabatic K-semistability

Let $f:(X,H)\to(B,L)$ be a smooth polarized fibration. The fibration is fibration stable, and $(B,L)$ has a twisted constant scalar curvature Kähler metric with respect to the Weil–Petersson metric. The polarization on the total space is $\delta H+f^*L$. Fibration-stability conjecture. If $f$ is fibration stable and $(B,L)$ has such a twisted cscK metric, then $(X,H)$ is adiabatically K-semistable; equivalently, $(X,\delta H+f^*L)$ is K-semistable for sufficiently small $\delta>0$. This predicts that stability of the fibration together with the appropriate metric condition on the base yields adiabatic K-semistability of the total space; the source provides no resolution status.