Dervan–Sektnan's automorphism-free fiber conjecture

Let $f:(X,H)\to(B,L)$ be a polarized smooth fibration such that every fiber $(X_b,H_b)$ is K-stable. Assume that $\operatorname{Aut}(X_b,H_b)=0$ for every $b\in B$. Dervan–Sektnan's automorphism-free fiber conjecture. Then $f$ is fibration stable in the original sense. This is a more specific proposed criterion for original fibration stability, adding the absence of polarized automorphisms on every fiber; the source provides no resolution status.