Birationally solid Fano 3-fold hypersurfaces

A Fano variety of Picard number $1$ is said to be $\mathit{\text{birationally}}\mathit{\text{solid}}$ if it is not birational to a Mori fiber space over a positive dimensional base. In this paper we complete the classification of quasi-smooth birationally solid Fano $3$-fold weighted hypersurfaces.