Conjecture on rational points of terminal Fano varieties over $C_1$ fields

Let $k$ be a field of characteristic $0$ that is $C_1$, meaning that every hypersurface of degree at most $n$ in $\mathbb{P}^n_k$ has a $k$-rational point. Let $X$ be a terminal $\mathbb{Q}$-factorial Fano variety over $k$ with Picard rank $1$. Fano-point conjecture. The variety $X$ has a $k$-rational point. This conjecture is the reduction of the $C_1$-conjecture for rationally connected varieties over $C_1$ fields of characteristic $0$ obtained from the paper's birational-geometric results; its general status is not resolved in the source.