Valuations detecting rational connectedness over tame valued fields

Let $K$ be a tame valued field with divisible value group and residue field $k$. Let $V$ be a separably rationally connected variety over $K$, and set $F=K(V)$. Valuation conjecture. There exists a valuation on $F$ whose residue field $k_F$ is the function field of a separably rationally connected variety over $k$. This conjecture would provide residue-field information for separably rationally connected varieties over tame valued fields and is used in the paper to motivate consequences for rational points over certain valued fields. Its status is not resolved in the provided text.