Kára and Král's exact minimum degree for 31-vertex cycle chords

For integers $n$ and $c$, let $f(n,c)$ be the least integer $d$ such that every $n$-vertex graph with minimum degree at least $d$ contains a cycle with at least $c$ chords. Kára and Král's conjecture.

$$f(31,31)=8.$$

Their known bounds are $8\leq f(31,31)\leq9$, so the conjecture asks whether the lower bound is sharp. The supplied text gives no resolution evidence.