The pretzel-knot surgery left-orderability conjecture

Let $s\ge 3$ be an integer, and let $M_{p/q}$ be the manifold obtained by Dehn surgery with slope $\frac{p}{q}$ along the $(-2,3,2s+1)$-pretzel knot. Pretzel-knot surgery conjecture. The fundamental group of $M_{p/q}$ is left-orderable if and only if

$$\frac{p}{q}<2s+3.$$

The paper proves non-left-orderability for slopes $\frac{p}{q}\ge 2s+3$ and left-orderability in a neighborhood of zero, so the conjecture remains open for the intervening slopes.