The braid-index–bridge-index conjecture for L-space knots

Let $K$ be an L-space knot, meaning a knot admitting a Dehn surgery yielding an L-space. Let $b(K)$ denote its bridge index and $\beta(K)$ its braid index. The L-space knot index conjecture. If $K$ is an L-space knot, then its braid index and bridge index agree, that is, $\beta(K)=b(K)$. The conjecture holds for several important families, including two-bridge knots, Montesinos knots, 1-bridge braids, and the Baker–Kegel family, but a classification of L-space knots remains elusive and the general claim is open.