Finiteness conjecture for bounded-genus L-space surgeries in twist families

Let $\{(K_n,r_n)\}$ be a twist family of surgeries, where $r_n$ is the corresponding surgery slope on $K_n$. Twist-family surgery finiteness conjecture. For every integer $N\geq 0$, there are only finitely many L-space surgeries $(K_n,r_n)$ such that $g(K_n)\leq N$. This is the surgery formulation of the bounded-genus conjecture for twist families, enabled by choosing slopes so that infinitely many bounded-genus L-space knots yield L-space surgeries. It remains open in the stated generality.