Hanselman's generalized splicing conjecture for L-spaces

Let $K_1$ and $K_2$ be knots in $S^3$, and let $M_i=S^3\smallsetminus\nu(K_i)$ for $i=1,2$. Let $h$ identify the torus boundaries of $M_1$ and $M_2$, and let $\mathcal{L}^\circ_{M_i}$ denote the relevant interiors of their L-space slope sets. A generalized splice is the manifold $M_1\cup_hM_2$ obtained by this identification. Generalized splicing conjecture. The generalized splice $M_1\cup_hM_2$ is an L-space if and only if, for every slope $\gamma$, either $\gamma\in\mathcal{L}^\circ_{M_1}$ or $h(\gamma)\in\mathcal{L}^\circ_{M_2}$. The conjecture is settled when both knots are L-space knots by the results discussed immediately afterward, but remains open in the general case.