The fiberedness conjecture for Floer simple knots in L-spaces

Let $Y$ be an L-space, and let $K\subset Y$ be a Floer simple knot with irreducible complement. Write $[K]^{\perp}$ for the orthogonal complement of the homology class $[K]$ under the linking form, and let $\langle [K]\rangle$ denote the subgroup generated by $[K]$. Fiberedness conjecture. If

$$[K]^{\perp}\subset \langle [K]\rangle,$$

then $K$ is fibered. The conjecture is motivated by the corresponding dual-knot situation arising from surgery on a knot in $S^1\times S^2$, and would extend the paper's fiberedness results for Floer simple knots. Its resolution is not given here.