Watson's diagonal grading characterization of strongly invertible L-space knots

Let $K$ be a non-trivial knot in $S^3$ admitting a strong inversion, an orientation-preserving involution of $S^3$ that reverses the orientation of $K$, and let $[?]$ be its Watson invariant, a finite-dimensional vector space with absolute homological grading $h$ and relative quantum grading $q$.

Watson's conjecture. $K$ is an L-space knot if and only if $[?]$ is supported in a single diagonal grading

$$\delta=q-2h.$$

Here an L-space knot is a knot admitting a surgery to a Heegaard Floer L-space. The conjecture proposes a Khovanov-homological characterization of strongly invertible L-space knots; the converse direction is stated in the paper to remain open.