The d-invariant characterization of amphichiral 2-bridge knots

Let $p,q\in\mathbb{N}$ with $p$ odd and $(p,q)=1$. Write $L(p,q)$ for the lens space associated to the 2-bridge knot $K(p/q)$, and let its Heegaard Floer correction terms be the values $d(L(p,q),\mathfrak{s})$ over ${\textup{Spin}^c}(L(p,q))$. The d-invariant characterization conjecture. The following are equivalent: the correction terms of $L(p,q)$ can be partitioned into multisets, each of the form $\{r,-r,r,-r\}$ for some $r\in\mathbb{Q}$, together with a single multiset $\{0\}$; the 2-bridge knot $K(p/q)$ is amphichiral; there is an orientation-reversing self-diffeomorphism of $L(p,q)$; and $q^2\equiv -1\pmod p$. This conjecture proposes that the correction-term pattern exactly characterizes amphichirality, equivalently the orientation-reversing symmetry of the lens space and the stated congruence condition. The paper notes that the pattern was checked for all 2-bridge knots with at most 12 crossings, but does not establish the equivalence in general.