Strong negative amphichirality criterion for 2-bridge knots

Let $K$ be a 2-bridge knot, and let $Y=\Sigma(S^3,K)$ be its double branched cover. Let $\widetilde{\sigma}$ be a lift of the strong negative amphichiral involution when one exists. Say that the condition in Theorem d-invariants is satisfied when the ${\textup{Spin}^c}(Y)$-orbits have one order-one orbit with correction term $0$, while every other orbit has order four and the correction terms along each orbit are $d(Y,\widetilde{\sigma}^i(\mathfrak{s}))=(-1)^i d(Y,\mathfrak{s})$. Strong negative amphichirality conjecture for 2-bridge knots. $K$ is strongly negative amphichiral if and only if the condition in Theorem d-invariants is satisfied. The condition is motivated by computations for 2-bridge knots with at most 12 crossings, where the correction-term pattern was found precisely for the strongly negative amphichiral knots; the general equivalence remains open.