Ichihara–Ito–Saito's chirally cosmetic surgery conjecture for knots in $S^3$

Let $K$ be a knot in $S^3$ that is not a $(2,r)$ torus knot, and let $N=S^3-K$. Let $(s,s')$ be a chirally cosmetic pair of slopes on $\partial N$. Ichihara–Ito–Saito's conjecture. Then $K$ has an orientation-reversing symmetry and $s'=-s$. The conjecture describes the restricted form of chirally cosmetic surgeries expected for non-torus knots in the 3-sphere. The paper states that its formulation is designed to avoid known counterexamples, so the broader unrestricted version is refuted; this restricted statement is presented as the conjecture under discussion.