The exotic cosmetic surgery conjecture

A cosmetic surgery is a pair of Dehn fillings on a knot or 3-manifold exterior that produce homeomorphic filled manifolds; it is truly cosmetic when the homeomorphism preserves the relevant orientation data rather than merely reversing it. Cosmetic surgery conjecture. Exotic cosmetic surgeries are never truly cosmetic. This is motivated by the fact that the known exotic examples on hyperbolic knot exteriors and the Seifert fibred examples are reflective; the source attributes the conjecture to problem 1.81 of Kirby's problem list, but gives no resolution.