The knot-surgery diffeomorphism conjecture for the K3 surface

Let $E(2)$ be the elliptic K3 surface, and let $X_{K_1}$ and $X_{K_2}$ denote the manifolds obtained from $E(2)$ by knot surgery using knots $K_1$ and $K_2$, respectively. Knot-surgery diffeomorphism conjecture. The manifolds $X_{K_1}$ and $X_{K_2}$ are diffeomorphic if and only if $K_1$ and $K_2$ are equivalent knots. This proposes that, for the K3 surface, the knot-surgery construction detects the knot type beyond the information captured by Seiberg–Witten invariants. The source does not provide evidence of a resolution, so the conjecture is recorded as open.