Akbulut–Kirby conjecture on concordance from homeomorphic 0-surgeries

Let $K$ and $K'$ be knots, and let $S^3_0(K)$ and $S^3_0(K')$ denote their 0-surgeries. Akbulut–Kirby conjecture. If $K$ and $K'$ have homeomorphic 0-surgeries, then $K$ and $K'$ are smoothly concordant. The conjecture asserts that the 0-surgery determines the smooth concordance class; it was disproved by counterexamples to the original formulation, motivating a revised version.