The $C_\infty$-equivalence conjecture for links in 3-manifolds

Let $M$ be a $3$-manifold, and let two links in $M$ be given. They are $C_\infty$-equivalent when they are $C_k$-equivalent for every $k\geq 1$. $C_\infty$-equivalence conjecture. Two links in $M$ are equivalent if and only if they are $C_\infty$-equivalent. This proposes that equivalence of links is completely detected by all finite stages of the clasper filtration; the supplied text does not indicate whether the conjecture has been resolved.