Higher-order Arf invariant conjecture

For a link, let ${\text{\rm sf K}}_{4j-2}$ denote the group of order $4j-2$ intersection invariants, and let ${\text{\rm sf L}}_j$ denote the degree-$j$ free Lie algebra component. The higher-order Arf invariant is a homomorphism

$$\operatorname{Arf}_{j}:{\text{\rm sf K}}_{4j-2}\to\mathbb Z_2\otimes {\text{\rm sf L}}_{j}.$$

Higher-order Arf invariant conjecture. The maps $\operatorname{Arf}_{j}$ are isomorphisms for all $j$. This is known for $j=1$, where it is given by the classical Arf invariants of the link components. Whether $\operatorname{Arf}_j$ is non-trivial for any $j>1$ remains open.