$k$-repeating higher-order Arf invariant conjecture

For $k\geq 4$ and $j\geq 1$, let ${\sf K}^{k\infty}_{4j-2}$ be the kernel of the $k$-repeating Milnor invariant map, and let $\mathrm{Arf}^k_j$ be the corresponding $k$-repeating higher-order Arf invariant

$$\mathrm{Arf}^k_j:{\sf K}^{k\infty}_{4j-2}\to(\mathbb Z_2\otimes {\sf L}^{\lfloor k/4\rfloor}_j)/\operatorname{Ker}\alpha^k_j.$$

$k$-repeating higher-order Arf conjecture. The map $\mathrm{Arf}^k_j$ is an isomorphism for all $k$ and $j$. This is the $k$-repeating analogue of the higher-order Arf invariant conjecture; its status is not resolved in the source.