The n-distal field conjecture

Let $K$ be a field in the ring language, and let $n$ be a positive integer. A theory is n-distal when it satisfies the corresponding $n$-ary distality condition. n-distal field conjecture. Every $n$-distal field is already $1$-distal. The source also asks whether, for every $n$, there are strongly $(n+1)$-distal but not $n$-distal groups, and whether such examples can be required to be NIP, in the pure group language. These questions propose a hierarchy and possible strictness phenomena for higher distality; no resolution is given in the supplied text.