Medvedev's solvable-subring conjecture for Lie p-rings

Let $L$ be a Lie $p$-ring admitting an automorphism of order $p^n$ with $p^m$ fixed points. A subring has $m$-bounded derived length if its derived length is bounded by a function of $m$, and an index is $(p,n,m)$-bounded if it is bounded by a function of $p$, $n$, and $m$.

Medvedev's conjecture. $L$ contains a solvable subring of $m$-bounded derived length whose index is $(p,n,m)$-bounded.

This is the Lie-ring analogue of the derived-length conjecture for finite $p$-groups with prime-power-order automorphisms. The source provides no resolution status for the general case.