Gordienko–Kochetov conjecture on ordinary and differential exponents

Let $L$ be a Lie $F$-algebra acting on a finite-dimensional algebra $A$ by derivations, so that $A$ is an $L$-algebra. Let $c_n(A)$ and $c_n^L(A)$ denote the ordinary and differential codimension sequences, respectively, and let $\exp(A)$ and $\exp^L(A)$ denote their exponential growth rates. Gordienko–Kochetov conjecture. If $A$ is a finite-dimensional $L$-algebra, then

$$\exp(A)=\exp^L(A).$$

Since ordinary identities are differential identities, one always has $\exp(A)\leq\exp^L(A)$. The conjecture asks whether allowing derivations can never increase the exponential rate of codimension growth for finite-dimensional algebras.