Kulakova–Lando conjecture on the \mathfrak{sl}_2 weight system and chord diagrams

Let $D$ be a chord diagram with $2m$ chords, where $m\geq 1$. Let $\pi_{2m}(D)$ be its projection to the primitive part, let $w_{\mathfrak{sl}_2,2}$ be the weight system associated with $\mathfrak{sl}_2$ and $2\langle\cdot,\cdot\rangle$, let $R_m(D)$ denote the corresponding coefficient, and let $c_2$ be the quadratic Casimir element.

Kulakova–Lando conjecture.

$$w_{\mathfrak{sl}_2,2}(\pi_{2m}(D))=2R_m(D)c_2^m+\text{ terms of degree less than }m\text{ in }c_2.$$

The conjecture is a consequence of the Melvin–Morton–Rozansky conjecture, which has been proved, so this statement is solved.