Lando's degree conjecture for the \mathfrak{sl}_2 weight system on complete bipartite graphs

Let $K_{l,n}$ be the complete bipartite graph with parts of sizes $l$ and $n$, and let $w_{\mathfrak{sl}_2}$ denote the $\mathfrak{sl}_2$ weight system.

Lando's complete-bipartite reformulation. The value of the $\mathfrak{sl}_2$ weight system at $K_{l,n}$ is a polynomial of degree $\min(l,n)$.

The paper presents this as a restatement of Lando's chord-diagram conjecture and verifies the cases with $l=1,2,3$ through explicit generating-function calculations. The general assertion remains open in the supplied text.