Lando's uniqueness conjecture for the sl(2)-weight system

A 4-invariant is a graph-theoretic counterpart of a weight system on chord diagrams; the $\mathfrak{sl}(2)$-weight system is the weight system associated with the Lie algebra $\mathfrak{sl}(2)$.

Lando's conjecture. There exists a unique 4-invariant that extends the $\mathfrak{sl}(2)$-weight system.

The conjecture asks whether the $\mathfrak{sl}(2)$-weight system has a unique extension from chord diagrams to a 4-invariant. The paper does not resolve it, but constructs an explicit 4-invariant extending the specialization at $c=\frac{3}{8}$.