The Lie-algebra construction conjecture for weight systems

Let ${\frak g}$ be a finite-dimensional Lie algebra with a metric and orthonormal basis $\{{\frak g}_a\}_{a=1}^{\dim{\frak g}}$, and let $R$ be a finite-dimensional representation. The construction in the source assigns a weight system $W_{{\frak g},R}$ to diagrams using the structure constants and traces in $R$. A weight system is an element of ${\cal A}^*$. The Lie-algebra construction conjecture. All weight systems come from this construction. This is stated after the construction of Lie-algebraic weight systems, but the source supplies no proof or resolution of the universality claim.