Generation conjecture for Vogel's algebra

Let $\Lambda$ be Vogel's algebra of three-legged Jacobi diagrams that are antisymmetric under permutations of their legs, with product defined by insertion at a vertex. Generation conjecture. The algebra $\Lambda$ is generated by the elements $t$ and $x_k$ with odd $k=3,5,\ldots$:

\begin{array}{c@{\qquad}c@{\qquad}c@{\qquad}c@{\qquad}c} t & x_3 & x_4 & x_5 & \cdots \\ \end{array}

The source labels this assertion as a conjecture but supplies no further information about its status.