Generic Lie algebra Hilbert-series conjecture

Let a Lie algebra of type $(n,r)$ be generated by $n$ degree-one elements with $r$ homogeneous quadratic relations. For a power series, let $[A(z)]$ denote the truncation operation defined by retaining coefficients through the first nonpositive coefficient, as in the source. Let $\operatorname{Log}$ denote the Lie-series operation defined in Section 2, equation (log). The generic Lie algebra Hilbert-series conjecture. A generic Lie algebra of type $(n,r)$ has Hilbert series

$$\left[\operatorname{Log}\left(\frac{1}{1-nz+rz^2}\right)\right].$$

This is presented as the Lie-algebra analogue of the preceding conjecture and is compared in the source with a conjecture of Fröberg and Löfwall. The supplied text does not state whether it has been resolved.