Weimar–Woods conjecture on isomorphism and normalization of graded contractions

Let $G$ be a grading group and let $\bar{1}_S$ denote the generic graded contraction with support $S$. For graded contractions $\varepsilon$ and $\varepsilon'$ of a $G$-graded Lie algebra, write $\varepsilon\simeq\varepsilon'$ when they are isomorphic and $\varepsilon\sim_{\rm n}\varepsilon'$ when they are equivalent via normalization.

Weimar–Woods conjecture. Two graded contractions $\varepsilon$ and $\varepsilon'$ are isomorphic if and only if they are equivalent via normalization:

$$\varepsilon\simeq\varepsilon' \Longleftrightarrow \varepsilon\sim_{\rm n}\varepsilon'.$$

The conjecture asserts that the two notions of equivalence arising from isomorphism in the category of $G$-graded vector spaces coincide. The source gives no evidence of a resolution.