Finest-granularity magma-graph faithfulness conjecture

Let $\mathfrak{g}$ be a complex finite-dimensional Lie algebra and $(\mathcal{M},\delta)$ an abelian magma such that $\mathfrak{g}$ is $\mathcal{M}$-magma-graded with finest granularity. Let $G_{\mathfrak{g}}(V,E)$ be the graph obtained from this pair by the modified graph-construction algorithm. Finest-granularity faithfulness conjecture. The graph $G_{\mathfrak{g}}(V,E)$ faithfully represents the internal structure of $\mathfrak{g}$ in the seven senses listed in the source: solvability, derived series, nilpotency, lower central series, ideals, simplicity, and semisimplicity. The source explicitly places this statement among open problems and conjectures, so it remains open.