Transitivity conjecture for classical r-matrices with signs

Let $n$ be a positive integer, let ${\mathfrak g}$ be a Lie algebra, and let $r\in {\mathfrak g}\otimes {\mathfrak g}$ solve the classical Yang–Baxter equation (CYBE). Let $\boldsymbol{\epsilon}$ be a transitive $n\times n$ matrix with entries in $\{1,-1\}$, and let $\mathbf r^{(\boldsymbol{\epsilon})}$ denote the associated tensor constructed from $r$. Transitivity conjecture. The tensor $\mathbf r^{(\boldsymbol{\epsilon})}$ solves the CYBE. This is presented as an ultimate justification of the notion of transitivity; the supplied context does not state whether the conjecture has been resolved.