The characteristic-three realization conjecture for generalized Cartan matrices

Let $A$ be a purely even, symmetrizable, indecomposable, generalized Cartan matrix of size $n$ with nonzero determinant whose off-diagonal entries lie between $-2$ and $0$, inclusive. Let $D$ be its Dynkin diagram. A boundary node is a node connected to exactly one other node by a single edge. Let $I$ be a subset of boundary nodes such that no two nodes in $I$ share an adjacent node, let $J$ be the set of corresponding adjacent nodes, and let $\widetilde{A}$ be obtained from $A$ by setting $a_{jj}=0$ for $j\in J$ and deleting the rows and columns indexed by $I$. Finally, let $e_I=\sum_{i\in I}e_i$. Characteristic-three realization conjecture. Under these hypotheses, $\mathfrak{g}(A)$ can be realized as an object in \operatorname*{Rep}{\text{\boldmath\alpha}}_3 with respect to $e_I$. If $\widetilde{A}$ has nonzero determinant, then $\overline{\mathfrak{g}(A)}^{gen}$ is isomorphic to $\mathfrak{g}(\widetilde{A})$. If $\sigma$ is any legal recoloring of $I$, the same statement also holds for $e_{\sigma(I)}$ in place of $e_I$. The conjecture proposes a systematic realization and generic semisimplification procedure for these Lie superalgebras in characteristic $3$; its resolution is not established by the supplied text.