Support-variety criterion for wild blocks of Lie superalgebras

Let $\mathcal{C}$ be the representation category under consideration, let $\mathcal{B}$ be a block of $\mathcal{C}$, and let $S\in\mathcal{B}$ be a simple supermodule. Write $\mathcal{V}_{\mathfrak{g}}(S)$ for the support variety of $S$.

Support-variety wildness conjecture. If there exists a simple supermodule $S$ in $\mathcal{B}$ such that

$$\dim \mathcal{V}_{\mathfrak{g}}(S)\geq 3,$$

then $\mathcal{B}$ has wild representation type. This conjecture is motivated by the analogous finite-group-scheme result and would connect the constructed support varieties of classical and Cartan-type Lie superalgebras with block representation type; the source gives no resolution.