Exhaustion conjecture for simple bounded cuspidal affine modules

Let $\mathfrak{g}$ be the basic classical Lie superalgebra, let $L(\mathfrak{g})$ be its loop superalgebra, and let $\widehat{\mathfrak{g}}$ be the corresponding affine Lie superalgebra. For a simple bounded cuspidal $L(\mathfrak{g})$-module $V$, write $L^i(V)$ for the simple modules in the decomposition associated with the affine construction. Exhaustion conjecture. If $M$ is a simple bounded cuspidal $\widehat{\mathfrak{g}}$-module, then there is a simple bounded cuspidal $L(\mathfrak{g})$-module $V$ for which

$$M\cong L^i(V)$$

for some $i\in\mathbb{N}$. The conjecture asserts that the family obtained from loop-algebra modules accounts for all simple bounded cuspidal affine modules; the source does not provide evidence of a resolution.