The q-compatibility characterization conjecture for the Monster

Let $\mathfrak{m}$ be the Monster Lie algebra, and let $G$ be the group of q-compatible automorphisms of $\mathfrak{m}$. The Monster group $\mathbb{M}$ is a subgroup of $G$. The q-compatibility characterization conjecture.

$$G \cong \mathbb{M}.$$

This would characterize the Monster as the group of symmetries of the Monster Lie algebra whose actions are compatible with quantization and directly generate genus-zero functions. The paper gives evidence both for and against the conjecture, and its status is not resolved here.