The umbral moonshine multiplier-system conjecture

Let $\Lambda=\{2,3,4,5,7,13\}$, let $G^{(\ell)}$ be the corresponding umbral group, and let $H^{(\ell)}_g$ be its vector-valued mock modular McKay–Thompson series. For each $g\in G^{(\ell)}$, let $(n_g,h_g)$ be the associated pair and let $\nu^{(\ell)}_{n|h}$ be the corresponding multiplier system on $\Gamma_0(n)$. Umbral moonshine multiplier-system conjecture. For all $\ell\in\Lambda$ and $g\in G^{(\ell)}$, the multiplier system of $H^{(\ell)}_g$ is $\nu^{(\ell)}_{n|h}$ with $n=n_g$ and $h=h_g$. The conjecture gives the predicted multipliers for all umbral McKay–Thompson series; the source does not establish it independently.