The equivariant topological modular forms refinement conjecture for Mathieu Moonshine

Let $\nu\in\mathrm{TMF}^{-3}(\mathrm{pt})$ be the class corresponding to $[\overline{\operatorname{Fer}(3)}]$, let $\{24\Delta\}\in\mathrm{TMF}^{-24}(\mathrm{pt})$ be the class corresponding to $[\overline{V^{f\natural}}]$, and let $\omega$ be the relevant $\mathrm M_{24}$-equivariant anomaly. Let $\mathrm M_{24}\subset\mathrm{Co}_1$. Equivariant TMF refinement conjecture. There is a distinguished refinement

$$\{24\Delta\}\in\mathrm{TMF}^{-24}(\mathrm{pt})$$

to a class in $\mathrm{TMF}^{-24}_{\omega}(\mathbb B\mathrm{Co}_1)$ such that, after multiplication by $\nu$ and restriction to $\mathrm M_{24}$,

$$\{24\Delta\}\nu=0\quad\text{in }\mathrm{TMF}^{-27}_{\omega}(\mathbb B\mathrm M_{24}).$$

This is the TMF formulation of the proposed SCFT nullhomotopy. The required equivariant refinement has not been established rigorously, and the paper explicitly says it is not expected to vanish $\mathrm{Co}_1$-equivariantly.