Ando's equivariant Witten genus conjecture

Let $X$ be a compact, differentiable, $G$-equivariant spin manifold of dimension $24d$. Assume that $\frac{p_1}{2}(X)=0$ and that

$$\left(\frac{p_1}{2}\right)_G(X)=\pi^*(\alpha),$$

where $\pi$ is the map from $X$ to a point and $\alpha\in H^4(BG;\mathbb Z)$. Ando's conjecture. The equivariant Witten genus of $X$ is a generalized Thompson series whose transformation behavior under $\operatorname{SL}_2(\mathbb Z)$ makes it a section of $\mathcal L^{-\alpha}$. The conjecture extends the equivariant Witten-genus framework to a nonzero anomaly class $\alpha$; the supplied text attributes it to Matthew Ando and gives no resolution status.