The no-exotic-obstructions conjecture for deformations of super Riemann surfaces

Let $(\mathcal{U}, \vartheta)$ be an algebraic deformation of a super Riemann surface $S(C, T^*_{C, -})$ over $\mathbb{A}^{0|n}_\mathbb{C}$. Its primary obstruction $\omega_{(\mathcal{U}, \vartheta)}$ is the obstruction to splitting the deformation. No-exotic-obstructions conjecture. If

$$\omega_{(\mathcal{U}, \vartheta)}=0,$$

then $(\mathcal{U}, \vartheta)$ is split. This conjecture asserts that deformations of super Riemann surfaces admit no higher obstructions once the primary obstruction vanishes; it was confirmed to second order, while the general case remains open.