Anomaly cascade for fermionic symmetry actions

Let $\mathcal{C}$ be a super modular tensor category with fermionic symmetry data $(G_b,s,\omega)$, and let $\mathcal{B}$ be a unitary modular tensor category that is a minimal modular extension of $\mathcal{C}$. Let $E_\infty^{p,q}$ denote the layers in total degree $4$ of the Atiyah–Hirzebruch spectral sequence for the relevant twisted spin bordism theory. The anomaly cascade. The anomaly of the super modular tensor category has four layers: the first, valued in $E_\infty^{0,4}$, is the obstruction to giving the modular extension time-reversal symmetry; the second, valued in $E_\infty^{2,2}$, is the obstruction to extending $\rho:G_b\to\operatorname{Aut}(\mathcal{C})$ to $\check\rho:G_b\to\operatorname{Aut}(\mathcal{B})$; the third, valued in $E_\infty^{3,1}$, is the obstruction to extending the symmetry-fractionalization data $\eta_a({\bf g},{\bf h})$; and the fourth, valued in $E_\infty^{4,0}$, is the anomaly of the extended $G_b$-action on $\mathcal{B}$. This describes the four obstruction layers governing fermionic symmetry anomalies through a minimal modular extension. The source presents this as an interpretation attributed to Bulmash and Barkeshli and does not state a resolution.