Congruence kernel conjecture for Higman representations

Let $\mathcal{C}$ be a non-semisimple modular category, and let $\rho:(\mathfrak{s},\mathfrak{t})\mapsto(S_{\mathrm{CW}},T_{\mathrm{CW}})$ be the associated Cohen-Westreich modular-data representation.

Congruence kernel conjecture. The projective representation of $\operatorname{SL}(2,\mathbb Z)$ given by $\rho$ has kernel that is a congruence subgroup of level $\operatorname{ord}(T_{\mathrm{CW}})$.

The conjecture proposes that the congruence subgroup theorem known for modular tensor categories extends to the Higman representation associated with arbitrary non-semisimple modular categories. The paper verifies the corresponding statement for the Higman representations of small quantum groups and doubled Nichols Hopf algebras, but the general case remains open.