Freed–Teleman–Walker conjecture for non-semisimple WRT theories via non-compact filled cobordisms

Let $\mathscr{V}$ be a non-semisimple modular tensor category. Consider the non-compact filled 321-dimensional cobordism category $Cob^{nc,filled}_{321}$, its quotient $\widetilde{Cob}^{nc}_{321}$, the De Renzi–Gainutdinov–Geer–Patureau-Mirand–Runkel theory $DGGPR_{\mathscr{V}}$, and the free functor into $Pr$. Let $\mathcal{A}_{\mathcal{V}}^{321}$ be the 321-part of the non-compact anomalous theory induced by an appropriate pair $(\mathcal{Z}_{\mathcal{V}},\mathcal{R}_{\mathcal{V}})$. Freed–Teleman–Walker conjecture. For an appropriate choice of $\mathcal{Z}_{\mathcal{V}}$ and $\mathcal{R}_{\mathcal{V}}$, the diagram comparing $\mathcal{A}_{\mathcal{V}}^{321}$ with $DGGPR_{\mathscr{V}}$ commutes up to isomorphism. This is the explicit 321-part formulation of the non-semisimple recovery claim; it remains open in the supplied text.