Classification conjecture for non-semisimple homological TQFTs

Let ${\cal V}$ be a non-semisimple TQFT whose mapping class group representations have precisely the Torelli groups as their kernels. Let ${\cal P}^+$ be the class of polynomials defining the positive homological TQFTs ${\cal V}^{(P)}$. Homological TQFT classification conjecture. The TQFT ${\cal V}$ is isomorphic to a sub-TQFT of ${\cal V}^{(P)}$ for some $P\in{\cal P}^+$. This would reduce the classification of such theories to the polynomial homological models and their symplectic representation-theoretic branching rules; the source leaves the assertion open.