Fidkowski's conjecture on invertible phases entangled by QCAs

Let $Y$ be the gravitational topological response associated with an invertible phase, and let a QCA be an operation that entangles this phase. The phase has a nontrivial partition function if its partition function is not equal to $1$ on some orientable manifold.

Fidkowski's conjecture. $Y$ is a nontrivial QCA if the invertible phase it entangles has a nontrivial partition function on some orientable manifold.

This conjecture is used to determine when gravitational topological responses cause the lattice operations $S$ and $T$ to mix with a nontrivial QCA. Its general status is not specified in the source.