Topological Orders in (4+1)-Dimensions

The authors seem to have overlooked my following comments

"My main concern is about the physical interpretation on the "super" case. Being a trivial n-supercategory nSVec does not physically guarantee gappability. Let's consider the example in 2+1D : if the operators are described by SVec, the corresponding classification (of invertible fermionic topological order) is given by $\mathbb Z$, or $\mathbb Z_{16}$ (modulo fermionic E8 state), and their boundaries are all gapless except the really trivial one with zero chiral central charge. Given such possibility, it is not justified to claim that "All 4d fermionic boundaries can be gapped". Further physical arguments should be provided to support the claim. However, I tend to believe that there are indeed obstructions to gap out the boundary: In analogy to the 16-fold way in 2+1D, the $\mathbb Z_{16}$ could be obtaind as the kernel of $\mathcal W\to \mathcal SW$; the results in this work basically say that in 4+1D $\mathcal SW$ is trivial while $\mathcal W$ is of infinite rank."

Let me add a few more sentences to clarity my point: if the analogy between 2+1D and 4+1D indeed works, the kenerl of $\mathcal W\to \mathcal SW$ still classify fermionic invertible phases in 4+1D. Then, by the mathematical results in this paper, such kernel is necessarily of infinite rank. It is hard to believe that a nontivial invertible phase can have a gapped boundary condition.

I'm also worried if the authors put enough care in the revision. I found, for example, in eq.(7)(8), there are still errors: in (7) $b_{y|x}$ should be $(b_{x|y})^{-1}$; in (7)(8) the direction of $R$ $S$ does not agree with the convention in (6). The typos and errors are not limited to the ones listed in my previous report and the authors should perform a careful enough proof reading.