Before revision:  The second result is that, at least in low dimensions, persistence-perfect gradient vector-fields not only exist but can be constructed by an algorithm based on local homotopy expansions . These results show a link between multi-parameter persistence and discrete Morse theory that can be leveraged for a better understanding of the former.
After revision:  The second result is that, at least in low dimensions, persistence-perfect gradient vector-fields not only exist but can be constructed by an algorithm based on local homotopy expansions allow for efficient computability over simplicial complexes up to dimension 2.