for proof of this statement, see Proposition 3 in the Appendix B. It is important to note that the converse is not true, i.e., isomorphism of extended reaction centers does not imply consistency of the reaction maps. Counterexamples such as the one in Figure of our previous work, however, turn out to be rare for chemical reaction data. We therefore use Ψ ∼ = Ψ ′ as an efficiently testable condition. For the comparison of AAMs, we employed this approximate condition detailed in Appendix A.1, which we subsequently used to develop ensemble atom mappings.