On the Stability of Interval Decomposable Persistence Modules

Abstract The algebraic stability theorem for persistence modules is a central result in the theory of persistent homology. We introduce new proof technique which we use to prove n -dimensional rectangle decomposable up constant $$2n-1$$ 2 n - 1 that generalizes theorem, and give an example showing bound cannot be improved $$n=2$$ = . then apply block modules, from novel results zigzag Reeb graphs follow. These are improvements on weaker bounds previous work, obtain optimal.