# The rank invariant stability via interleavings

arXiv: https://arxiv.org/abs/1412.3374 · HTML: https://mlsanity.com/paper/1412.3374/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Dec 2014.

## Built on by (most cited first, 4 of 4)

- [A Framework for Fast and Stable Representations of Multiparameter Persistent Homology Decompositions](https://mlsanity.com/paper/2306.11170/) (2023)
- [Stability for Inference with Persistent Homology Rank Functions](https://mlsanity.com/paper/2307.02904/) (2023)
- [ToMAToMP: Robust and Multi-Parameter Topological Clustering](https://mlsanity.com/paper/2605.14824/) (2026)
- [COMPLEX: A Closed-Form Certified Embedding of Multiparameter Persistence Modules](https://mlsanity.com/paper/2609.22012/) (2026)

## Abstract (arXiv)

A lower bound for the interleaving distance on persistence vector spaces is given in terms of rank invariants. This offers an alternative proof of the stability of rank invariants.