Stepwise Smith Normal Form Is Not a Complete Invariant for Persistence Modules over Z

This note constructs two persistence modules over Z with identical stalks, identical Smith normal form at every structure map, and identical cokernel multisets, but which are not isomorphic.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-05-17
DOI
https://doi.org/10.5281/zenodo.20252298
Primary Topic
Topological and Geometric Data Analysis
Type
preprint
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preprint

Stepwise Smith Normal Form Is Not a Complete Invariant for Persistence Modules over Z

Yiqi Xie
Zenodo (CERN European Organization for Nuclear Research)
Topological and Geometric Data Analysis
preprint

Stepwise Smith Normal Form Is Not a Complete Invariant for Persistence Modules over Z

Yiqi Xie
preprint en

Abstract

This note constructs two persistence modules over Z with identical stalks, identical Smith normal form at every structure map, and identical cokernel multisets, but which are not isomorphic.

Zenodo (CERN European Organization for Nuclear Research)
Topological and Geometric Data Analysis
DOIOpen Access PDFOpenAlex
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Stepwise Smith Normal Form Is Not a Complete Invariant for Persistence Modules over Z — Yiqi Xie · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS