Pith. sign in

REVIEW 3 cited by

Decomposition of pointwise finite-dimensional persistence modules

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1210.0819 v3 pith:Y3GZ26QZ submitted 2012-10-02 math.RT

William Crawley-Boevey This is my paper · ORCID
classification math.RT
keywords modulespersistencefinite-dimensionalchainconditionconsistingdecompositiondescending
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

We show that a persistence module (for a totally ordered indexing set) consisting of finite-dimensional vector spaces is a direct sum of interval modules. The result extends to persistence modules with the descending chain condition on images and kernels.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Modules over posets: commutative and homological algebra

    math.AC 2019-08 conditional novelty 8.0 of 10

    Tame modules over arbitrary posets are proved to have finite encodings, fringe presentations, indicator resolutions, and primary decompositions, leading to proofs of two sheaf-theoretic conjectures.

  2. Negative Calabi-Yau discrete cluster categories via Nakayama representations and persistence theory

    math.RT 2025-08 unverdicted novelty 7.0 of 10

    The paper constructs infinite discrete Nakayama representations via persistence theory and stabilizes them into negative Calabi-Yau versions of Igusa-Todorov discrete cluster categories of type A, with geometric model...

  3. Quantum encodings that preserve persistent homology

    quant-ph 2026-05 unverdicted novelty 5.0 of 10

    Investigates which quantum encodings of classical datasets preserve persistent homology so that quantum algorithms can extract topological features directly from the data.

Pith tools