Paper Citation Record · LEDGER

Decomposing zero-dimensional persistent homology over rooted tree quivers

As of 19 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 3 inbound Pith citation observations for arXiv:2411.19319.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2411.19319 v1

Coverage vector

measured 27 of 27 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T10:30:10.003475Z

measured 30 of 30 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T20:28:28.391677Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-06-30T03:04:14.113290Z

Reference resolution

27 of 27 outbound references displayed

verified exact0
verified fuzzy24
unresolved3
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 55d9ba70-6062-46f8-bb62-4ca0dc3c380c · outbound

This paper cites an unresolved cited work.

Decomposing zero-dimensional persistent homology over rooted tree quivers Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-12T10:30:10.404562Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ea0e6019-b7d8-4793-9a33-40c5c4d5a76f · outbound

This paper cites Elements of the representation theory of associative algebras.

Decomposing zero-dimensional persistent homology over rooted tree quivers Elements of the representation theory of associative algebras

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:30:10.392369Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 047bff84-24ae-46b6-8c4e-17ec8c92dae3 · outbound

This paper cites Botnan, Steﬀen Oppermann, and Jo han Steen.

Decomposing zero-dimensional persistent homology over rooted tree quivers Botnan, Steﬀen Oppermann, and Jo han Steen

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:30:10.381365Z

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Observation cf77f7e6-1dd8-4697-84d0-08f1bb66dcc9 · outbound

This paper cites An introductio n to multiparameter persistence.

Decomposing zero-dimensional persistent homology over rooted tree quivers An introductio n to multiparameter persistence

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:30:10.370247Z

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Observation 9db11294-f100-43f8-833e-ce76da1f4c8b · outbound

This paper cites O n the complexity of zero-dimensional multi- parameter persistence, 2020.

Decomposing zero-dimensional persistent homology over rooted tree quivers O n the complexity of zero-dimensional multi- parameter persistence, 2020

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:30:10.359372Z

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Observation f05dac10-ad7d-424f-8178-5e37c52f57e7 · outbound

This paper cites Coarse nodal count and topological persi stence.

Decomposing zero-dimensional persistent homology over rooted tree quivers Coarse nodal count and topological persi stence

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:30:10.348485Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 03273e3e-61f1-4c79-864e-209fa96b7531 · outbound

This paper cites Eld er-rule-staircodes for augmented metric spaces.

Decomposing zero-dimensional persistent homology over rooted tree quivers Eld er-rule-staircodes for augmented metric spaces

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:30:10.336175Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c7f1342b-9bc6-4b84-90b1-f8c08796cd21 · outbound

This paper cites Guibas, Steve Y.

Decomposing zero-dimensional persistent homology over rooted tree quivers Guibas, Steve Y

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:30:10.323401Z

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Observation 8fce147e-4fbd-42f8-86b6-536228162c0c · outbound

This paper cites An introduction to topological data analysis: Fundamental and practical aspects for data scientists.

Decomposing zero-dimensional persistent homology over rooted tree quivers An introduction to topological data analysis: Fundamental and practical aspects for data scientists

Reference 9

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Source-reported events for the cited work

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Observation 058c6936-25f1-49cc-b6f4-1a05c8f9b92d · outbound

This paper cites The ﬁber of the persistence map for functi ons on the interval.

Decomposing zero-dimensional persistent homology over rooted tree quivers The ﬁber of the persistence map for functi ons on the interval

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:30:10.298613Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 40615f3f-f55f-4767-a2ea-6a493b5891b5 · outbound

This paper cites From trees to barcodes and back again II: Combinatorial and proba bilistic aspects of a topological inverse problem.

Decomposing zero-dimensional persistent homology over rooted tree quivers From trees to barcodes and back again II: Combinatorial and proba bilistic aspects of a topological inverse problem

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:30:10.287456Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 77a93938-4817-4401-88b5-936a7e5ee062 · outbound

This paper cites An introduction to quiver representations , volume 184 of Graduate Studies in Mathematics.

Decomposing zero-dimensional persistent homology over rooted tree quivers An introduction to quiver representations , volume 184 of Graduate Studies in Mathematics

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:30:10.274379Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e5caf117-155b-455e-a54f-6e9368a68d76 · outbound

This paper cites an unresolved cited work.

Decomposing zero-dimensional persistent homology over rooted tree quivers Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-12T10:30:10.254148Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8dcc89f2-018e-4b4c-ac6a-3745c1c9a482 · outbound

This paper cites Escolar and Yasuaki Hiraoka.

Decomposing zero-dimensional persistent homology over rooted tree quivers Escolar and Yasuaki Hiraoka

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:30:10.239958Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9df2b399-61d2-4cf2-97ed-e82299eb2e9f · outbound

This paper cites Barcodes: the persistent topology of da ta.

Decomposing zero-dimensional persistent homology over rooted tree quivers Barcodes: the persistent topology of da ta

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:30:10.227230Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 0e129539-1674-48bd-ba15-606734756422 · outbound

This paper cites A survey of topological machine learning methods.

Decomposing zero-dimensional persistent homology over rooted tree quivers A survey of topological machine learning methods

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:30:10.211112Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c0e0c9ef-d0d6-4d67-995f-0eb34e3cd257 · outbound

This paper cites Reduced representatio ns of rooted trees.

Decomposing zero-dimensional persistent homology over rooted tree quivers Reduced representatio ns of rooted trees

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:30:10.197144Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 80b759f1-5741-439c-88a7-c43fe3a49deb · outbound

This paper cites Rank functions on rooted tree quivers.

Decomposing zero-dimensional persistent homology over rooted tree quivers Rank functions on rooted tree quivers

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:30:10.182141Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 70b8c4d1-402b-40b8-b723-0597cb28b6bb · outbound

This paper cites Computing minimal presentations and bigraded Betti numbers of 2-parameter persistent homology.

Decomposing zero-dimensional persistent homology over rooted tree quivers Computing minimal presentations and bigraded Betti numbers of 2-parameter persistent homology

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:30:10.165657Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 6e3cb823-cce0-41d1-bc70-40567b4fe78f · outbound

This paper cites Indecomposable representations of ﬁnite ordered sets.

Decomposing zero-dimensional persistent homology over rooted tree quivers Indecomposable representations of ﬁnite ordered sets

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:30:10.150482Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ed003046-b7d6-4482-9f47-53f39ee32f02 · outbound

This paper cites an unresolved cited work.

Decomposing zero-dimensional persistent homology over rooted tree quivers Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-12T10:30:10.137486Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9f51065b-db68-4475-802d-cdec301e4ca3 · outbound

This paper cites Topological persistence in geom- etry and analysis , volume 74 of University Lecture Series.

Decomposing zero-dimensional persistent homology over rooted tree quivers Topological persistence in geom- etry and analysis , volume 74 of University Lecture Series

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:30:10.124626Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 7a3f43f8-ca17-4635-8538-8e274a762388 · outbound

This paper cites Exceptional modules are tree mod ules.

Decomposing zero-dimensional persistent homology over rooted tree quivers Exceptional modules are tree mod ules

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:30:10.108580Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1fd51dd4-c75d-4816-a5fb-e70c5a2b0242 · outbound

This paper cites Distinguished bases of exceptio nal modules.

Decomposing zero-dimensional persistent homology over rooted tree quivers Distinguished bases of exceptio nal modules

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:30:10.096372Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2a22676e-8d5d-446b-a763-5fb114f69ddb · outbound

This paper cites Stable and consiste nt density-based clustering via multiparameter persistence.

Decomposing zero-dimensional persistent homology over rooted tree quivers Stable and consiste nt density-based clustering via multiparameter persistence

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:30:10.082429Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1e7fbf15-044f-419b-ad34-c8f4980bb3d7 · outbound

This paper cites On the Hofer-Zehnder conjecture.

Decomposing zero-dimensional persistent homology over rooted tree quivers On the Hofer-Zehnder conjecture

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:30:10.064490Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 72f1d7fa-0b22-4c32-ac7d-e93e79005f03 · outbound

This paper cites Data structures and network algorithms , volume 44 of CBMS-NSF Regional Conference Series in Applied Mathematics.

Decomposing zero-dimensional persistent homology over rooted tree quivers Data structures and network algorithms , volume 44 of CBMS-NSF Regional Conference Series in Applied Mathematics

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T10:30:10.044735Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

Observation 2b2e0666-3129-4c47-bf5e-1a51982c3bd4 · inbound

Counts and end-curves in two-parameter persistence cites this paper.

Counts and end-curves in two-parameter persistence Decomposing zero-dimensional persistent homology over rooted tree quivers

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-15T20:28:28.391677Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ac566ef9-ea06-44f2-b04e-8045a8458829 · inbound

Rooted tree modules cites this paper.

Rooted tree modules Decomposing zero-dimensional persistent homology over rooted tree quivers

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-05T22:11:11.433102Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 57190649-c6b7-4b98-bab5-f745ff13a59e · inbound

From Frames to Features: Scalable Zigzag Persistence for Binary Video cites this paper.

From Frames to Features: Scalable Zigzag Persistence for Binary Video Decomposing zero-dimensional persistent homology over rooted tree quivers

Reference 36

Resolution: verified exact; arxiv_id, observed 2026-06-30T03:04:14.115420Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.