Paper Citation Record · LEDGER

The fiber of multiparameter persistent homology for simplicial complexes

As of 8 August 2026, this Paper Citation Record lists 50 of 50 outbound references and 0 inbound Pith citation observations for arXiv:2608.04640.

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

pith.paper-citation-record.v1
2608.04640 v1

Coverage vector

measured 50 of 50 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-06T20:17:33.715109Z

measured 50 of 50 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

50 of 50 outbound references displayed

verified exact25
verified fuzzy2
unresolved10
parse uncertain0
malformed identifier10
metadata mismatch3

External citation measurements

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Outbound references

Observation 3b778c07-b388-46d3-9598-df4c6495a26e · outbound

This paper cites Botnan, Steffen Oppermann and Johan Steen.

The fiber of multiparameter persistent homology for simplicial complexes Botnan, Steffen Oppermann and Johan Steen

Reference 1

Resolution: verified exact; doi, observed 2026-08-06T20:17:34.814883Z

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Observation c2144f46-fcb6-4f10-93d9-e4aec3cd6ac3 · outbound

This paper cites An Algebraic Introduction to Persistence.

The fiber of multiparameter persistent homology for simplicial complexes An Algebraic Introduction to Persistence

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:17:34.797831Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c441b623-1ee7-4da8-981d-e2204a6791f9 · outbound

This paper cites 2026.doi:10.48550/ARXIV.2603.12049.url:https: //arxiv.org/abs/2603.12049.

The fiber of multiparameter persistent homology for simplicial complexes 2026.doi:10.48550/ARXIV.2603.12049.url:https: //arxiv.org/abs/2603.12049

Reference 3

Resolution: verified exact; doi, observed 2026-08-06T20:17:34.772509Z

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Observation a1f3f989-258e-4e85-a18c-abfc033e6309 · outbound

This paper cites ‘Multi-parameter Persistence Modules are Generically Indecom- posable’.

The fiber of multiparameter persistent homology for simplicial complexes ‘Multi-parameter Persistence Modules are Generically Indecom- posable’

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-06T20:17:30.013846Z

Source-reported events for the cited work

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Observation bd9acea1-e3bd-4fe2-b8c3-66be1dd75549 · outbound

This paper cites Fibers of point cloud persistence.

The fiber of multiparameter persistent homology for simplicial complexes Fibers of point cloud persistence

Reference 5

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Source-reported events for the cited work

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Observation 9c3d90d0-bc7a-455a-91bb-33db53e771ac · outbound

This paper cites ‘The fiber of persistent homology for trees’.

The fiber of multiparameter persistent homology for simplicial complexes ‘The fiber of persistent homology for trees’

Reference 6

Resolution: malformed identifier; doi_truncated, observed 2026-08-06T20:17:34.629046Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 46959c20-bf62-4b43-b273-82d9033a8183 · outbound

This paper cites Kepple, Rui Qi, Zhouchun Shang, Yanan Xing, Yanru An, Nannan Zhang, Yong Hou, Tanya L.

The fiber of multiparameter persistent homology for simplicial complexes Kepple, Rui Qi, Zhouchun Shang, Yanan Xing, Yanru An, Nannan Zhang, Yong Hou, Tanya L

Reference 7

Resolution: malformed identifier; doi_truncated, observed 2026-08-06T20:17:34.610985Z

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Observation 1e217a4c-1280-4811-afb6-18cfae177bac · outbound

This paper cites ‘Stabilizing Decomposition of Multiparameter Persistence Modules’.

The fiber of multiparameter persistent homology for simplicial complexes ‘Stabilizing Decomposition of Multiparameter Persistence Modules’

Reference 8

Resolution: verified exact; doi, observed 2026-08-06T20:17:34.592751Z

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Observation fd28c09f-6413-42b8-a7b3-4aa62b75d2ca · outbound

This paper cites an unresolved cited work.

The fiber of multiparameter persistent homology for simplicial complexes Unresolved cited work

Reference 9

Resolution: verified exact; doi, observed 2026-08-06T20:17:34.574252Z

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Observation 12198c9d-bb5c-4271-b5d7-7e5ebb51607c · outbound

This paper cites Blumberg and Michael Lesnick.

The fiber of multiparameter persistent homology for simplicial complexes Blumberg and Michael Lesnick

Reference 10

Resolution: verified exact; doi, observed 2026-08-06T20:17:34.557297Z

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Observation c289ffd0-6386-485b-9bb7-f36f2afade50 · outbound

This paper cites ‘Decomposition of persistence modules’.

The fiber of multiparameter persistent homology for simplicial complexes ‘Decomposition of persistence modules’

Reference 11

Resolution: verified exact; doi, observed 2026-08-06T20:17:34.540644Z

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Observation 061cff07-d9b3-4ecd-b520-2e72e9b41805 · outbound

This paper cites an unresolved cited work.

The fiber of multiparameter persistent homology for simplicial complexes Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:17:35.424610Z

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Observation 0a4d4b7a-e367-474b-a451-8e220937adc0 · outbound

This paper cites ‘On the bottleneck stability of rank decompositions of multi-parameter persistence modules’.

The fiber of multiparameter persistent homology for simplicial complexes ‘On the bottleneck stability of rank decompositions of multi-parameter persistence modules’

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-06T20:17:30.981809Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 12ed1e66-1ee6-4d14-a651-7358abbf76e8 · outbound

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

The fiber of multiparameter persistent homology for simplicial complexes Counts and end-curves in two-parameter persistence

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-06T20:17:31.071757Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7367fcdc-82a9-4e8e-abfd-1045bda422cb · outbound

This paper cites ‘Topological spaces of persistence modules and their properties’.

The fiber of multiparameter persistent homology for simplicial complexes ‘Topological spaces of persistence modules and their properties’

Reference 15

Resolution: malformed identifier; doi_truncated, observed 2026-08-06T20:17:34.505350Z

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Observation 29884e78-3eb0-43ab-96fd-4a5670692a58 · outbound

This paper cites ‘The Theory of Multidimensional Persistence’.

The fiber of multiparameter persistent homology for simplicial complexes ‘The Theory of Multidimensional Persistence’

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-06T20:17:31.203908Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8bce60e4-a562-4630-8092-8cc50adf6569 · outbound

This paper cites Catanzaro, Justin M.

The fiber of multiparameter persistent homology for simplicial complexes Catanzaro, Justin M

Reference 17

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation bb944532-3234-4964-818a-f9d98206090e · outbound

This paper cites Guibas and Steve Y.

The fiber of multiparameter persistent homology for simplicial complexes Guibas and Steve Y

Reference 18

Resolution: metadata mismatch; raw_fallback, observed 2026-08-06T20:17:35.265947Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 902c7890-a4c8-4ede-9303-2e42b46c66bf · outbound

This paper cites Springer International Publishing, 2016.isbn: 9783319425450.doi:10.

The fiber of multiparameter persistent homology for simplicial complexes Springer International Publishing, 2016.isbn: 9783319425450.doi:10

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-06T20:17:31.425690Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a666ea4c-49d3-4c61-9341-373553127e31 · outbound

This paper cites ‘A multi-parameter persistence framework for mathematical morphology’.

The fiber of multiparameter persistent homology for simplicial complexes ‘A multi-parameter persistence framework for mathematical morphology’

Reference 20

Resolution: verified exact; doi, observed 2026-08-06T20:17:34.449152Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 78b28341-8a6c-40d9-ab5b-cf0559cb1bfd · outbound

This paper cites ‘The representation theorem of persistence revisited and gen- eralized’.

The fiber of multiparameter persistent homology for simplicial complexes ‘The representation theorem of persistence revisited and gen- eralized’

Reference 21

Resolution: malformed identifier; doi_truncated, observed 2026-08-06T20:17:34.432994Z

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Observation a2ffc0f4-d7e7-4cac-afa7-d59958d0f377 · outbound

This paper cites ‘Decomposition of pointwise finite-dimensional persistence modules’.

The fiber of multiparameter persistent homology for simplicial complexes ‘Decomposition of pointwise finite-dimensional persistence modules’

Reference 22

Resolution: verified exact; doi, observed 2026-08-06T20:17:34.415951Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 908f594f-7256-4610-90f9-a9c7da2d579d · outbound

This paper cites ‘The fiber of the persistence map for functions on the interval’.

The fiber of multiparameter persistent homology for simplicial complexes ‘The fiber of the persistence map for functions on the interval’

Reference 23

Resolution: verified exact; doi, observed 2026-08-06T20:17:34.265581Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 28c996cc-08d8-470a-ad11-9b90e3d6ad64 · outbound

This paper cites Dey, Jan Jendrysiak and Michael Kerber.Decomposing Multiparameter Persistence Modules.

The fiber of multiparameter persistent homology for simplicial complexes Dey, Jan Jendrysiak and Michael Kerber.Decomposing Multiparameter Persistence Modules

Reference 24

Resolution: verified exact; doi, observed 2026-08-06T20:17:34.248792Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 64f48b8c-0fad-4dff-96c2-7b4f61dc8ce4 · outbound

This paper cites Harder-Narasimhan filtrations of persistence modules: metric stability.

The fiber of multiparameter persistent homology for simplicial complexes Harder-Narasimhan filtrations of persistence modules: metric stability

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:17:34.174984Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d8dbe380-5150-4f28-b17f-495c2754269a · outbound

This paper cites ‘Harder–Narasimhan filtra- tions of persistence modules’.

The fiber of multiparameter persistent homology for simplicial complexes ‘Harder–Narasimhan filtra- tions of persistence modules’

Reference 26

Resolution: verified exact; doi, observed 2026-08-06T20:17:34.150065Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 8f260253-0124-4f1e-acec-918c56fc6d88 · outbound

This paper cites 2026.doi:10.48550/ ARXIV.2603.23560.url:https://arxiv.org/abs/2603.23560.

The fiber of multiparameter persistent homology for simplicial complexes 2026.doi:10.48550/ ARXIV.2603.23560.url:https://arxiv.org/abs/2603.23560

Reference 27

Resolution: verified exact; doi, observed 2026-08-06T20:17:34.132780Z

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Observation 76f58164-b970-4160-9443-5643cb8dc7da · outbound

This paper cites ‘Continuation of point clouds via per- sistence diagrams’.

The fiber of multiparameter persistent homology for simplicial complexes ‘Continuation of point clouds via per- sistence diagrams’

Reference 28

Resolution: verified exact; doi, observed 2026-08-06T20:17:34.004371Z

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Observation fdd032bf-9271-48e9-8280-2f06a5828910 · outbound

This paper cites Gardner, Erik Hermansen, Marius Pachitariu, Yoram Burak, Nils A.

The fiber of multiparameter persistent homology for simplicial complexes Gardner, Erik Hermansen, Marius Pachitariu, Yoram Burak, Nils A

Reference 29

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 973d3081-81e5-46e6-a39a-23767b61f002 · outbound

This paper cites ‘Morse inequalities for the Koszul complex of multi-persistence’.

The fiber of multiparameter persistent homology for simplicial complexes ‘Morse inequalities for the Koszul complex of multi-persistence’

Reference 30

Resolution: malformed identifier; doi_truncated, observed 2026-08-06T20:17:35.173363Z

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Observation 575d1406-04f3-40c7-ab11-212250239851 · outbound

This paper cites an unresolved cited work.

The fiber of multiparameter persistent homology for simplicial complexes Unresolved cited work

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-06T20:17:32.681678Z

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Unavailable: canonical work link unavailable.

Observation 5ff6b940-9e23-4f11-8a95-cd2dee587eb4 · outbound

This paper cites an unresolved cited work.

The fiber of multiparameter persistent homology for simplicial complexes Unresolved cited work

Reference 32

Resolution: verified exact; raw_fallback, observed 2026-08-06T20:17:35.081092Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 48070b02-34f0-42ff-aaa3-863883c141ed · outbound

This paper cites Graphcode: Learning from multiparameter persistent homology using graph neural networks.

The fiber of multiparameter persistent homology for simplicial complexes Graphcode: Learning from multiparameter persistent homology using graph neural networks

Reference 33

Resolution: metadata mismatch; local_arxiv, observed 2026-08-06T20:17:33.964610Z

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Observation 545ab88e-eb07-4868-9cd9-018a7e6b42ed · outbound

This paper cites ‘Relative-perfectness of discrete gradient vector fields and multi-parameter persistent homology’.

The fiber of multiparameter persistent homology for simplicial complexes ‘Relative-perfectness of discrete gradient vector fields and multi-parameter persistent homology’

Reference 34

Resolution: verified exact; doi, observed 2026-08-06T20:17:33.940807Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation de685cd4-75e2-4518-89b4-b5dd9a58615b · outbound

This paper cites ‘The Theory of the Interleaving Distance on Multidimensional Persistence Mod- ules’.

The fiber of multiparameter persistent homology for simplicial complexes ‘The Theory of the Interleaving Distance on Multidimensional Persistence Mod- ules’

Reference 35

Resolution: malformed identifier; doi_truncated, observed 2026-08-06T20:17:33.922927Z

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Observation a4a000ea-69a3-4129-a17d-b20dfd31ea44 · outbound

This paper cites 2023.url:https : //www.albany.edu/~ML644186/840_2022/Math840_Notes_22.pdf.

The fiber of multiparameter persistent homology for simplicial complexes 2023.url:https : //www.albany.edu/~ML644186/840_2022/Math840_Notes_22.pdf

Reference 36

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0b6e2a93-384e-4f6a-87f5-a176d2191d0e · outbound

This paper cites Interactive Visualization of 2-D Persistence Modules.

The fiber of multiparameter persistent homology for simplicial complexes Interactive Visualization of 2-D Persistence Modules

Reference 37

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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 180f9939-bb9e-4c25-91c5-cf0f006a3819 · outbound

This paper cites ‘Fiber of persistent homology on morse functions’.

The fiber of multiparameter persistent homology for simplicial complexes ‘Fiber of persistent homology on morse functions’

Reference 38

Resolution: verified exact; doi, observed 2026-08-06T20:17:33.886438Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a4c6d40d-7482-4e8b-9998-30556935a76f · outbound

This paper cites ‘Algorithmic reconstruction of the fiber of persistent homology on cell complexes’.

The fiber of multiparameter persistent homology for simplicial complexes ‘Algorithmic reconstruction of the fiber of persistent homology on cell complexes’

Reference 39

Resolution: verified exact; doi, observed 2026-08-06T20:17:33.869583Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0bf7b4ec-2cc7-4734-8e7d-61be7131cdb2 · outbound

This paper cites ‘The fiber of persistent homology for simplicial complexes’.

The fiber of multiparameter persistent homology for simplicial complexes ‘The fiber of persistent homology for simplicial complexes’

Reference 40

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Observation 2b50654a-cacd-4052-b5a6-d74c35af2ee6 · outbound

This paper cites an unresolved cited work.

The fiber of multiparameter persistent homology for simplicial complexes Unresolved cited work

Reference 41

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation fa0e017e-9b91-49e1-a899-2c7427cef879 · outbound

This paper cites an unresolved cited work.

The fiber of multiparameter persistent homology for simplicial complexes Unresolved cited work

Reference 42

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Observation 60bed363-fe0d-4798-9cd0-75057526ced8 · outbound

This paper cites Nardini, Bernadette J.

The fiber of multiparameter persistent homology for simplicial complexes Nardini, Bernadette J

Reference 43

Resolution: verified exact; doi, observed 2026-08-06T20:17:33.850832Z

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Observation 737d3f43-482a-414c-89a7-f9a08858883d · outbound

This paper cites ‘On the Stability of Multigraded Betti Numbers and Hilbert Functions’.

The fiber of multiparameter persistent homology for simplicial complexes ‘On the Stability of Multigraded Betti Numbers and Hilbert Functions’

Reference 44

Resolution: verified exact; doi, observed 2026-08-06T20:17:33.831272Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation cb5da254-8c48-426f-9b93-1623b0c7d7bf · outbound

This paper cites ‘On the Stability of Multigraded Betti Numbers and Hilbert Functions’.

The fiber of multiparameter persistent homology for simplicial complexes ‘On the Stability of Multigraded Betti Numbers and Hilbert Functions’

Reference 45

Resolution: verified exact; doi, observed 2026-08-06T20:17:33.811943Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2fb86cd1-bec4-4601-9812-05e359d3c012 · outbound

This paper cites S´ anchez-Garc ´ ıa.

The fiber of multiparameter persistent homology for simplicial complexes S´ anchez-Garc ´ ıa

Reference 46

Resolution: verified exact; doi, observed 2026-08-06T20:17:33.794184Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 49c5a648-94b4-4596-8187-c00106d3fb7c · outbound

This paper cites ‘Differen- tiability and optimization of multiparameter persistent homology’.

The fiber of multiparameter persistent homology for simplicial complexes ‘Differen- tiability and optimization of multiparameter persistent homology’

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:17:35.369101Z

Source-reported events for the cited work

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Observation af95349e-8d5b-4616-9f9f-889455995cf8 · outbound

This paper cites ‘Generic families of finite metric spaces with identical or trivial 1-dimensional persistence’.

The fiber of multiparameter persistent homology for simplicial complexes ‘Generic families of finite metric spaces with identical or trivial 1-dimensional persistence’

Reference 48

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Observation 14d41d87-144c-4f72-a44b-862465afe8e5 · outbound

This paper cites Bull, Philip S.

The fiber of multiparameter persistent homology for simplicial complexes Bull, Philip S

Reference 49

Resolution: verified exact; doi, observed 2026-08-06T20:17:33.756610Z

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No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 789ad47a-f1ac-40ae-ba8b-97705f8c3725 · outbound

This paper cites An Introduction to Multiparameter Persistence.

The fiber of multiparameter persistent homology for simplicial complexes An Introduction to Multiparameter Persistence

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-06T20:17:30.894564Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.