Paper Citation Record · LEDGER

Path representations in multiparameter persistent homology

As of 9 August 2026, this Paper Citation Record lists 47 of 47 outbound references and 0 inbound Pith citation observations for arXiv:2507.23762.

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

pith.paper-citation-record.v1
2507.23762 v1

Coverage vector

measured 47 of 47 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T10:32:45.952876Z

measured 47 of 47 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

47 of 47 outbound references displayed

verified exact10
verified fuzzy31
unresolved5
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5f84952d-15cf-4bdb-8220-3a388f75a81d · outbound

This paper cites Computing the interleaving distance is NP-hard.

Path representations in multiparameter persistent homology Computing the interleaving distance is NP-hard

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.603747Z

Source-reported events for the cited work

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Observation a7b55cf8-76de-4482-b1c1-1474e2d838df · outbound

This paper cites $\ell^p$-Distances on Multiparameter Persistence Modules.

Path representations in multiparameter persistent homology $\ell^p$-Distances on Multiparameter Persistence Modules

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-06T10:32:45.781253Z

Source-reported events for the cited work

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Observation d5fce9bf-1d79-455a-915f-71235b9ba0fe · outbound

This paper cites An Introduction to Multiparameter Persistence.

Path representations in multiparameter persistent homology An Introduction to Multiparameter Persistence

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-06T10:32:45.785059Z

Source-reported events for the cited work

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Observation 750849d9-a816-409c-9a5b-41e8db99fcbe · outbound

This paper cites Exact weights, path metrics, and algebraic Wasserstein distances.

Path representations in multiparameter persistent homology Exact weights, path metrics, and algebraic Wasserstein distances

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-08-06T10:32:46.226291Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 89f3cffc-6e21-4723-83cf-d1408ccb6ffe · outbound

This paper cites Embeddings of per- sistence diagrams into Hilbert spaces.

Path representations in multiparameter persistent homology Embeddings of per- sistence diagrams into Hilbert spaces

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.592114Z

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Observation 183e1501-3e86-410e-86e4-97e0541955b2 · outbound

This paper cites The theory of mul- tidimensional persistence.

Path representations in multiparameter persistent homology The theory of mul- tidimensional persistence

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.582088Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d9c6418a-d022-43d8-a916-2e7debac7794 · outbound

This paper cites On the Metric Distortion of Embedding Persistence Diagrams into separable Hilbert spaces.

Path representations in multiparameter persistent homology On the Metric Distortion of Embedding Persistence Diagrams into separable Hilbert spaces

Reference 7

Resolution: verified exact; local_arxiv, observed 2026-08-06T10:32:46.209145Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d949dbd3-d551-4b89-8e12-1c596c47ac08 · outbound

This paper cites Multiparameter persistence image for topological machine learning.

Path representations in multiparameter persistent homology Multiparameter persistence image for topological machine learning

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.572315Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 09383ea0-05d4-4615-9794-d2d8d4f63b2b · outbound

This paper cites Sliced Wasserstein kernel for persistence diagrams.

Path representations in multiparameter persistent homology Sliced Wasserstein kernel for persistence diagrams

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.560767Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation dc87d5dc-0c84-486c-af24-c3c884ee89e0 · outbound

This paper cites On the ge- ometrical properties of the coherent matching distance in 2D persistent homology.

Path representations in multiparameter persistent homology On the ge- ometrical properties of the coherent matching distance in 2D persistent homology

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.548463Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d26d7eed-83af-4106-aa2f-0f37fa25dede · outbound

This paper cites Betti numbers in multidimensional per- sistent homology are stable functions.

Path representations in multiparameter persistent homology Betti numbers in multidimensional per- sistent homology are stable functions

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.536346Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation b3cbca07-276b-4ee2-811d-c82d802f50c4 · outbound

This paper cites The Shift-Dimension of Multipersistence Modules.

Path representations in multiparameter persistent homology The Shift-Dimension of Multipersistence Modules

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-08-06T10:32:46.001981Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 4d6e5c26-0fa7-46ab-9e50-8a932f74b837 · outbound

This paper cites Geometric Inference for Probability Measures.

Path representations in multiparameter persistent homology Geometric Inference for Probability Measures

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.526243Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 565dbd27-bf76-4f56-bbee-2b377fab71d1 · outbound

This paper cites Proximity of Persistence Modules and Their Diagrams.

Path representations in multiparameter persistent homology Proximity of Persistence Modules and Their Diagrams

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.515367Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 693b4cb8-2a47-46dc-8e30-11c0a7be3122 · outbound

This paper cites Stability of Persistence Diagrams.

Path representations in multiparameter persistent homology Stability of Persistence Diagrams

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.504216Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 01125a9c-d860-4360-a7c9-89311be7355a · outbound

This paper cites The representation the- orem of persistence revisited and generalized.

Path representations in multiparameter persistent homology The representation the- orem of persistence revisited and generalized

Reference 16

Resolution: malformed identifier; doi_truncated, observed 2026-08-06T10:32:45.982850Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 7fbabcb3-463e-4284-9aab-eeb1c7a1b51c · outbound

This paper cites A kernel for multi-parameter persistent homology.

Path representations in multiparameter persistent homology A kernel for multi-parameter persistent homology

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.493283Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6c21b3ad-4dbf-46e4-968d-108cdf9f5c61 · outbound

This paper cites Computing the Multicover Bifiltration.

Path representations in multiparameter persistent homology Computing the Multicover Bifiltration

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.482283Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 57f0d3b7-0268-427e-8373-9600c24ff17d · outbound

This paper cites ToDD: Topological compound finger- printing in computer-aided drug discovery.

Path representations in multiparameter persistent homology ToDD: Topological compound finger- printing in computer-aided drug discovery

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.472591Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e87b166d-eeae-4854-b0b3-e195e09431a8 · outbound

This paper cites Commutative Algebra: With a View Toward Algebraic Geometry.

Path representations in multiparameter persistent homology Commutative Algebra: With a View Toward Algebraic Geometry

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.462683Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0f68d8b7-dc2b-4840-86fe-9956b77b4f72 · outbound

This paper cites Unzerlegbare Darstellungen I.

Path representations in multiparameter persistent homology Unzerlegbare Darstellungen I

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.452746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f656ee0b-ec17-408c-9565-8a0d836cbc32 · outbound

This paper cites Stable Invariants for Multiparameter Persistence.

Path representations in multiparameter persistent homology Stable Invariants for Multiparameter Persistence

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-06T10:32:45.857059Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1e7b7b83-87f9-4699-9944-0bd5a64a63a9 · outbound

This paper cites Barcodes: the persistent topology of data.

Path representations in multiparameter persistent homology Barcodes: the persistent topology of data

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.443358Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 549934d3-e228-4958-b60a-3cd31bddcf63 · outbound

This paper cites Stratifying multiparameter persistent homology.

Path representations in multiparameter persistent homology Stratifying multiparameter persistent homology

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-08-06T10:32:46.181481Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation afb99f4b-976c-43e6-9784-5129b409b1ea · outbound

This paper cites Per- sistent Homology for Virtual Screening.

Path representations in multiparameter persistent homology Per- sistent Homology for Virtual Screening

Reference 26

Resolution: verified exact; raw_fallback, observed 2026-08-06T10:32:46.163588Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 5f9a4447-3abc-4809-b284-36e9dade8a25 · outbound

This paper cites Exact Computation of the Matching Distance on 2-Parameter Per- sistence Modules.

Path representations in multiparameter persistent homology Exact Computation of the Matching Distance on 2-Parameter Per- sistence Modules

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.432104Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 66ec2d8b-4417-4546-9dd2-7d6740fe36af · outbound

This paper cites Ge- ometry Helps to Compare Persistence Diagrams.

Path representations in multiparameter persistent homology Ge- ometry Helps to Compare Persistence Diagrams

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.421634Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f51a2402-5f66-4807-8037-9427dfc0dcfd · outbound

This paper cites Efficient Approxima- tion of the Matching Distance for 2-Parameter Persistence.

Path representations in multiparameter persistent homology Efficient Approxima- tion of the Matching Distance for 2-Parameter Persistence

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.410463Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 7fc88528-c0fb-402f-94f6-945b542148c7 · outbound

This paper cites Per- sistence weighted Gaussian kernel for topological data anal- ysis.

Path representations in multiparameter persistent homology Per- sistence weighted Gaussian kernel for topological data anal- ysis

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.399552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0ef2d119-12ce-479e-8304-1d9997799311 · outbound

This paper cites The rank invariant stability via interleavings.

Path representations in multiparameter persistent homology The rank invariant stability via interleavings

Reference 31

Resolution: verified exact; local_arxiv, observed 2026-08-06T10:32:46.096791Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 3dc2d307-eaa1-439d-bcec-acdabd59c92a · outbound

This paper cites The theory of the interleaving distance on multidimensional persistence modules.

Path representations in multiparameter persistent homology The theory of the interleaving distance on multidimensional persistence modules

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.387542Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation cec4ff9b-4f4e-497e-a193-91c086acccaf · outbound

This paper cites Computing Minimal Presentations and Bigraded Betti Numbers of 2-Parameter Persistent Homology.

Path representations in multiparameter persistent homology Computing Minimal Presentations and Bigraded Betti Numbers of 2-Parameter Persistent Homology

Reference 33

Resolution: verified exact; local_arxiv, observed 2026-08-06T10:32:46.078012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6242606e-cc92-4f6b-aecd-c88ab7fd27f5 · outbound

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

Path representations in multiparameter persistent homology Interactive Visualization of 2-D Persistence Modules

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-06T10:32:45.900452Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation be1b432d-7c6d-4a49-b029-088bd1c0ace0 · outbound

This paper cites Proba- bility measures on the space of persistence diagrams.

Path representations in multiparameter persistent homology Proba- bility measures on the space of persistence diagrams

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.374348Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d2cd58ae-db1e-42e6-abed-7df2ab68cdae · outbound

This paper cites Data structures for real multiparameter persistence modules.

Path representations in multiparameter persistent homology Data structures for real multiparameter persistence modules

Reference 36

Resolution: verified exact; local_arxiv, observed 2026-08-06T10:32:46.052232Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 26805ba3-bb17-4bd7-b7bd-d4838803ecf1 · outbound

This paper cites an unresolved cited work.

Path representations in multiparameter persistent homology Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-08-06T10:32:46.364014Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 9f1d9c6f-e10f-4782-8f9f-ddc4608a1f90 · outbound

This paper cites Topological autoencoders.

Path representations in multiparameter persistent homology Topological autoencoders

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.353812Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation dccd9b4b-0c60-4347-95cc-101d7abe9c7c · outbound

This paper cites A stable multi-scale kernel for topo- logical machine learning.

Path representations in multiparameter persistent homology A stable multi-scale kernel for topo- logical machine learning

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.342329Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 201291e4-6ea9-4cf3-a487-61697b33334b · outbound

This paper cites Generalized persistence analysis based on stable rank invariant.

Path representations in multiparameter persistent homology Generalized persistence analysis based on stable rank invariant

Reference 40

Resolution: verified exact; local_arxiv, observed 2026-08-06T10:32:46.033970Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 3d887650-df1c-4383-b7ef-e5fab43b712a · outbound

This paper cites Multidimensional persistence and noise.

Path representations in multiparameter persistent homology Multidimensional persistence and noise

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.330779Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 9ba0ace9-c70c-4562-8f5b-e94bef3e33c7 · outbound

This paper cites A Multicover Nerve for Geometric In- ference.

Path representations in multiparameter persistent homology A Multicover Nerve for Geometric In- ference

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.317374Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 8180f292-04ab-4daa-b1a2-925dd7d46a88 · outbound

This paper cites ReinBo: Machine learning pipeline conditional hierarchy search and configu- ration with Bayesian optimization embedded reinforcement learning.

Path representations in multiparameter persistent homology ReinBo: Machine learning pipeline conditional hierarchy search and configu- ration with Bayesian optimization embedded reinforcement learning

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.304629Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0cfb27dd-2bf0-4e27-bf36-8bee6f5944c8 · outbound

This paper cites Reinforcement learning.

Path representations in multiparameter persistent homology Reinforcement learning

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.290749Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e721d49f-68fd-4f10-b538-481ddb82ef35 · outbound

This paper cites Invariants and Metrics for Multiparame- ter Persistent Homology.

Path representations in multiparameter persistent homology Invariants and Metrics for Multiparame- ter Persistent Homology

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.280799Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation f8893048-2bdd-4dae-92f7-db5216198420 · outbound

This paper cites Fréchet means for distributions of persistence diagrams.

Path representations in multiparameter persistent homology Fréchet means for distributions of persistence diagrams

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.269222Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 864c687e-c07e-4d3e-bb68-012d2343d4e4 · outbound

This paper cites Multiparameter Persistence Landscapes.

Path representations in multiparameter persistent homology Multiparameter Persistence Landscapes

Reference 47

Resolution: verified exact; local_arxiv, observed 2026-08-06T10:32:46.018741Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d3a76b37-2d40-4cd9-9974-85d0918ea299 · outbound

This paper cites Nonembeddability of persistence dia- grams with p> 2 Wasserstein metric.

Path representations in multiparameter persistent homology Nonembeddability of persistence dia- grams with p> 2 Wasserstein metric

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:32:46.257181Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Pith citing papers

No inbound Pith citation observations are available.