Paper Citation Record · LEDGER

Barcoding Invariants and Their Comparison

As of 12 August 2026, this Paper Citation Record lists 65 of 65 outbound references and 2 inbound Pith citation observations for arXiv:2412.04995.

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

pith.paper-citation-record.v1
2412.04995 v3

Coverage vector

measured 65 of 65 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T21:14:32.710233Z

measured 67 of 67 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T11:47:50.267009Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-11T05:45:57.347948Z

Reference resolution

65 of 65 outbound references displayed

verified exact3
verified fuzzy41
unresolved21
parse uncertain0
malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation e0c9a77a-21bb-4011-9e52-beb027a9e159 · outbound

This paper cites Mathematische Annalen, 256(3):401–418, 1981.

Barcoding Invariants and Their Comparison Mathematische Annalen, 256(3):401–418, 1981

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:34.075874Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 54ce3903-17ba-46cc-883f-96b54152733c · outbound

This paper cites Invariants of persistence modules defined by order-embeddings.

Barcoding Invariants and Their Comparison Invariants of persistence modules defined by order-embeddings

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-08-11T21:14:33.300871Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 224562b2-9209-4bd0-be53-b234050da10b · outbound

This paper cites Summand-injectivity of interval covers and monotonicity of interval resolution global dimensions.

Barcoding Invariants and Their Comparison Summand-injectivity of interval covers and monotonicity of interval resolution global dimensions

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-11T21:14:32.407657Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cd2fcc54-37ea-477d-b26d-3104cbbf0b42 · outbound

This paper cites Approx- imation by interval-decomposables and interval resolutions of persistence modules.

Barcoding Invariants and Their Comparison Approx- imation by interval-decomposables and interval resolutions of persistence modules

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:34.060625Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 6d0bf54f-aa01-4e3f-8d9d-9b4b52e9f0e2 · outbound

This paper cites On ap- proximation of 2D persistence modules by interval-decomposables.Journal of Compu- tational Algebra, 6:100007, 2023.

Barcoding Invariants and Their Comparison On ap- proximation of 2D persistence modules by interval-decomposables.Journal of Compu- tational Algebra, 6:100007, 2023

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:34.043315Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c572d72c-d287-4ef8-ad83-dd72f21671c5 · outbound

This paper cites Interval replacements of persis- tence modules.arXiv preprint arXiv:2403.08308, 2024.

Barcoding Invariants and Their Comparison Interval replacements of persis- tence modules.arXiv preprint arXiv:2403.08308, 2024

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-11T21:14:32.422441Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cfc01179-300d-4120-8acf-c618b09a19d2 · outbound

This paper cites Cotorsion tor- sion triples and the representation theory of filtered hierarchical clustering.Advances in Mathematics, 369:107171, 2020.

Barcoding Invariants and Their Comparison Cotorsion tor- sion triples and the representation theory of filtered hierarchical clustering.Advances in Mathematics, 369:107171, 2020

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:34.026089Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation cd6c3c29-d5f0-4da5-b265-342971090c78 · outbound

This paper cites an unresolved cited work.

Barcoding Invariants and Their Comparison Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:14:34.008731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 395652d5-6369-426c-a661-384a72875171 · outbound

This paper cites Exact structures for persistence modules.

Barcoding Invariants and Their Comparison Exact structures for persistence modules

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-11T21:14:32.438413Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a7ca00cb-f2d5-47d0-8a88-bc837dd61320 · outbound

This paper cites Handbookofcategoricalalgebra: volume1,Basiccategorytheory ,volume1.

Barcoding Invariants and Their Comparison Handbookofcategoricalalgebra: volume1,Basiccategorytheory ,volume1

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.993003Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d25e3fde-09ad-4222-b7e1-7ed76bab8516 · outbound

This paper cites Handbook of Categorical Algebra: Volume 2, Categories and Structures, volume 2.

Barcoding Invariants and Their Comparison Handbook of Categorical Algebra: Volume 2, Categories and Structures, volume 2

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.976791Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1dfde62f-4a6d-4101-aa7d-779221fd98c7 · outbound

This paper cites Decompositionofpersistencemodules.

Barcoding Invariants and Their Comparison Decompositionofpersistencemodules

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.958805Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c3c62000-c93a-4512-bcfa-593544173723 · outbound

This paper cites Algebraic stability of zigzag persistence mod- ules.

Barcoding Invariants and Their Comparison Algebraic stability of zigzag persistence mod- ules

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.940363Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation cf477957-829d-4da3-ba7e-a637ec45a6ce · outbound

This paper cites An Introduction to Multiparameter Persistence.

Barcoding Invariants and Their Comparison An Introduction to Multiparameter Persistence

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-11T21:14:32.464158Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1af3f315-b8fc-4a29-85b3-4643b16787d3 · outbound

This paper cites Signed barcodes for multi-parameterpersistenceviarankdecompositionsandrank-exactresolutions.

Barcoding Invariants and Their Comparison Signed barcodes for multi-parameterpersistenceviarankdecompositionsandrank-exactresolutions

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.923093Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e10e3417-3011-4177-87b5-232bc5b4a6a6 · outbound

This paper cites Metrics for generalized persistence modules.

Barcoding Invariants and Their Comparison Metrics for generalized persistence modules

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.906819Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e3af8430-1c9a-432e-8e3d-e757db78ac6f · outbound

This paper cites Exact categories.Expositiones Mathematicae, 28(1):1–69, 2010.

Barcoding Invariants and Their Comparison Exact categories.Expositiones Mathematicae, 28(1):1–69, 2010

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.891445Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 220a7f97-2f52-44ff-88ba-c9aae28ca382 · outbound

This paper cites Elder-rule-staircodes for augmentedmetricspaces.

Barcoding Invariants and Their Comparison Elder-rule-staircodes for augmentedmetricspaces

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.874534Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 2d804e86-4e3a-4583-b0e8-3599b6af4efa · outbound

This paper cites A topological approach for protein classification.

Barcoding Invariants and Their Comparison A topological approach for protein classification

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-11T21:14:32.487618Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1884d286-a61d-4f4e-92b5-88f604cf9d02 · outbound

This paper cites Cambridge University Press, 2021.

Barcoding Invariants and Their Comparison Cambridge University Press, 2021

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.845050Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8f79e35a-0301-4985-b04e-ea820196a0d1 · outbound

This paper cites The theory of multidimensional persistence.

Barcoding Invariants and Their Comparison The theory of multidimensional persistence

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-11T21:14:32.497859Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f35f3bfb-94c2-43bc-8abc-1ba1c9dd4eb3 · outbound

This paper cites Koszul complexes and relative homological algebra of functors over posets.

Barcoding Invariants and Their Comparison Koszul complexes and relative homological algebra of functors over posets

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.817244Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 8c792395-4fc0-4d71-80f9-a963ad894c66 · outbound

This paper cites Persistent homology over directed acyclic graphs.

Barcoding Invariants and Their Comparison Persistent homology over directed acyclic graphs

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.799799Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 858084b1-e0b4-4ca8-8dac-91be055ce741 · outbound

This paper cites Topology of viral evolu- tion.

Barcoding Invariants and Their Comparison Topology of viral evolu- tion

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.782576Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 082d1151-4751-4a3c-894d-3026b9b43fc0 · outbound

This paper cites Meta-Diagrams for 2-Parameter Persistence.

Barcoding Invariants and Their Comparison Meta-Diagrams for 2-Parameter Persistence

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-11T21:14:32.517235Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1a0b441b-cf57-45fe-9f0e-e656097e55a8 · outbound

This paper cites The Generalized Rank Invariant: M\"obius invertibility, Discriminating Power, and Connection to Other Invariants.

Barcoding Invariants and Their Comparison The Generalized Rank Invariant: M\"obius invertibility, Discriminating Power, and Connection to Other Invariants

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-11T21:14:32.521996Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 819e88ff-47ea-4481-b17a-ec0b9ecad412 · outbound

This paper cites Stability of persistence diagrams.

Barcoding Invariants and Their Comparison Stability of persistence diagrams

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-11T21:14:32.527334Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7408c09b-6c06-46eb-b6f4-3d48d47f1ee5 · outbound

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

Barcoding Invariants and Their Comparison Decomposition of pointwise finite-dimensional persistence modules

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-11T21:14:32.532190Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation deef6885-41b4-4f95-9f65-0e50e7e68d7c · outbound

This paper cites A topological paradigm for hip- pocampal spatial map formation using persistent homology.PLoS Computational Biol- ogy, 8(8), 2012.

Barcoding Invariants and Their Comparison A topological paradigm for hip- pocampal spatial map formation using persistent homology.PLoS Computational Biol- ogy, 8(8), 2012

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.744731Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 4d206e43-7545-42fd-b02f-5a0c50846ea9 · outbound

This paper cites SE(3)-Invariant Multiparameter Persistent Homology for Chiral-Sensitive Molecular Property Prediction.

Barcoding Invariants and Their Comparison SE(3)-Invariant Multiparameter Persistent Homology for Chiral-Sensitive Molecular Property Prediction

Reference 30

Resolution: verified exact; local_arxiv, observed 2026-08-11T21:14:33.115483Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 19cd2691-205d-4b55-9a0e-1e9272b627be · outbound

This paper cites Quiver representations.

Barcoding Invariants and Their Comparison Quiver representations

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.729245Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 857d3485-bdff-4d8f-b238-0a6fa9dd7e40 · outbound

This paper cites Computing generalized rank invari- ant for 2-parameter persistence modules via zigzag persistence and its applications.

Barcoding Invariants and Their Comparison Computing generalized rank invari- ant for 2-parameter persistence modules via zigzag persistence and its applications

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.713917Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation bbed6193-5634-49b0-b546-fba1a486b800 · outbound

This paper cites Persistencemodulesoncommutativeladders of finite type.Discrete & Computational Geometry, 55:100–157, 2016.

Barcoding Invariants and Their Comparison Persistencemodulesoncommutativeladders of finite type.Discrete & Computational Geometry, 55:100–157, 2016

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.698114Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 34e086ea-a7d1-4e20-bcb2-fb95f9d2e21a · outbound

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

Barcoding Invariants and Their Comparison Harder-Narasimhan filtrations of persistence modules: metric stability

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-11T21:14:32.562726Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 90126253-0c49-4a83-9a1d-22f5e6cd3e80 · outbound

This paper cites Harder- narasimhan filtrations of persistence modules.arXiv preprint arXiv:2303.16075, 2023.

Barcoding Invariants and Their Comparison Harder- narasimhan filtrations of persistence modules.arXiv preprint arXiv:2303.16075, 2023

Reference 35

Resolution: verified exact; raw_fallback, observed 2026-08-11T21:14:33.071411Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation acde9cc6-a541-4f6d-9b97-62ac42c9f818 · outbound

This paper cites Harper & Row New York, 1964.

Barcoding Invariants and Their Comparison Harper & Row New York, 1964

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.681491Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 50ecf4cc-0bad-4761-8ded-dd160ff9a4c2 · outbound

This paper cites Springer Science & Business Media, 1992.

Barcoding Invariants and Their Comparison Springer Science & Business Media, 1992

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.665345Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 9468e0f0-59d8-46bc-8935-82858f5ebecb · outbound

This paper cites Global dimension of real-exponent polynomial rings.

Barcoding Invariants and Their Comparison Global dimension of real-exponent polynomial rings

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.649309Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 2340316b-f024-4623-8877-06c380552a2e · outbound

This paper cites Galois Connections in Persistent Homology.

Barcoding Invariants and Their Comparison Galois Connections in Persistent Homology

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-11T21:14:32.587310Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0004cff1-6842-416d-8d4c-4fe1ecb87c9d · outbound

This paper cites Grassmannian Persistence Diagrams.

Barcoding Invariants and Their Comparison Grassmannian Persistence Diagrams

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-11T21:14:32.592445Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2050c067-23f0-4f48-84c9-2d5cfa9832f5 · outbound

This paper cites Applications of persistent homology in nuclear collisions.Phys.

Barcoding Invariants and Their Comparison Applications of persistent homology in nuclear collisions.Phys

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.632310Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 1c105599-5801-4a49-b969-39383125a708 · outbound

This paper cites Hierarchical structures of amorphous solids char- acterized by persistent homology.

Barcoding Invariants and Their Comparison Hierarchical structures of amorphous solids char- acterized by persistent homology

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.615464Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7726c505-b8f7-4936-ac66-55e10f5e5d9e · outbound

This paper cites Refinement of Interval Approximations for Fully Commutative Quivers.

Barcoding Invariants and Their Comparison Refinement of Interval Approximations for Fully Commutative Quivers

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-11T21:14:32.606249Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b1ed24ee-c3d6-44eb-92d1-f0df8f6c70af · outbound

This paper cites Generalized persistence diagrams for persistence modules over posets.Journal of Applied and Computational Topology, 5(4):533–581, 2021.

Barcoding Invariants and Their Comparison Generalized persistence diagrams for persistence modules over posets.Journal of Applied and Computational Topology, 5(4):533–581, 2021

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.598061Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d0f65d2d-26ed-4eb5-9911-f134bcf02d2a · outbound

This paper cites Spatiotemporal persistent homology for dynamic metric spaces.Discrete & Computational Geometry, 66(3):831–875, 2021.

Barcoding Invariants and Their Comparison Spatiotemporal persistent homology for dynamic metric spaces.Discrete & Computational Geometry, 66(3):831–875, 2021

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.582581Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 08e07eda-f6f9-4b6e-8b2c-3d5f2a5e2d15 · outbound

This paper cites Persistence over posets.Notices of the American Mathematical Society, 70(08), 2023.

Barcoding Invariants and Their Comparison Persistence over posets.Notices of the American Mathematical Society, 70(08), 2023

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.567332Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation bd45d929-9846-4463-8c30-ee08ef238f90 · outbound

This paper cites Journal of Applied and Computatioal Topology, 2024.

Barcoding Invariants and Their Comparison Journal of Applied and Computatioal Topology, 2024

Reference 47

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.550654Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e91d01de-8c65-4bb1-ba91-b1ff9eacdbac · outbound

This paper cites The rank of a quiver representation.Journal of Algebra, 320(6):2363–2387, 2008.

Barcoding Invariants and Their Comparison The rank of a quiver representation.Journal of Algebra, 320(6):2363–2387, 2008

Reference 48

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.534106Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation cc83fd71-2e69-41d5-ab7c-49158f66e509 · outbound

This paper cites Krull–schmidt categories and projective covers.Expositiones Mathe- maticae, 33(4):535–549, 2015.

Barcoding Invariants and Their Comparison Krull–schmidt categories and projective covers.Expositiones Mathe- maticae, 33(4):535–549, 2015

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.517957Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 94f81f12-db4c-4e4c-90be-681cbd6d80d4 · outbound

This paper cites an unresolved cited work.

Barcoding Invariants and Their Comparison Unresolved cited work

Reference 50

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:14:33.502095Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 017bd33f-1b1f-4d1f-9c3a-86149405199a · outbound

This paper cites Computing fringe presentations of multigraded persistence modules.

Barcoding Invariants and Their Comparison Computing fringe presentations of multigraded persistence modules

Reference 51

Resolution: unresolved; no resolver link, observed 2026-08-11T21:14:32.644043Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fd63505a-6725-4ca1-bba4-e47db882d001 · outbound

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

Barcoding Invariants and Their Comparison Interactive Visualization of 2-D Persistence Modules

Reference 52

Resolution: unresolved; no resolver link, observed 2026-08-11T21:14:32.649038Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 48ef47ab-44b9-484c-afbb-6bd10c15f7c0 · outbound

This paper cites Algebraicstructuresongrothendieckgroups.

Barcoding Invariants and Their Comparison Algebraicstructuresongrothendieckgroups

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.485667Z

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Observation c8d07281-0651-41e3-b34b-30e4e932868a · outbound

This paper cites Categoriesfortheworkingmathematician ,volume5.

Barcoding Invariants and Their Comparison Categoriesfortheworkingmathematician ,volume5

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.468106Z

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Observation e20de5f6-9eac-45b9-a0df-fb497b1d5984 · outbound

This paper cites Edit distance and persistence diagrams over lat- tices.

Barcoding Invariants and Their Comparison Edit distance and persistence diagrams over lat- tices

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.450004Z

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Observation 84cb5996-77c0-4eaa-b130-294fc9ab1331 · outbound

This paper cites Homological algebra of modules over posets.

Barcoding Invariants and Their Comparison Homological algebra of modules over posets

Reference 56

Resolution: unresolved; no resolver link, observed 2026-08-11T21:14:32.668253Z

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Observation b6abec5c-c878-471e-a41c-ae7139c633ab · outbound

This paper cites Combinatorial commutative algebra, volume 227.

Barcoding Invariants and Their Comparison Combinatorial commutative algebra, volume 227

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.431172Z

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Observation 039b511f-218d-4f38-afb3-c8995d456e18 · outbound

This paper cites On the stability of multigraded betti numbers and hilbert functions.SIAM Journal on Applied Algebra and Geometry, 8(1):54–88, 2024.

Barcoding Invariants and Their Comparison On the stability of multigraded betti numbers and hilbert functions.SIAM Journal on Applied Algebra and Geometry, 8(1):54–88, 2024

Reference 58

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.414660Z

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Observation b46f3aef-fd0a-4864-b1b4-741fcc3d3c8d · outbound

This paper cites Generalized persistence diagrams.

Barcoding Invariants and Their Comparison Generalized persistence diagrams

Reference 59

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.398833Z

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Observation f722f7c3-b31a-4f2a-a585-74630efecde3 · outbound

This paper cites OnthefoundationsofcombinatorialtheoryI:TheoryofMöbiusfunc- tions.

Barcoding Invariants and Their Comparison OnthefoundationsofcombinatorialtheoryI:TheoryofMöbiusfunc- tions

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.383082Z

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Observation e4cbec28-ec99-4401-89b7-a88aa6081b6e · outbound

This paper cites Graphcode: Learning from multiparameter per- sistent homology using graph neural networks.

Barcoding Invariants and Their Comparison Graphcode: Learning from multiparameter per- sistent homology using graph neural networks

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.365177Z

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Observation a6caae24-0671-4d17-9799-33a8d8dfee9b · outbound

This paper cites Enumerative combinatorics volume 1 second edition.Cambridge studies in advanced mathematics, 2011.

Barcoding Invariants and Their Comparison Enumerative combinatorics volume 1 second edition.Cambridge studies in advanced mathematics, 2011

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Resolution: unresolved; no resolver link, observed 2026-08-11T21:14:32.695670Z

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Observation 9fc6c6ec-481e-49dd-b96e-2a4ccd5b698f · outbound

This paper cites Relational persistent homology for multispecies data with application to the tumor microenvironment.

Barcoding Invariants and Their Comparison Relational persistent homology for multispecies data with application to the tumor microenvironment

Reference 63

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Observation cb091780-6c15-4686-9b5a-9ca2d4495a6b · outbound

This paper cites PhD thesis, Duke University, 2019.

Barcoding Invariants and Their Comparison PhD thesis, Duke University, 2019

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.334469Z

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Observation 48533509-6ff0-43b7-80c4-b3c97169add4 · outbound

This paper cites Computing persistent homology.Discrete & Computational Geometry, 33(2):249–274, 2005.

Barcoding Invariants and Their Comparison Computing persistent homology.Discrete & Computational Geometry, 33(2):249–274, 2005

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Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T21:14:33.317429Z

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Pith citing papers

Observation 40add9d9-8648-4f0f-8c81-de73a5e0c95b · inbound

Stabilization of the Spread-Global Dimension cites this paper.

Stabilization of the Spread-Global Dimension Barcoding Invariants and Their Comparison

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-07T11:47:50.267009Z

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Observation bd2a5524-6afa-4f66-a2ae-2320c2c0d444 · inbound

An Algebraic Introduction to Persistence cites this paper.

An Algebraic Introduction to Persistence Barcoding Invariants and Their Comparison

Reference 100

Resolution: verified exact; arxiv_id, observed 2026-06-30T02:15:33.021711Z

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