Paper Citation Record · LEDGER

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent

As of 12 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:2412.05900.

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

pith.paper-citation-record.v1
2412.05900 v2

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T20:19:01.032157Z

measured 34 of 34 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 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

34 of 34 outbound references displayed

verified exact4
verified fuzzy25
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 47aa870a-ca4c-4eb1-9ba5-2e8800311d37 · outbound

This paper cites Interval replacements of persistence modules.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent Interval replacements of persistence modules

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-11T20:19:00.885243Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 01957f8a-ecdb-484b-8d8c-6f6ac9e7dc00 · outbound

This paper cites Corrections and supplementaries to my paper concerning K rull- R emak- S chmidt’s theorem.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent Corrections and supplementaries to my paper concerning K rull- R emak- S chmidt’s theorem

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:19:01.613138Z

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 ff9738e6-be77-452b-978d-295840675683 · outbound

This paper cites Cotorsion torsion triples and the representation theory of filtered hierarchical clustering.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent Cotorsion torsion triples and the representation theory of filtered hierarchical clustering

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:19:01.597733Z

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 5af39aae-492a-468e-8ed9-18d277d43abf · outbound

This paper cites Decomposition of persistence modules.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent Decomposition of persistence modules

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:19:01.583551Z

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 d47b09ab-9f51-435f-8813-d06e754e0a0e · outbound

This paper cites Algebraic stability of zigzag persistence modules.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent Algebraic stability of zigzag persistence modules

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:19:01.570144Z

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 93e9f7c0-2f4e-4c42-8e9b-deb522bab8a1 · outbound

This paper cites An introduction to multiparameter persistence.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent An introduction to multiparameter persistence

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:19:01.555653Z

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 0a76f9ec-3b93-41d2-9929-4dd3d4383874 · outbound

This paper cites Signed barcodes for multi-parameter persistence via rank decompositions and rank-exact resolutions.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent Signed barcodes for multi-parameter persistence via rank decompositions and rank-exact resolutions

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:19:01.542003Z

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 6feccd33-d7a0-4d31-81de-838310af459f · outbound

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

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent On the bottleneck stability of rank decompositions of multi-parameter persistence modules

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:19:01.529073Z

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 3bf2aff4-a95f-4dfd-8bf8-02f2c4aca9a7 · outbound

This paper cites The theory of multidimensional persistence.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent The theory of multidimensional persistence

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-11T20:19:00.922981Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fb7988c7-6c51-4a24-9388-41560c8bf726 · outbound

This paper cites Multiparameter persistence image for topological machine learning.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent Multiparameter persistence image for topological machine learning

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:19:01.507557Z

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 d0ae526c-cc7b-43c0-8f93-3f446d98f056 · outbound

This paper cites Proximity of persistence modules and their diagrams.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent Proximity of persistence modules and their diagrams

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:19:01.493626Z

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 e01e754f-a187-435c-a9b4-b46edbbe81d2 · outbound

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

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent The Generalized Rank Invariant: M\"obius invertibility, Discriminating Power, and Connection to Other Invariants

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-11T20:19:00.935486Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation db024957-586b-45b2-8ca2-40baa7250925 · outbound

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

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent A kernel for multi-parameter persistent homology

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:19:01.479799Z

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 aa488f98-7ec0-47e2-bf28-a685ee03c529 · outbound

This paper cites The UCR Time Series Archive.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent The UCR Time Series Archive

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-11T20:19:00.944081Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b139fbf8-3493-41e5-81f4-8d6d2e835f44 · outbound

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

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent Computing generalized rank invariant for 2-parameter persistence modules via zigzag persistence and its applications

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:19:01.465742Z

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 49fb8679-cccf-4aa8-abd1-a8d15ae2fa0a · outbound

This paper cites Computing Generalized Ranks of Persistence Modules via Unfolding to Zigzag Modules.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent Computing Generalized Ranks of Persistence Modules via Unfolding to Zigzag Modules

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-11T20:19:01.133955Z

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 120ffd58-d4e1-4b79-8ca7-efb1d9a2d4ed · outbound

This paper cites Computational topology: an introduction.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent Computational topology: an introduction

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:19:01.451368Z

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 0d9485e7-70b1-4dcc-ac22-9c6131cf4eb8 · outbound

This paper cites Super-Polynomial Growth of the Generalized Persistence Diagram.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent Super-Polynomial Growth of the Generalized Persistence Diagram

Reference 18

Resolution: verified exact; local_arxiv, observed 2026-08-11T20:19:01.113243Z

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 786e8c63-079a-4746-acca-499b91feceda · outbound

This paper cites Generalized persistence diagrams for persistence modules over posets.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent Generalized persistence diagrams for persistence modules over posets

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-11T20:19:00.965989Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1a735df7-bd83-426d-8e91-6d37cb1f5d75 · outbound

This paper cites Spatiotemporal persistent homology for dynamic metric spaces.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent Spatiotemporal persistent homology for dynamic metric spaces

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:19:01.428054Z

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 9795ed04-050f-4dc8-98fc-a8680b78a4a6 · outbound

This paper cites Persistence over posets.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent Persistence over posets

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:19:01.415553Z

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 7da46ace-0530-4b1e-bf4d-cf87c0ce937f · outbound

This paper cites Extracting persistent clusters in dynamic data via m \"o bius inversion.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent Extracting persistent clusters in dynamic data via m \"o bius inversion

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:19:01.402984Z

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 7475bccb-82df-4fea-9ab4-377f9027b9a6 · outbound

This paper cites Bigraded B etti numbers and generalized persistence diagrams.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent Bigraded B etti numbers and generalized persistence diagrams

Reference 23

Resolution: verified exact; doi, observed 2026-08-11T20:19:01.069426Z

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 2fa82285-9156-4f17-80c5-310c69ac4ad7 · outbound

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

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent The theory of the interleaving distance on multidimensional persistence modules

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:19:01.388843Z

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 8f82c72d-57bc-441c-8e12-492eb7a7f985 · outbound

This paper cites A framework for fast and stable representations of multiparameter persistent homology decompositions.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent A framework for fast and stable representations of multiparameter persistent homology decompositions

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:19:01.377087Z

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 18b58620-752e-4590-b926-30cca03135f1 · outbound

This paper cites multipers: Multiparameter persistence for machine learning.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent multipers: Multiparameter persistence for machine learning

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:19:01.363889Z

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 49f00200-d0b8-4cd3-9d94-9d402b7bb164 · outbound

This paper cites Stable vectorization of multiparameter persistent homology using signed barcodes as measures.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent Stable vectorization of multiparameter persistent homology using signed barcodes as measures

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:19:01.351422Z

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 f184d02c-8d03-4722-bf63-0bd4f959a354 · outbound

This paper cites Zigzag persistent homology in matrix multiplication time.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent Zigzag persistent homology in matrix multiplication time

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:19:01.337250Z

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 8c9c0ae0-fe1d-4593-8d31-9775a426a0d6 · outbound

This paper cites D-GRIL: End-to-End Topological Learning with 2-parameter Persistence.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent D-GRIL: End-to-End Topological Learning with 2-parameter Persistence

Reference 29

Resolution: verified exact; local_arxiv, observed 2026-08-11T20:19:01.090228Z

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 b58000ec-2c47-4bd3-bc0f-933481e21f75 · outbound

This paper cites Generalized persistence diagrams.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent Generalized persistence diagrams

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:19:01.322262Z

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 94a05604-153f-4724-be48-4e19271692cd · outbound

This paper cites Differentiability and optimization of multiparameter persistent homology.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent Differentiability and optimization of multiparameter persistent homology

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:19:01.308885Z

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 ffe3802f-0e37-4e58-96ad-9eeedc0a7aec · outbound

This paper cites Multiparameter persistence landscapes.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent Multiparameter persistence landscapes

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:19:01.295083Z

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 299a3e05-e1b4-45fa-a588-e592edd5ac79 · outbound

This paper cites Capturing dynamics of time-varying data via topology.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent Capturing dynamics of time-varying data via topology

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:19:01.281622Z

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 b19afea9-aaa0-40fd-b508-592ff5b01c9d · outbound

This paper cites GRIL: A 2-parameter persistence based vectorization for machine learning.

Sparsification of the Generalized Persistence Diagrams for Scalability through Gradient Descent GRIL: A 2-parameter persistence based vectorization for machine learning

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T20:19:01.268170Z

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.

Pith citing papers

No inbound Pith citation observations are available.