Paper Citation Record · LEDGER

Lower Bounds for Approximating the Vietoris-Rips Filtration

As of 17 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 0 inbound Pith citation observations for arXiv:2607.06524.

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pith.paper-citation-record.v1
2607.06524 v1

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measured 41 of 41 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-07-08T03:11:39.283786Z

measured 41 of 41 standing notices

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Reference resolution

41 of 41 outbound references displayed

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verified fuzzy2
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Outbound references

Observation 8bb05c3b-2421-4b65-97f0-1b3de50c1f00 · outbound

This paper cites Clique complexes and graph powers.Israel Journal of Mathematics, 196:295–319, 2013.

Lower Bounds for Approximating the Vietoris-Rips Filtration Clique complexes and graph powers.Israel Journal of Mathematics, 196:295–319, 2013

Reference 1

Resolution: verified exact; doi, observed 2026-07-08T03:14:31.479780Z

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Observation dd8aef2b-68db-400e-b0de-673b0ba53157 · outbound

This paper cites Extremal problems related to Betti numbers of flag complexes.Discrete Applied Mathematics, 173:8–15, 2014.

Lower Bounds for Approximating the Vietoris-Rips Filtration Extremal problems related to Betti numbers of flag complexes.Discrete Applied Mathematics, 173:8–15, 2014

Reference 2

Resolution: verified exact; doi, observed 2026-07-08T03:14:31.418954Z

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Observation 93baab56-3ff8-4fc9-a710-18c4ab7ce11c · outbound

This paper cites Lower bounds on the homology of Vietoris– Rips complexes of hypercube graphs.Bulletin of the Malaysian Mathematical Sciences Society, 47(3):72, 2024.

Lower Bounds for Approximating the Vietoris-Rips Filtration Lower bounds on the homology of Vietoris– Rips complexes of hypercube graphs.Bulletin of the Malaysian Mathematical Sciences Society, 47(3):72, 2024

Reference 3

Resolution: verified exact; doi, observed 2026-07-08T03:14:31.453185Z

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Observation 54ea8e56-f0d5-4baf-9279-85ef49e14a0b · outbound

This paper cites A sparse multicover bifiltration of linear size.

Lower Bounds for Approximating the Vietoris-Rips Filtration A sparse multicover bifiltration of linear size

Reference 4

Resolution: verified exact; doi, observed 2026-07-08T03:14:31.426962Z

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Observation d3a980f0-4c9d-4ef2-b940-db2a53ee8fc2 · outbound

This paper cites Extremal Betti numbers and persis- tence in flag complexes.

Lower Bounds for Approximating the Vietoris-Rips Filtration Extremal Betti numbers and persis- tence in flag complexes

Reference 5

Resolution: verified exact; doi, observed 2026-07-08T03:14:31.481797Z

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Observation 9daf109e-85d6-4704-8f95-e3e058cbc78a · outbound

This paper cites Extremal Betti Numbers and Persistence in Flag Complexes.

Lower Bounds for Approximating the Vietoris-Rips Filtration Extremal Betti Numbers and Persistence in Flag Complexes

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-07-08T03:14:31.435707Z

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Observation 1289995a-bb12-43b2-a249-764e388d1b72 · outbound

This paper cites Note: Combinatorial Alexander duality— a short and elementary proof.Discrete & Computational Geometry, 42(4): 586–593, 2009.

Lower Bounds for Approximating the Vietoris-Rips Filtration Note: Combinatorial Alexander duality— a short and elementary proof.Discrete & Computational Geometry, 42(4): 586–593, 2009

Reference 7

Resolution: verified exact; doi, observed 2026-07-08T03:14:31.477794Z

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Observation dcb8b54a-44a9-4d0d-bfce-74ea7d203fe8 · outbound

This paper cites Universality of the homotopy interleaving distance.

Lower Bounds for Approximating the Vietoris-Rips Filtration Universality of the homotopy interleaving distance

Reference 8

Resolution: metadata mismatch; doi, observed 2026-07-08T03:14:31.449222Z

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Observation 2ff6814e-67ce-402b-9704-80cc7d9a648e · outbound

This paper cites Blumberg and Michael Lesnick.

Lower Bounds for Approximating the Vietoris-Rips Filtration Blumberg and Michael Lesnick

Reference 9

Resolution: verified exact; doi, observed 2026-07-08T03:14:31.433179Z

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Observation 8f966313-742a-4f6a-b139-9590a89e8950 · outbound

This paper cites An introduction to multipa- rameter persistence.

Lower Bounds for Approximating the Vietoris-Rips Filtration An introduction to multipa- rameter persistence

Reference 10

Resolution: verified exact; doi, observed 2026-07-08T03:14:31.445402Z

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Observation 90876041-0c58-4a61-a5ed-0e3f6526277e · outbound

This paper cites Approximating persistent homol- ogy in Euclidean space through collapses.Applicable Algebra in Engineering, 14 KENNETH MCCABE Communication and Computing, 26(1–2):73–101, 2015.

Lower Bounds for Approximating the Vietoris-Rips Filtration Approximating persistent homol- ogy in Euclidean space through collapses.Applicable Algebra in Engineering, 14 KENNETH MCCABE Communication and Computing, 26(1–2):73–101, 2015

Reference 11

Resolution: malformed identifier; doi_truncated, observed 2026-07-08T03:14:31.455072Z

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Observation 7fc50b6f-a5b9-4533-949a-dde2ef45a47f · outbound

This paper cites Sparse Dowker nerves.Journal of Applied and Computational Topology, 3(1–2):1–28, 2019.

Lower Bounds for Approximating the Vietoris-Rips Filtration Sparse Dowker nerves.Journal of Applied and Computational Topology, 3(1–2):1–28, 2019

Reference 12

Resolution: verified exact; doi, observed 2026-07-08T03:14:31.443497Z

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Observation 1475f47d-ff9a-416f-a2c4-4a92b51ec3a9 · outbound

This paper cites Oudot, and Donald R.

Lower Bounds for Approximating the Vietoris-Rips Filtration Oudot, and Donald R

Reference 13

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Observation 2c0acd91-6799-4504-af59-7d899b971501 · outbound

This paper cites Dornelas, and Michael Kerber.

Lower Bounds for Approximating the Vietoris-Rips Filtration Dornelas, and Michael Kerber

Reference 14

Resolution: verified exact; doi, observed 2026-07-08T03:14:31.424943Z

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Observation c93514ff-981d-4886-b7ef-9abc40026193 · outbound

This paper cites The theory of multidimen- sional persistence.Discrete & Computational Geometry, 42(1):71–93, 2009.

Lower Bounds for Approximating the Vietoris-Rips Filtration The theory of multidimen- sional persistence.Discrete & Computational Geometry, 42(1):71–93, 2009

Reference 15

Resolution: verified exact; doi, observed 2026-07-08T03:14:31.409321Z

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Observation 65b9d8e6-dc96-4548-a473-e43aedba5696 · outbound

This paper cites Cavanna, Mahmoodreza Jahanseir, and Donald R.

Lower Bounds for Approximating the Vietoris-Rips Filtration Cavanna, Mahmoodreza Jahanseir, and Donald R

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T03:14:31.798258Z

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Observation 55e568b0-cf62-4728-8ca3-7a625df7ee02 · outbound

This paper cites Vinhage and Z.

Lower Bounds for Approximating the Vietoris-Rips Filtration Vinhage and Z

Reference 17

Resolution: malformed identifier; doi_truncated, observed 2026-07-08T03:14:31.441585Z

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Observation 8df7bd4a-738f-41cb-9101-f49c3409c87f · outbound

This paper cites Improved topo- logical approximations by digitization.

Lower Bounds for Approximating the Vietoris-Rips Filtration Improved topo- logical approximations by digitization

Reference 18

Resolution: verified exact; doi, observed 2026-07-08T03:14:31.416916Z

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Observation 47c431ca-b806-472b-ae38-b9def20128ab · outbound

This paper cites Polynomial-sized topological approximations using the permutahedron.Discrete & Computa- tional Geometry, 61(1):42–80, 2019.

Lower Bounds for Approximating the Vietoris-Rips Filtration Polynomial-sized topological approximations using the permutahedron.Discrete & Computa- tional Geometry, 61(1):42–80, 2019

Reference 19

Resolution: verified exact; doi, observed 2026-07-08T03:14:31.475592Z

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Observation e9a5b92c-2277-4983-94a1-dca8ff30ea0d · outbound

This paper cites Improved approximate Rips filtrations with shifted integer lattices and cubical com- plexes.Journal of Applied and Computational Topology, 5(3):425–458, 2021.

Lower Bounds for Approximating the Vietoris-Rips Filtration Improved approximate Rips filtrations with shifted integer lattices and cubical com- plexes.Journal of Applied and Computational Topology, 5(3):425–458, 2021

Reference 20

Resolution: verified exact; doi, observed 2026-07-08T03:14:31.471568Z

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Observation 88e1cc22-89c5-4e2b-af6d-47efb3538af1 · outbound

This paper cites Computing the multicover bifiltration.Discrete & Computational Geometry, 70(2):376– 405, 2023.

Lower Bounds for Approximating the Vietoris-Rips Filtration Computing the multicover bifiltration.Discrete & Computational Geometry, 70(2):376– 405, 2023

Reference 21

Resolution: verified exact; doi, observed 2026-07-08T03:14:31.469544Z

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Observation 3a0b4ef2-33a0-442c-ac4b-4ef188b0ee6d · outbound

This paper cites Computing Topological Persistence for Simplicial Maps.

Lower Bounds for Approximating the Vietoris-Rips Filtration Computing Topological Persistence for Simplicial Maps

Reference 22

Resolution: metadata mismatch; arxiv_id, observed 2026-07-08T03:14:31.465574Z

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Observation b4e7f40f-60ae-4235-a5b4-6ae2ca6509ba · outbound

This paper cites and Shi, Dayu and Wang, Yusu , title =.

Lower Bounds for Approximating the Vietoris-Rips Filtration and Shi, Dayu and Wang, Yusu , title =

Reference 23

Resolution: verified exact; doi, observed 2026-07-08T03:14:31.467413Z

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Observation 00fc8193-d996-4552-8cde-9ef9fe322d90 · outbound

This paper cites The multi-cover persistence of Eu- clidean balls.Discrete & Computational Geometry, 65(4):1296–1313, 2021.

Lower Bounds for Approximating the Vietoris-Rips Filtration The multi-cover persistence of Eu- clidean balls.Discrete & Computational Geometry, 65(4):1296–1313, 2021

Reference 24

Resolution: verified exact; doi, observed 2026-07-08T03:14:31.437644Z

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Observation ded87dfb-f53b-43a4-964b-bd49b94842d9 · outbound

This paper cites Maximum persis- tent Betti numbers of ˇ cech complexes.Journal of Applied and Computational Topology, 10(1):5, 2026.

Lower Bounds for Approximating the Vietoris-Rips Filtration Maximum persis- tent Betti numbers of ˇ cech complexes.Journal of Applied and Computational Topology, 10(1):5, 2026

Reference 25

Resolution: verified exact; doi, observed 2026-07-08T03:14:31.483739Z

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Observation 831ac38a-67e7-4a39-a76e-8dd0afa537f7 · outbound

This paper cites The nonexistence of certain generalized poly- gons.Journal of Algebra, 1(2):114–131, 1964.

Lower Bounds for Approximating the Vietoris-Rips Filtration The nonexistence of certain generalized poly- gons.Journal of Algebra, 1(2):114–131, 1964

Reference 26

Resolution: malformed identifier; doi_truncated, observed 2026-07-08T03:14:31.423265Z

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Observation bd578ef8-0dc4-44a7-a897-c0cdd00f22a2 · outbound

This paper cites Extremal Betti numbers of Vietoris–Rips complexes.Discrete & Computational Geometry, 46(1):132–155, 2011.

Lower Bounds for Approximating the Vietoris-Rips Filtration Extremal Betti numbers of Vietoris–Rips complexes.Discrete & Computational Geometry, 46(1):132–155, 2011

Reference 27

Resolution: malformed identifier; doi_truncated, observed 2026-07-08T03:14:31.428776Z

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Observation 8f2e419d-8dfc-4bd6-a6d7-a26a9e122dc8 · outbound

This paper cites Density Sensitive Bifiltered Dowker Complexes via Total Weight.

Lower Bounds for Approximating the Vietoris-Rips Filtration Density Sensitive Bifiltered Dowker Complexes via Total Weight

Reference 28

Resolution: metadata mismatch; local_arxiv, observed 2026-07-08T03:14:31.457753Z

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Observation ca945e6b-1664-44ae-a682-5834fcaf2921 · outbound

This paper cites Barcodes of towers and a streaming algorithm for persistent homology.Discrete & Computational Geometry, 61 (4):852–879, 2019.

Lower Bounds for Approximating the Vietoris-Rips Filtration Barcodes of towers and a streaming algorithm for persistent homology.Discrete & Computational Geometry, 61 (4):852–879, 2019

Reference 29

Resolution: verified exact; doi, observed 2026-07-08T03:14:31.439544Z

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Observation cabc1702-d77b-433d-bf76-051ce9c93e97 · outbound

This paper cites Ustimenko, and Andrew J.

Lower Bounds for Approximating the Vietoris-Rips Filtration Ustimenko, and Andrew J

Reference 30

Resolution: verified exact; doi, observed 2026-07-08T03:14:31.459489Z

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Observation cebcb2d7-2ca7-4e84-952f-d840168a61b8 · outbound

This paper cites It’s all about covers: Persistent homology of cover refinements,.

Lower Bounds for Approximating the Vietoris-Rips Filtration It’s all about covers: Persistent homology of cover refinements,

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T03:14:31.796506Z

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Observation 15863ae9-f581-4bcc-8752-46ef3b10507b · outbound

This paper cites It's All About Covers: Persistent Homology of Cover Refinements.

Lower Bounds for Approximating the Vietoris-Rips Filtration It's All About Covers: Persistent Homology of Cover Refinements

Reference 32

Resolution: verified exact; local_arxiv, observed 2026-07-08T03:14:31.421480Z

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Observation 97c946cd-67a2-448c-a7ba-91d20b86f528 · outbound

This paper cites Nerve Models of Subdivision Bifiltrations.

Lower Bounds for Approximating the Vietoris-Rips Filtration Nerve Models of Subdivision Bifiltrations

Reference 33

Resolution: verified exact; local_arxiv, observed 2026-07-08T03:14:31.411842Z

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Observation 5f3cf3de-14eb-4b34-8801-582783c9e6a1 · outbound

This paper cites Sparse Approximation of the Subdivision-Rips Bifiltration for Doubling Metrics.

Lower Bounds for Approximating the Vietoris-Rips Filtration Sparse Approximation of the Subdivision-Rips Bifiltration for Doubling Metrics

Reference 34

Resolution: verified exact; local_arxiv, observed 2026-07-08T03:14:31.414859Z

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Observation adb43384-e8bc-444b-aba5-f39dc1c177eb · outbound

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

Lower Bounds for Approximating the Vietoris-Rips Filtration Interactive Visualization of 2-D Persistence Modules

Reference 35

Resolution: verified exact; local_arxiv, observed 2026-07-08T03:14:31.431353Z

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Observation cc8996b0-387b-464a-a989-45e6c335dc5f · outbound

This paper cites Springer Basel, Basel, 1998.

Lower Bounds for Approximating the Vietoris-Rips Filtration Springer Basel, Basel, 1998

Reference 36

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Observation 5c95bc4c-384a-44fe-95d8-f4e9b1bb183f · outbound

This paper cites Construction of universal bundles. II.

Lower Bounds for Approximating the Vietoris-Rips Filtration Construction of universal bundles. II

Reference 37

Resolution: verified exact; doi, observed 2026-07-08T03:14:31.447360Z

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Observation bc229c84-c972-4253-8440-48a8fc40d133 · outbound

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Lower Bounds for Approximating the Vietoris-Rips Filtration Unresolved cited work

Reference 38

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Observation fbe6cf64-77f7-4a3c-82a9-ea8ec4c47514 · outbound

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Lower Bounds for Approximating the Vietoris-Rips Filtration Unresolved cited work

Reference 39

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Observation 286b82ec-ef9d-44e4-bc28-20eaf0019a46 · outbound

This paper cites Primoz Skraba and Katharine Turner.

Lower Bounds for Approximating the Vietoris-Rips Filtration Primoz Skraba and Katharine Turner

Reference 40

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Observation 91e89875-6c42-45a0-9114-bd6648c5c57a · outbound

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Lower Bounds for Approximating the Vietoris-Rips Filtration Unresolved cited work

Reference 41

Resolution: verified exact; doi, observed 2026-07-08T03:14:31.461324Z

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