Paper Citation Record · LEDGER

Piecewise-linear Ricci curvature flows on weighted graphs

As of 9 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 5 inbound Pith citation observations for arXiv:2505.15395.

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

pith.paper-citation-record.v1
2505.15395 v1

Coverage vector

measured 33 of 33 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T15:29:01.544593Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

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

measured 5 of 5 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-27T15:29:24.205378Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-04T14:39:58.093157Z

Reference resolution

33 of 33 outbound references displayed

verified exact1
verified fuzzy22
unresolved10
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 14a4d90e-bbeb-438c-b32f-2af242775d77 · outbound

This paper cites an unresolved cited work.

Piecewise-linear Ricci curvature flows on weighted graphs Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:29:08.866620Z

Source-reported events for the cited work

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

Observation 511068c2-a855-4e6b-821d-6fe88507ccf5 · outbound

This paper cites an unresolved cited work.

Piecewise-linear Ricci curvature flows on weighted graphs Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:29:08.762125Z

Source-reported events for the cited work

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

Observation bf620aa3-9426-4f24-956b-6bde4123e9c0 · outbound

This paper cites Bhowmick, B.

Piecewise-linear Ricci curvature flows on weighted graphs Bhowmick, B

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:29:08.439504Z

Source-reported events for the cited work

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

Observation fdf5fb6a-05f3-41a4-bea1-badf265cf4c4 · outbound

This paper cites Clauset, M.

Piecewise-linear Ricci curvature flows on weighted graphs Clauset, M

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:29:08.140068Z

Source-reported events for the cited work

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

Observation 938a10a7-b415-4d6e-ae93-7200a7db2961 · outbound

This paper cites Danon, J.

Piecewise-linear Ricci curvature flows on weighted graphs Danon, J

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:29:07.815190Z

Source-reported events for the cited work

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

Observation 33bbfbde-7129-477a-ae3f-e53afbd270f9 · outbound

This paper cites Forman, Bochner’s method for cell complexes and combinatorial Ricci curvature, Discrete Comput.

Piecewise-linear Ricci curvature flows on weighted graphs Forman, Bochner’s method for cell complexes and combinatorial Ricci curvature, Discrete Comput

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:29:07.575488Z

Source-reported events for the cited work

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

Observation ace3dbb0-69a8-4e02-9db5-f20940d8a950 · outbound

This paper cites Girvan, M.

Piecewise-linear Ricci curvature flows on weighted graphs Girvan, M

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:29:07.276662Z

Source-reported events for the cited work

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

Observation eb7d6b89-4865-475d-b98d-4f7be1363a82 · outbound

This paper cites Guillaume, Fast unfolding of communities in large networks, J.

Piecewise-linear Ricci curvature flows on weighted graphs Guillaume, Fast unfolding of communities in large networks, J

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:29:07.060176Z

Source-reported events for the cited work

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

Observation ca605070-1e8b-46ba-979e-d4261f40a8e7 · outbound

This paper cites Haantjes, Discrete geometry: curvature in abstract metric spaces, Proc.

Piecewise-linear Ricci curvature flows on weighted graphs Haantjes, Discrete geometry: curvature in abstract metric spaces, Proc

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:29:06.918154Z

Source-reported events for the cited work

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

Observation e6d4ec9f-2dc3-4836-bbbf-1936a5b4bded · outbound

This paper cites Hamilton, Three-manifolds with positive ricci curvature, J.

Piecewise-linear Ricci curvature flows on weighted graphs Hamilton, Three-manifolds with positive ricci curvature, J

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:29:06.752484Z

Source-reported events for the cited work

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

Observation 14e6aa6c-7991-4c4d-9074-eaf809759130 · outbound

This paper cites Variational Graph Auto-Encoders.

Piecewise-linear Ricci curvature flows on weighted graphs Variational Graph Auto-Encoders

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-07T15:28:58.697227Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9d62e546-d20d-410a-98d8-7aa32e8014f6 · outbound

This paper cites an unresolved cited work.

Piecewise-linear Ricci curvature flows on weighted graphs Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:29:06.507053Z

Source-reported events for the cited work

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

Observation 46c6fe2d-dee0-4311-ab31-9760764e9115 · outbound

This paper cites Lancichinetti, S.

Piecewise-linear Ricci curvature flows on weighted graphs Lancichinetti, S

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:29:06.347736Z

Source-reported events for the cited work

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

Observation 7470a517-e458-481b-87d1-c1b2d04b8034 · outbound

This paper cites Leskovec, SNAP datasets: Stanford large network dataset collection, http: //snap.stanford.edu/data, 2014.

Piecewise-linear Ricci curvature flows on weighted graphs Leskovec, SNAP datasets: Stanford large network dataset collection, http: //snap.stanford.edu/data, 2014

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:29:06.156546Z

Source-reported events for the cited work

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

Observation a0d441f0-5a51-4c6c-90c1-27567f1eaa8e · outbound

This paper cites an unresolved cited work.

Piecewise-linear Ricci curvature flows on weighted graphs Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-07T15:28:59.318489Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation afd92470-e716-4748-a2e0-d0c592d189cc · outbound

This paper cites an unresolved cited work.

Piecewise-linear Ricci curvature flows on weighted graphs Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:29:05.982636Z

Source-reported events for the cited work

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

Observation ae78f016-f1e5-44c7-ad37-0d18293d0335 · outbound

This paper cites A modified Ricci flow on arbitrary weighted graph.

Piecewise-linear Ricci curvature flows on weighted graphs A modified Ricci flow on arbitrary weighted graph

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-08-07T15:29:01.816875Z

Source-reported events for the cited work

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

Observation e692f46d-dc2b-4223-b2ef-7376e9426cbb · outbound

This paper cites Evolution of weights on a connected finite graph.

Piecewise-linear Ricci curvature flows on weighted graphs Evolution of weights on a connected finite graph

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-07T15:28:59.721383Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 570117e4-31ec-4466-b07a-d94fc2415d22 · outbound

This paper cites Menger, Untersuchungen ¨uber allgemeine metrik, vierte untersuchung, zur metrik der kurven, Math.

Piecewise-linear Ricci curvature flows on weighted graphs Menger, Untersuchungen ¨uber allgemeine metrik, vierte untersuchung, zur metrik der kurven, Math

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:29:05.746668Z

Source-reported events for the cited work

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

Observation 57070968-e4cf-4c9c-8d19-cf1a9c8b7b8e · outbound

This paper cites Newman, Networks: an introduction, Oxford Univ.

Piecewise-linear Ricci curvature flows on weighted graphs Newman, Networks: an introduction, Oxford Univ

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:29:05.492511Z

Source-reported events for the cited work

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

Observation 534c64f4-9135-4123-b630-35532a69e44b · outbound

This paper cites an unresolved cited work.

Piecewise-linear Ricci curvature flows on weighted graphs Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:29:05.267957Z

Source-reported events for the cited work

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

Observation 36cc1df3-52d1-40f6-bbcb-0e7fa4680b8b · outbound

This paper cites Ollivier, Ricci curvature of markov chains on metric spaces, J.

Piecewise-linear Ricci curvature flows on weighted graphs Ollivier, Ricci curvature of markov chains on metric spaces, J

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:29:05.025885Z

Source-reported events for the cited work

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

Observation c33bc83e-c41a-4aa9-9e15-446600b09988 · outbound

This paper cites Perelman, The entropy formula for the ricci flow and its geometric applications, arXiv: 0211159, 2002.

Piecewise-linear Ricci curvature flows on weighted graphs Perelman, The entropy formula for the ricci flow and its geometric applications, arXiv: 0211159, 2002

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:29:04.797490Z

Source-reported events for the cited work

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

Observation 007b6612-55e2-4c8b-ba5d-de8bf872ea61 · outbound

This paper cites Pons and M.

Piecewise-linear Ricci curvature flows on weighted graphs Pons and M

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:29:04.406066Z

Source-reported events for the cited work

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

Observation 04a93f23-453a-4886-859f-70b6e3159372 · outbound

This paper cites Raghavan, R.

Piecewise-linear Ricci curvature flows on weighted graphs Raghavan, R

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:29:04.171646Z

Source-reported events for the cited work

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

Observation 0d915dc8-6726-4a03-9c25-cc2c2f988d81 · outbound

This paper cites Rosvall, C.

Piecewise-linear Ricci curvature flows on weighted graphs Rosvall, C

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:29:03.911371Z

Source-reported events for the cited work

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

Observation 1733ed01-f168-4ccf-beb4-4c4e9dedc164 · outbound

This paper cites Samal, H.

Piecewise-linear Ricci curvature flows on weighted graphs Samal, H

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:29:03.649006Z

Source-reported events for the cited work

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

Observation d87d51c4-0ec8-4fbf-ae4d-6c63030448b0 · outbound

This paper cites Serrat, Knowledge solutions: Tools, methods, and approaches to drive organizational performance, Springer, 2017.

Piecewise-linear Ricci curvature flows on weighted graphs Serrat, Knowledge solutions: Tools, methods, and approaches to drive organizational performance, Springer, 2017

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:29:03.405146Z

Source-reported events for the cited work

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

Observation 8525cf13-6d2e-48ee-8115-38781a17ae83 · outbound

This paper cites Sreejith, K.

Piecewise-linear Ricci curvature flows on weighted graphs Sreejith, K

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:29:03.165126Z

Source-reported events for the cited work

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

Observation 28b42794-3bc6-45a7-b439-e59e460ec4be · outbound

This paper cites Tauro, C.

Piecewise-linear Ricci curvature flows on weighted graphs Tauro, C

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:29:02.896502Z

Source-reported events for the cited work

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

Observation 317cea63-b337-47f2-91c9-c3ac38f709c5 · outbound

This paper cites an unresolved cited work.

Piecewise-linear Ricci curvature flows on weighted graphs Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:29:02.638778Z

Source-reported events for the cited work

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

Observation 1d5ce735-f846-4519-8b4c-a4e6c0f9365a · outbound

This paper cites an unresolved cited work.

Piecewise-linear Ricci curvature flows on weighted graphs Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:29:02.360738Z

Source-reported events for the cited work

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

Observation 6215382d-8f32-48b3-bd0b-c8b6951224cc · outbound

This paper cites Zachary, An information flow model for conflict and fission in small groups, J.

Piecewise-linear Ricci curvature flows on weighted graphs Zachary, An information flow model for conflict and fission in small groups, J

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:29:02.190471Z

Source-reported events for the cited work

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

Pith citing papers

Observation 1b9e672e-c45f-4442-ad9c-9e9e052b5a57 · inbound

The Ricci flow with prescribed curvature on graphs cites this paper.

The Ricci flow with prescribed curvature on graphs Piecewise-linear Ricci curvature flows on weighted graphs

Reference 22

Resolution: verified exact; arxiv_id, observed 2026-05-15T13:30:01.732415Z

Source-reported events for the cited work

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

Observation fbd18360-c703-4f7b-8b72-7734eb55a58f · inbound

The Calabi flow with prescribed curvature on finite graphs cites this paper.

The Calabi flow with prescribed curvature on finite graphs Piecewise-linear Ricci curvature flows on weighted graphs

Reference 22

Resolution: verified exact; arxiv_id, observed 2026-05-13T18:53:08.310198Z

Source-reported events for the cited work

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

Observation 3ed87c23-2afc-4638-9e5d-341de857c334 · inbound

An Efficient Entropy Flow on Weighted Graphs: Theory and Applications cites this paper.

An Efficient Entropy Flow on Weighted Graphs: Theory and Applications Piecewise-linear Ricci curvature flows on weighted graphs

Reference 19

Resolution: verified exact; arxiv_id, observed 2026-05-11T06:41:00.694029Z

Source-reported events for the cited work

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

Observation 6d12ea71-14a5-43f5-b5d7-8239c18e83f6 · inbound

The Ollivier Ricci flow with prescribed curvature on infinite graphs cites this paper.

The Ollivier Ricci flow with prescribed curvature on infinite graphs Piecewise-linear Ricci curvature flows on weighted graphs

Reference 25

Resolution: verified exact; arxiv_id, observed 2026-07-03T03:07:35.510790Z

Source-reported events for the cited work

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

Observation d18455ce-62b1-4b81-ba02-e29f7797e8b0 · inbound

Evolving edge weights via local entropy flow and cohesion flow on graphs cites this paper.

Evolving edge weights via local entropy flow and cohesion flow on graphs Piecewise-linear Ricci curvature flows on weighted graphs

Reference 36

Resolution: verified exact; arxiv_id, observed 2026-07-04T14:39:58.094622Z

Source-reported events for the cited work

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