Paper Citation Record · LEDGER

Lin-Lu-Yau Ricci curvature on hypergraphs

As of 9 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 1 inbound Pith citation observation for arXiv:2507.04109.

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

pith.paper-citation-record.v1
2507.04109 v1

Coverage vector

measured 35 of 35 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T20:04:41.917920Z

measured 36 of 36 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T19:18:57.072680Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-07T19:18:57.231988Z

Reference resolution

35 of 35 outbound references displayed

verified exact4
verified fuzzy13
unresolved18
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 45e4affa-c5fe-4e1c-98fb-b4e42188c1e5 · outbound

This paper cites Akamatsu, A New Transport Distance and Its Associated Ricci Curvature of Hypergraphs, Analysis and Geometry in Metric Spaces 10 (1) (2022) 90–108.

Lin-Lu-Yau Ricci curvature on hypergraphs Akamatsu, A New Transport Distance and Its Associated Ricci Curvature of Hypergraphs, Analysis and Geometry in Metric Spaces 10 (1) (2022) 90–108

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:04:42.924773Z

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 0435b5c2-4eef-4f63-9032-2855400a1afa · outbound

This paper cites Weak Kantorovich difference and associated Ricci curvature of hypergraphs.

Lin-Lu-Yau Ricci curvature on hypergraphs Weak Kantorovich difference and associated Ricci curvature of hypergraphs

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:04:42.216158Z

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 7fb66e4b-c427-4f85-9ae8-840ea0746b8d · outbound

This paper cites Signless Normalized Laplacian for Hypergraphs.

Lin-Lu-Yau Ricci curvature on hypergraphs Signless Normalized Laplacian for Hypergraphs

Reference 3

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:04:42.188213Z

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 2f9999a7-8e3d-409a-8a45-4e603c750116 · outbound

This paper cites Asoodeh, T.

Lin-Lu-Yau Ricci curvature on hypergraphs Asoodeh, T

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:04:42.906170Z

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 f0bc96c9-0b50-4ebf-9fb0-30df632fc937 · outbound

This paper cites an unresolved cited work.

Lin-Lu-Yau Ricci curvature on hypergraphs Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:04:42.882806Z

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 c20cdd85-cb06-4766-be84-ee17a57a8f0f · outbound

This paper cites an unresolved cited work.

Lin-Lu-Yau Ricci curvature on hypergraphs Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:04:42.858615Z

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 30a75238-776b-45aa-9f3b-768636a10e30 · outbound

This paper cites Bauer, J.

Lin-Lu-Yau Ricci curvature on hypergraphs Bauer, J

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:04:42.838317Z

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 c72abc4a-74f3-4ee4-9f31-054069709c84 · outbound

This paper cites Benson, P.

Lin-Lu-Yau Ricci curvature on hypergraphs Benson, P

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:04:42.818367Z

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 86d85413-eebd-41a7-bdc9-2986e5114428 · outbound

This paper cites an unresolved cited work.

Lin-Lu-Yau Ricci curvature on hypergraphs Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:04:42.789881Z

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 a76d25a3-387b-4b5b-ade4-c2439678fbde · outbound

This paper cites Brezis, Remarks on the Monge–Kantorovich problem in the discrete setting, C.

Lin-Lu-Yau Ricci curvature on hypergraphs Brezis, Remarks on the Monge–Kantorovich problem in the discrete setting, C

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:04:42.763324Z

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 36fcdfa0-e25f-474d-b29e-2d6474771a96 · outbound

This paper cites Brezis, J.-M.

Lin-Lu-Yau Ricci curvature on hypergraphs Brezis, J.-M

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:04:42.735535Z

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 2b04129f-4884-49e5-91fe-696ec4b9344f · outbound

This paper cites Ollivier-Ricci Curvature for Hypergraphs: A Unified Framework.

Lin-Lu-Yau Ricci curvature on hypergraphs Ollivier-Ricci Curvature for Hypergraphs: A Unified Framework

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-08-06T20:04:42.155638Z

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 fed6f8fa-6628-4fd7-a233-d70cda965250 · outbound

This paper cites an unresolved cited work.

Lin-Lu-Yau Ricci curvature on hypergraphs Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:04:42.716972Z

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 b40f862a-bad5-4a9b-847a-312bb95b49f3 · outbound

This paper cites Devriendt, R.

Lin-Lu-Yau Ricci curvature on hypergraphs Devriendt, R

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:04:42.698628Z

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 c708862d-ba89-4211-8c7a-f6ecadbcdbc1 · outbound

This paper cites an unresolved cited work.

Lin-Lu-Yau Ricci curvature on hypergraphs Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:04:42.680910Z

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 31928fc3-1e4c-4900-b25f-74ef1a904bab · outbound

This paper cites an unresolved cited work.

Lin-Lu-Yau Ricci curvature on hypergraphs Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:04:42.656790Z

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 7034d9a3-8eec-4cf2-b87a-a9ff46aef418 · outbound

This paper cites an unresolved cited work.

Lin-Lu-Yau Ricci curvature on hypergraphs Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:04:42.625793Z

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 2d7abc2c-7ae0-454a-b182-2fbe9a40db4e · outbound

This paper cites Ikeda, Y.

Lin-Lu-Yau Ricci curvature on hypergraphs Ikeda, Y

Reference 18

Resolution: verified exact; raw_fallback, observed 2026-08-06T20:04:42.116008Z

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 96ac1999-dde9-4dac-874c-8c363b16772b · outbound

This paper cites an unresolved cited work.

Lin-Lu-Yau Ricci curvature on hypergraphs Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:04:42.598164Z

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 483e9f89-0f43-492a-9595-d60bb0607dcc · outbound

This paper cites an unresolved cited work.

Lin-Lu-Yau Ricci curvature on hypergraphs Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:04:42.567290Z

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 ebd9399e-1d4b-4c10-9648-97ab75cc74f2 · outbound

This paper cites an unresolved cited work.

Lin-Lu-Yau Ricci curvature on hypergraphs Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:04:42.538497Z

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 b49aa1bb-6c99-4f73-99a1-135b175aec5b · outbound

This paper cites an unresolved cited work.

Lin-Lu-Yau Ricci curvature on hypergraphs Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:04:42.495947Z

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 d2747c55-c4f8-44cd-9585-17fb7174510a · outbound

This paper cites an unresolved cited work.

Lin-Lu-Yau Ricci curvature on hypergraphs Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-06T20:04:41.840711Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8e684955-5365-4f8b-9881-06dabae6876d · outbound

This paper cites Lin, S.-T.

Lin-Lu-Yau Ricci curvature on hypergraphs Lin, S.-T

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:04:42.439096Z

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 78f3a730-4548-478e-ba93-4275320a1e95 · outbound

This paper cites an unresolved cited work.

Lin-Lu-Yau Ricci curvature on hypergraphs Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:04:42.404557Z

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 f73a5fe2-1b2e-40bb-ac76-0de0d346c9e3 · outbound

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

Lin-Lu-Yau Ricci curvature on hypergraphs Evolution of weights on a connected finite graph

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-06T20:04:41.855901Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a4699930-1ccd-4922-8868-a6196d4ac4bf · outbound

This paper cites Kantorovich distance on a finite metric space.

Lin-Lu-Yau Ricci curvature on hypergraphs Kantorovich distance on a finite metric space

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-06T20:04:41.865276Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e9081ff9-f68a-4d64-8f1c-e58410a6c74f · outbound

This paper cites Mulas, Sharp bounds for the largest eigenvalue, Math.

Lin-Lu-Yau Ricci curvature on hypergraphs Mulas, Sharp bounds for the largest eigenvalue, Math

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:04:42.380364Z

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 4874ba49-0360-4174-b392-61504555ab4f · outbound

This paper cites M ¨unch, R.

Lin-Lu-Yau Ricci curvature on hypergraphs M ¨unch, R

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:04:42.356759Z

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 dc7ef739-6a6f-44d7-86e2-8d84fddf8716 · outbound

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

Lin-Lu-Yau Ricci curvature on hypergraphs Ollivier, Ricci curvature of Markov chains on metric spaces, J

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-06T20:04:41.888059Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7bb54e45-56c7-4739-a560-1c3416e7cc60 · outbound

This paper cites Ozawa, Y.

Lin-Lu-Yau Ricci curvature on hypergraphs Ozawa, Y

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:04:42.318599Z

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 2ad46583-0519-4e94-810e-714c37d04f22 · outbound

This paper cites an unresolved cited work.

Lin-Lu-Yau Ricci curvature on hypergraphs Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:04:42.300437Z

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 0caecf67-954c-40a6-8aff-2e64d8c87203 · outbound

This paper cites Villani, Topics in optimal transportation, vol.

Lin-Lu-Yau Ricci curvature on hypergraphs Villani, Topics in optimal transportation, vol

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:04:42.284170Z

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 85e81ccd-dd3e-4986-8546-4a0fb2e79c7e · outbound

This paper cites Yamada, The Ricci curvature on directed graphs, J.

Lin-Lu-Yau Ricci curvature on hypergraphs Yamada, The Ricci curvature on directed graphs, J

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:04:42.264110Z

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 7886ddb6-b0a8-419f-8956-9a2ce48a597f · outbound

This paper cites an unresolved cited work.

Lin-Lu-Yau Ricci curvature on hypergraphs Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:04:42.244179Z

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

Observation 146ca594-48e0-4388-be6f-7332925755b3 · inbound

Edge-connectivity and LLY curvature of hypergraphs cites this paper.

Edge-connectivity and LLY curvature of hypergraphs Lin-Lu-Yau Ricci curvature on hypergraphs

Reference 11

Resolution: verified exact; local_arxiv, observed 2026-08-07T19:18:57.236356Z

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.