Paper Citation Record · LEDGER

Quantitative Obata's theorem in discrete setting

As of 21 August 2026, this Paper Citation Record lists 9 of 9 outbound references and 0 inbound Pith citation observations for arXiv:2508.20815.

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

pith.paper-citation-record.v1
2508.20815 v1

Coverage vector

measured 9 of 9 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T14:52:49.079745Z

measured 9 of 9 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+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

9 of 9 outbound references displayed

verified exact0
verified fuzzy8
unresolved1
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 4c1ebe9e-b679-4848-a64a-0fd79e7917e3 · outbound

This paper cites Pincement sur le spectre et le volume en courbure de Ricci positive.

Quantitative Obata's theorem in discrete setting Pincement sur le spectre et le volume en courbure de Ricci positive

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:52:49.209026Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 819fed4e-21ee-4bed-862e-bd30902cd77e · outbound

This paper cites Curvature and higher order Buser inequalities for the graph connection Laplacian.

Quantitative Obata's theorem in discrete setting Curvature and higher order Buser inequalities for the graph connection Laplacian

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:52:49.123748Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 732dad2d-40b3-4131-b076-e129aeec9beb · outbound

This paper cites Volume doubling, Poincar´ e inequality and Gaussian heat kernel esti- mate for non-negatively curved graphs.

Quantitative Obata's theorem in discrete setting Volume doubling, Poincar´ e inequality and Gaussian heat kernel esti- mate for non-negatively curved graphs

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:52:49.147588Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ad4400b4-ed31-451a-9615-0fc6a7ed05e5 · outbound

This paper cites Curvature and transport inequalities for Markov chains in discrete spaces.

Quantitative Obata's theorem in discrete setting Curvature and transport inequalities for Markov chains in discrete spaces

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:52:49.185021Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 51ef4d18-bbbb-446c-a20c-ea87f49d8bbf · outbound

This paper cites an unresolved cited work.

Quantitative Obata's theorem in discrete setting Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-05T14:52:49.111097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 32771030-efb7-4c79-b2c3-0842e350625e · outbound

This paper cites Leibniz Int.

Quantitative Obata's theorem in discrete setting Leibniz Int

Reference 117

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:52:49.158367Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation f9a5ee09-5066-45a3-ba54-de8384e24244 · outbound

This paper cites Bakry- ´Emery curvature and diameter bounds on graphs.

Quantitative Obata's theorem in discrete setting Bakry- ´Emery curvature and diameter bounds on graphs

Reference 130

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:52:49.136069Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 3fe8c49e-dbeb-4258-bfbf-12072d3f1e7e · outbound

This paper cites Graph similarity and ap- proximate isomorphism.

Quantitative Obata's theorem in discrete setting Graph similarity and ap- proximate isomorphism

Reference 152

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:52:49.171105Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 97ff650f-7065-4abe-9a0a-6f19863e0670 · outbound

This paper cites Bakry- ´Emery curvature func- tions on graphs.

Quantitative Obata's theorem in discrete setting Bakry- ´Emery curvature func- tions on graphs

Reference 348

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:52:49.197273Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Pith citing papers

No inbound Pith citation observations are available.