Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-05T14:52:49.079745Z
Paper Citation Record · LEDGER
Quantitative Obata's theorem in discrete setting
As of 20 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.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
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 2026-08-20T06:33:59.587034+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 2026-08-20T06:33:59.587034+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 2026-08-20T06:33:59.587034+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 2026-08-20T06:33:59.587034+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 2026-08-20T06:33:59.587034+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 2026-08-20T06:33:59.587034+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 2026-08-20T06:33:59.587034+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 2026-08-20T06:33:59.587034+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 2026-08-20T06:33:59.587034+00:00.
Pith citing papers
No inbound Pith citation observations are available.