Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T10:44:00.344061Z
Paper Citation Record · LEDGER
Cheng's eigenvalue comparison on metric measure spaces and applications
As of 19 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 2 inbound Pith citation observations for arXiv:2507.23671.
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 2026-08-19T06:32:44.657259+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-05-15T12:35:57.084364Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-05-15T12:40:00.880415Z
Reference resolution
31 of 31 outbound references displayed
- verified exact0
- verified fuzzy27
- unresolved4
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 43c89493-629f-44dd-995e-188afefe4002 · outbound
This paper cites Ambrosio, N.
Cheng's eigenvalue comparison on metric measure spaces and applications Ambrosio, N
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T10:44:09.288019Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 2b9db25b-9fa0-47d5-a9f7-a95071eda112 · outbound
This paper cites Ambrosio, N.
Cheng's eigenvalue comparison on metric measure spaces and applications Ambrosio, N
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T10:44:08.961596Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 5f53d2b2-666d-420e-aef2-3cb5d75847ea · outbound
This paper cites J., 163 (2014), pp.
Cheng's eigenvalue comparison on metric measure spaces and applications J., 163 (2014), pp
Reference 3
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- verified fuzzy
- raw_fallback, observed 2026-08-06T10:44:08.653518Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 09754aba-ed7c-459c-a62b-85ccda1729c7 · outbound
This paper cites Ambrosio and S.
Cheng's eigenvalue comparison on metric measure spaces and applications Ambrosio and S
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T10:44:08.332833Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 464925cc-9b8d-4729-bb0f-94365bea9fbc · outbound
This paper cites Bachas and J.
Cheng's eigenvalue comparison on metric measure spaces and applications Bachas and J
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T10:44:08.097130Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation a24f18bd-0f1f-43de-8855-72a90e9be669 · outbound
This paper cites Bacher and K.-T.
Cheng's eigenvalue comparison on metric measure spaces and applications Bacher and K.-T
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T10:44:07.832684Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 104ea1ec-82f7-4e13-b414-51b06dcd14cf · outbound
This paper cites Borisov and P.
Cheng's eigenvalue comparison on metric measure spaces and applications Borisov and P
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T10:44:07.595359Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 379432fb-0e62-496d-ad9c-9b06b9b0dcfb · outbound
This paper cites Ca v alletti and E.
Cheng's eigenvalue comparison on metric measure spaces and applications Ca v alletti and E
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T10:44:07.316734Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 17f4a273-295e-4b49-83db-8aaa06d7c21e · outbound
This paper cites Ca v alletti and A.
Cheng's eigenvalue comparison on metric measure spaces and applications Ca v alletti and A
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T10:44:07.084425Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation a401ecf5-ed32-4596-b079-0e3692905fcb · outbound
This paper cites PDE, 13 (2020), pp.
Cheng's eigenvalue comparison on metric measure spaces and applications PDE, 13 (2020), pp
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T10:44:06.752460Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation b17efd9e-84c0-4dc5-9550-6348dd76dce1 · outbound
This paper cites Cheng , Eigenvalue comparison theorems and its geometric applications, Mathematische Zeitschrift, 143 (1975), pp.
Cheng's eigenvalue comparison on metric measure spaces and applications Cheng , Eigenvalue comparison theorems and its geometric applications, Mathematische Zeitschrift, 143 (1975), pp
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T10:44:06.452868Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation adda3fb0-926e-495d-9b82-aeaef22ce7da · outbound
This paper cites Csaki, J.
Cheng's eigenvalue comparison on metric measure spaces and applications Csaki, J
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T10:44:06.163688Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 138ee030-dbe9-4d31-9ddb-f1af18a09c82 · outbound
This paper cites an unresolved cited work.
Cheng's eigenvalue comparison on metric measure spaces and applications Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T10:44:05.869030Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 3a22ade8-5ada-44f3-9540-f6d756bee987 · outbound
This paper cites an unresolved cited work.
Cheng's eigenvalue comparison on metric measure spaces and applications Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T10:44:05.553082Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation b8edb2af-5be7-41e9-95b1-ff4ebe7b19e9 · outbound
This paper cites an unresolved cited work.
Cheng's eigenvalue comparison on metric measure spaces and applications Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T10:44:05.296506Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 935aa677-b141-408a-b82b-f995f3d03114 · outbound
This paper cites De Philippis and N.
Cheng's eigenvalue comparison on metric measure spaces and applications De Philippis and N
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T10:44:05.029043Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 476f2fe2-7623-4ddd-9257-37121111856f · outbound
This paper cites Donnelly, On the essential spectrum of a complete Riemannian manifold, Topology, 20 (1981), pp.
Cheng's eigenvalue comparison on metric measure spaces and applications Donnelly, On the essential spectrum of a complete Riemannian manifold, Topology, 20 (1981), pp
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T10:44:04.757641Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation bc3d9c01-070b-4b7f-a85f-3dd5b02ab8c9 · outbound
This paper cites Gigli, On the differential structure of metric measure spaces and applications, Mem.
Cheng's eigenvalue comparison on metric measure spaces and applications Gigli, On the differential structure of metric measure spaces and applications, Mem
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T10:44:04.498529Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation bc9ebe88-4a11-408b-94a2-61523e2d7ee5 · outbound
This paper cites Gigli, A.
Cheng's eigenvalue comparison on metric measure spaces and applications Gigli, A
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T10:44:04.246505Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 382fef3e-6867-4e0d-8e88-36256c48ca6f · outbound
This paper cites Ketterer, Cones over metric measure spaces and the maximal diameter the- orem, J.
Cheng's eigenvalue comparison on metric measure spaces and applications Ketterer, Cones over metric measure spaces and the maximal diameter the- orem, J
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T10:44:03.988213Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 28b6aa61-4d52-46c1-84a5-fb71740ac976 · outbound
This paper cites Kristály, New features of the first eigenvalue on negatively curved spaces, Advances in Calculus of Variations, 15 (2022), pp.
Cheng's eigenvalue comparison on metric measure spaces and applications Kristály, New features of the first eigenvalue on negatively curved spaces, Advances in Calculus of Variations, 15 (2022), pp
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T10:44:03.726534Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 2039fcc3-5e39-4b4a-8bff-b7420135c78d · outbound
This paper cites Levitin, D.
Cheng's eigenvalue comparison on metric measure spaces and applications Levitin, D
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T10:44:03.406861Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 12dd8903-557b-4885-9510-5ce9baaf77d8 · outbound
This paper cites Li, The globalization theorem forCD(K, N) on locally finite spaces, Annali di matematica pura ed applicata, 203 (2024), pp.
Cheng's eigenvalue comparison on metric measure spaces and applications Li, The globalization theorem forCD(K, N) on locally finite spaces, Annali di matematica pura ed applicata, 203 (2024), pp
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T10:44:03.135285Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 280cac66-0d43-4b39-9364-f5b492371a62 · outbound
This paper cites Lott and C.
Cheng's eigenvalue comparison on metric measure spaces and applications Lott and C
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T10:44:02.809624Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 7daf2b22-671b-49fb-8769-479cdf442f68 · outbound
This paper cites Milman, Sharp isoperimetric inequalities and model spaces for the curvature- dimension-diameter condition, Journal of the European Mathematical Society, 17 (2015), pp.
Cheng's eigenvalue comparison on metric measure spaces and applications Milman, Sharp isoperimetric inequalities and model spaces for the curvature- dimension-diameter condition, Journal of the European Mathematical Society, 17 (2015), pp
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T10:44:02.510709Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation f4ec0887-e04c-4488-8955-83c7b2e87564 · outbound
This paper cites Rajala and K.-T.
Cheng's eigenvalue comparison on metric measure spaces and applications Rajala and K.-T
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T10:44:02.219593Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 168103ee-d478-46be-8503-e7a93fa45057 · outbound
This paper cites an unresolved cited work.
Cheng's eigenvalue comparison on metric measure spaces and applications Unresolved cited work
Reference 27
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T10:44:01.875897Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 46e22f5b-474c-49fe-a6fe-0ae5c348813e · outbound
This paper cites Sturm , On the geometry of metric measure spaces.
Cheng's eigenvalue comparison on metric measure spaces and applications Sturm , On the geometry of metric measure spaces
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T10:44:01.534630Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 9579c0ab-f701-4605-9341-ce12b8307794 · outbound
This paper cites II, Acta Math., 196 (2006), pp.
Cheng's eigenvalue comparison on metric measure spaces and applications II, Acta Math., 196 (2006), pp
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T10:44:01.257107Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 0c5aa426-b1be-44c6-85f4-30a858835697 · outbound
This paper cites Villani, Optimal transport, Old and new, vol.
Cheng's eigenvalue comparison on metric measure spaces and applications Villani, Optimal transport, Old and new, vol
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T10:44:00.936901Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation cc19ae3f-223a-45a9-86f3-2589e8edaa96 · outbound
This paper cites Yin and Q.
Cheng's eigenvalue comparison on metric measure spaces and applications Yin and Q
Reference 31
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T10:44:00.666439Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Pith citing papers
Observation 1716a5fd-0989-40f0-b488-a7d1481af1b7 · inbound
Alice in Warpland: KK modes, Warped Compactifications and the Swampland cites this paper.
Alice in Warpland: KK modes, Warped Compactifications and the Swampland Cheng's eigenvalue comparison on metric measure spaces and applications
Reference 13
- Resolution
- verified exact
- arxiv_id, observed 2026-05-15T12:40:00.882594Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.
Observation 9ba2b300-2381-47a3-9296-838325252bc0 · inbound
Optimal paths across potentials on scalar field space cites this paper.
Optimal paths across potentials on scalar field space Cheng's eigenvalue comparison on metric measure spaces and applications
Reference 57
- Resolution
- verified exact
- arxiv_id, observed 2026-05-11T22:41:35.453520Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.