Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-07-08T04:08:00.890757Z
Paper Citation Record · LEDGER
Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound
As of 12 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 1 inbound Pith citation observation for arXiv:2607.06508.
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 2026-08-12T06:34:41.77262+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-06T00:50:12.806953Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-06T00:50:12.891262Z
Reference resolution
23 of 23 outbound references displayed
- verified exact5
- verified fuzzy16
- unresolved2
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 20728244-24cc-4dcf-ab67-9af4f78c114a · outbound
This paper cites A sharp spectral splitting theorem.
Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound A sharp spectral splitting theorem
Reference 1
- Resolution
- verified exact
- local_arxiv, observed 2026-07-08T04:14:29.567303Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 23987b04-929e-474b-9670-af67f57532a9 · outbound
This paper cites Geometric Rigidity via Almost-Harmonic Twisted Spinors.
Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound Geometric Rigidity via Almost-Harmonic Twisted Spinors
Reference 2
- Resolution
- verified exact
- local_arxiv, observed 2026-07-08T04:14:29.561652Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 6867ea17-ab27-4ca0-8c3e-b52f4c869f0d · outbound
This paper cites Brooks, The fundamental group and the spectrum of the Laplacian, Comment.
Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound Brooks, The fundamental group and the spectrum of the Laplacian, Comment
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-08T04:14:29.744936Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 882644cf-c8a2-4fd1-9b75-1326d224fad2 · outbound
This paper cites Cheng, Eigenvalue comparison theorems and its geometric applications, Math.
Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound Cheng, Eigenvalue comparison theorems and its geometric applications, Math
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-08T04:14:29.754221Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 05b74d17-04b0-4aa2-a6c7-8c562b1b23b8 · outbound
This paper cites Chodosh and C.
Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound Chodosh and C
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-08T04:14:29.730917Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 38ce1a06-e7fa-480b-96b5-d4a8c3a83516 · outbound
This paper cites Chodosh, C.
Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound Chodosh, C
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-08T04:14:29.723894Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 0f425ee3-e101-41a1-8a4a-52de80caf97d · outbound
This paper cites Davaux, An optimal inequality between scalar curvature and spectrum of the Laplacian, Math.
Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound Davaux, An optimal inequality between scalar curvature and spectrum of the Laplacian, Math
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-08T04:14:29.746371Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 4d62107d-861c-4882-9772-2eb91678db96 · outbound
This paper cites Positive curvature, macroscopic dimension, spectral gaps and higher signatures.
Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound Positive curvature, macroscopic dimension, spectral gaps and higher signatures
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-08T04:14:29.761941Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation b06ec2eb-ac73-4d75-b6a6-f1ed5b6d81a2 · outbound
This paper cites an unresolved cited work.
Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-07-08T04:14:29.759012Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation f399424f-f084-4ab3-b685-7cc0c4578799 · outbound
This paper cites Gromov, Four lectures on scalar curvature, in Perspectives in Scalar Curvature, Vol.
Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound Gromov, Four lectures on scalar curvature, in Perspectives in Scalar Curvature, Vol
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-08T04:14:29.739847Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 5643b5ec-0a8e-4429-a418-d4452770e1af · outbound
This paper cites Gromov and H.
Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound Gromov and H
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-08T04:14:29.767496Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 71776c34-3cda-4b67-b5ef-c3b092a2ac8c · outbound
This paper cites Hirsch, D.
Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound Hirsch, D
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-08T04:14:29.735169Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation f94ce71c-38c2-4a3b-b25f-eb8d48552548 · outbound
This paper cites Li, Geometric Analysis, Cambridge Stud.
Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound Li, Geometric Analysis, Cambridge Stud
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-08T04:14:29.759837Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 01fbff1b-77b9-4ae5-b6f5-66f853ef7209 · outbound
This paper cites Li and L.F.
Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound Li and L.F
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-08T04:14:29.755984Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation dc3c3f3e-e0bc-49fb-9be9-2793ccc68ec4 · outbound
This paper cites Liu, A sharp inequality between scalar curvature and the bottom spectrum on complete manifolds, arXiv:2603.20864.
Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound Liu, A sharp inequality between scalar curvature and the bottom spectrum on complete manifolds, arXiv:2603.20864
Reference 15
- Resolution
- verified exact
- arxiv_id, observed 2026-07-08T04:14:29.557671Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 3ef47343-991f-4949-8773-7f5233712ad5 · outbound
This paper cites Munteanu and J.
Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound Munteanu and J
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-08T04:14:29.764420Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation b5f3b72a-f9f5-4f24-a457-cea365c11632 · outbound
This paper cites Munteanu and J.
Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound Munteanu and J
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-08T04:14:29.747355Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 47c15767-89c6-4879-8b75-21a5842d1f70 · outbound
This paper cites Schoen and S.
Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound Schoen and S
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-08T04:14:29.757786Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation c0443b10-9b06-4038-8067-28f22f55c5a3 · outbound
This paper cites Schoen and S.T.
Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound Schoen and S.T
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-08T04:14:29.752014Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 9e069fca-ba0a-4942-bb13-c01c2a9dc9c7 · outbound
This paper cites Wang and B.
Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound Wang and B
Reference 20
- Resolution
- verified exact
- arxiv_id, observed 2026-07-08T04:14:29.573826Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation f59c5eeb-720b-4e77-931e-31a842efe25c · outbound
This paper cites Scalar curvature, sharp bottom spectrum and geometric rigidity.
Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound Scalar curvature, sharp bottom spectrum and geometric rigidity
Reference 21
- Resolution
- verified exact
- local_arxiv, observed 2026-07-08T04:14:29.573956Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation d9c0cff6-18da-401b-bf40-ab862821c8d4 · outbound
This paper cites Witten and S.
Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound Witten and S
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-08T04:14:29.757404Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 769184b3-b105-4b39-88a2-17178f6fcc54 · outbound
This paper cites an unresolved cited work.
Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound Unresolved cited work
Reference 23
- Resolution
- unresolved
- raw_fallback, observed 2026-07-08T04:14:29.744616Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Pith citing papers
Observation e8ff6698-22e3-49b2-8a75-03604ffeb9d0 · inbound
McKean Rigidity for Cocompact Negatively Curved Manifolds and the \(p\)-Laplacian cites this paper.
McKean Rigidity for Cocompact Negatively Curved Manifolds and the \(p\)-Laplacian Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound
Reference 41
- Resolution
- metadata mismatch
- local_arxiv, observed 2026-08-06T00:50:12.972357Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.