Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T11:53:47.060889Z
Paper Citation Record · LEDGER
An improved lower bound for the logarithmic energy on $\mathbb S^2$
As of 8 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2506.01660.
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 2026-08-08T06:32:00.761636+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
28 of 28 outbound references displayed
- verified exact0
- verified fuzzy20
- unresolved8
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 1f76ee4c-0ce3-4a4a-ac92-196ca58b5263 · outbound
This paper cites Beltr\'an, N.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ Beltr\'an, N
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:53:51.998575Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation ff43611a-a794-42b3-96fb-fbcf16bb687c · outbound
This paper cites Beltr\'an, U.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ Beltr\'an, U
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:53:51.860479Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation ef72ad69-83d7-4be9-a137-a28748645b12 · outbound
This paper cites Beltr\'an, F.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ Beltr\'an, F
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:53:51.690405Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 14e0e560-d883-46c4-931d-65e57d6b1eed · outbound
This paper cites Beltr\'an, F.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ Beltr\'an, F
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:53:51.443577Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 39304c5d-e567-4196-b1ee-a759dad2f883 · outbound
This paper cites B\'etermin, E.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ B\'etermin, E
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:53:51.170165Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 2e1e1971-9d32-46a3-9bb6-46fedf977fa0 · outbound
This paper cites Borodachov, D.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ Borodachov, D
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:53:50.910354Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation b4f2f485-1aa3-4d27-a40d-322a87cea29b · outbound
This paper cites an unresolved cited work.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:53:50.586461Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation bf6f58a5-4217-4451-8d7e-dee2fed357d1 · outbound
This paper cites Fejes T\'oth, The isepiphan problem for n -hedra.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ Fejes T\'oth, The isepiphan problem for n -hedra
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:53:50.360054Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 815d10b6-ea60-49de-8d3c-df66df67e019 · outbound
This paper cites Fejes T\'oth, G.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ Fejes T\'oth, G
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:53:50.159582Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 055c35d6-1582-4e83-9f98-9cac02729527 · outbound
This paper cites García-Zelada, Concentration for Coulomb gases on compact manifolds.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ García-Zelada, Concentration for Coulomb gases on compact manifolds
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:53:50.020186Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 08e8b7d0-e1d4-4615-999f-bc8e47d3ca28 · outbound
This paper cites an unresolved cited work.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:53:49.868223Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 4ea348ad-00be-40df-9765-f988b1adbc8e · outbound
This paper cites Kloeckner, Approximation by finitely supported measures.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ Kloeckner, Approximation by finitely supported measures
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:53:49.675036Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 8dc60236-4975-4543-97d8-e953b0f13db5 · outbound
This paper cites an unresolved cited work.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:53:49.497476Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 56606861-9188-4592-bcbe-1da9d4688f56 · outbound
This paper cites an unresolved cited work.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:53:49.363799Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 51ccee44-6ba3-4862-abb4-5fe64cf64293 · outbound
This paper cites an unresolved cited work.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:53:49.210566Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation e803a6cb-7efd-4b3d-a0e1-2fc862015082 · outbound
This paper cites Marzo, A.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ Marzo, A
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:53:49.057800Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 41df8b59-b9ac-4e77-85c9-5b10857c9569 · outbound
This paper cites Peyre, Comparison between W_2 distance and H _ -1 norm, and localization of Wasserstein distance.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ Peyre, Comparison between W_2 distance and H _ -1 norm, and localization of Wasserstein distance
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:53:48.903823Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation cd6b3494-4d74-4ebd-af18-112d0a514c0e · outbound
This paper cites an unresolved cited work.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:53:48.762323Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 4121a769-ceb2-4149-bda2-86503b260a1c · outbound
This paper cites Sandier, S.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ Sandier, S
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:53:48.640888Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation b2dfdfe7-487b-4e45-8df0-683edb6a1854 · outbound
This paper cites an unresolved cited work.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:53:48.445212Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 2083dc9d-2518-4af7-8d55-85cbc5577186 · outbound
This paper cites an unresolved cited work.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:53:48.316675Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 8fabac9a-f2b9-4900-9920-32112949286d · outbound
This paper cites Skinner, Logarithmic potential theory on Riemann surfaces (PhD thesis), 2015.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ Skinner, Logarithmic potential theory on Riemann surfaces (PhD thesis), 2015
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:53:48.169491Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation efd0c323-911a-4840-8e54-398a3acf4e16 · outbound
This paper cites Smale, Mathematical problems for the next century.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ Smale, Mathematical problems for the next century
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:53:48.024187Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 8e0145f4-6124-411f-8a14-15f7772b5810 · outbound
This paper cites Steinerberger, On the Logarithmic Energy of Points on S ^2.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ Steinerberger, On the Logarithmic Energy of Points on S ^2
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:53:47.894044Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 9f0a7556-fb8b-4ac9-9673-ec2f3afa2d92 · outbound
This paper cites Tsuji, Potential Theory in Modern Function Theory.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ Tsuji, Potential Theory in Modern Function Theory
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:53:47.725012Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 71dc0ac2-817f-4446-b80e-0303ef25d4bc · outbound
This paper cites Villani, Topics in Optimal Transportation.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ Villani, Topics in Optimal Transportation
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:53:47.543863Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 4feb6bbf-1d09-44df-ab96-fb287c58207e · outbound
This paper cites Wagner, On the product of distances to a point set on a sphere.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ Wagner, On the product of distances to a point set on a sphere
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:53:47.392948Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 637bf252-1c38-4da4-96d2-ce01209d3137 · outbound
This paper cites Wolff, Fekete points on spheres, Unpublished manuscript.
An improved lower bound for the logarithmic energy on $\mathbb S^2$ Wolff, Fekete points on spheres, Unpublished manuscript
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:53:47.226360Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Pith citing papers
No inbound Pith citation observations are available.