Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T15:14:16.948941Z
Paper Citation Record · LEDGER
Slow convergence of Birkhoff ergodic averages
As of 19 August 2026, this Paper Citation Record lists 5 of 5 outbound references and 1 inbound Pith citation observation for arXiv:2507.16740.
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 2026-08-15T15:43:03.635816Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-15T18:16:14.067578Z
Reference resolution
5 of 5 outbound references displayed
- verified exact0
- verified fuzzy4
- unresolved1
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation b3e9e7a1-0c51-4f71-aea5-b8195d6a5299 · outbound
This paper cites Krengel, On the speed of convergence in the ergodic theorem Monatsh.
Slow convergence of Birkhoff ergodic averages Krengel, On the speed of convergence in the ergodic theorem Monatsh
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:14:17.036409Z
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 6ca4f812-c4af-47ad-8b90-7c21cd828e43 · outbound
This paper cites Подвигин, О скоростях сходимости в эргодической теореме Биркгофа, Сиб.
Slow convergence of Birkhoff ergodic averages Подвигин, О скоростях сходимости в эргодической теореме Биркгофа, Сиб
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:14:17.026308Z
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 14cf30fd-7be9-4c25-93c9-bcc936035205 · outbound
This paper cites Рыжиков, Медленные сходимости эргодических средних, Матем.
Slow convergence of Birkhoff ergodic averages Рыжиков, Медленные сходимости эргодических средних, Матем
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:14:17.010484Z
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 5cffc96e-65d4-4767-b0b2-429c060b6459 · outbound
This paper cites Рыжиков, Медленная сходимость взвешенных средних для потоков и дей- ствий счетных аменабельных групп.
Slow convergence of Birkhoff ergodic averages Рыжиков, Медленная сходимость взвешенных средних для потоков и дей- ствий счетных аменабельных групп
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T15:14:16.992796Z
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 ae831f3f-acc2-434d-81a1-3f68cb0ea513 · outbound
This paper cites an unresolved cited work.
Slow convergence of Birkhoff ergodic averages Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T15:14:16.982624Z
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 51e74d44-0690-4c82-a41e-90c78a61e86d · inbound
Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity cites this paper.
Exponential convergence can happen in weighted Birkhoff averages via quasi-periodicity with arbitrary nonresonance and low regularity Slow convergence of Birkhoff ergodic averages
Reference 32
- Resolution
- verified exact
- local_arxiv, observed 2026-08-15T15:43:03.945458Z
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.