Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T05:21:24.027196Z
Paper Citation Record · LEDGER
Multiple sums with the M\"obius function
As of 11 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 0 inbound Pith citation observations for arXiv:2506.08787.
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 2026-08-11T06:34:44.6726+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
18 of 18 outbound references displayed
- verified exact2
- verified fuzzy10
- unresolved6
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 59c778e4-a972-4165-b675-a2802c7a7134 · outbound
This paper cites an unresolved cited work.
Multiple sums with the M\"obius function Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:21:27.260147Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation c67d9743-f9c9-4ec4-a2d1-2b69a365700a · outbound
This paper cites Bergelson and A.
Multiple sums with the M\"obius function Bergelson and A
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:21:27.056996Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 9b95be2e-75da-4cc1-b3ae-3496819476da · outbound
This paper cites Cai, A remark on the Goldbach-Vinogradov theorem, Funct.
Multiple sums with the M\"obius function Cai, A remark on the Goldbach-Vinogradov theorem, Funct
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:21:26.922384Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 508dc21a-759f-4e35-bf91-970f7a2a265d · outbound
This paper cites Davenport, On some infinite series involving arithmetical functions II, Quart.
Multiple sums with the M\"obius function Davenport, On some infinite series involving arithmetical functions II, Quart
Reference 4
- Resolution
- verified exact
- doi, observed 2026-08-07T05:21:24.256081Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation e99fb942-68e8-4289-b623-427d52aa6bfe · outbound
This paper cites Fouvry and S.
Multiple sums with the M\"obius function Fouvry and S
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:21:26.754057Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 91f26571-95f2-4ef9-9923-ef247a69fc4c · outbound
This paper cites Gafni and N.
Multiple sums with the M\"obius function Gafni and N
Reference 6
- Resolution
- verified exact
- raw_fallback, observed 2026-08-07T05:21:24.577292Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 18f27226-bc5f-4dea-b7f6-ebc8ca7dcf1a · outbound
This paper cites an unresolved cited work.
Multiple sums with the M\"obius function Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:21:26.552795Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 25b75c5a-afeb-405a-b0bd-f9fd4d56290b · outbound
This paper cites Hajela and B.
Multiple sums with the M\"obius function Hajela and B
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:21:26.419009Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 5f4eddbf-63ea-4ff8-b6bb-416dfe14826f · outbound
This paper cites an unresolved cited work.
Multiple sums with the M\"obius function Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:21:26.296124Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 5b162e54-03c0-4b06-bc9b-912841a34318 · outbound
This paper cites an unresolved cited work.
Multiple sums with the M\"obius function Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:21:26.153593Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 9fadc024-8df0-42d9-9223-9d23727406bd · outbound
This paper cites Iwaniec and E.
Multiple sums with the M\"obius function Iwaniec and E
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:21:25.941042Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 7d4b8915-6702-4ee7-8b4a-6725b195e33b · outbound
This paper cites Matom¨ aki, X.
Multiple sums with the M\"obius function Matom¨ aki, X
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:21:25.707939Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 4ec41350-cbc7-491a-8bd6-8b67cb24f088 · outbound
This paper cites Matthiesen, J.
Multiple sums with the M\"obius function Matthiesen, J
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:21:25.485166Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation e570de69-8fa3-4984-b4f5-5f5d367e064c · outbound
This paper cites an unresolved cited work.
Multiple sums with the M\"obius function Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:21:25.337963Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 8ebd95f9-1631-4ce8-af16-6e840a66565d · outbound
This paper cites Sarnak,Three lectures on the M¨ obius function, randomness and dynamics, 2011 (avail- able fromhttps://publications.ias.edu/node/506).
Multiple sums with the M\"obius function Sarnak,Three lectures on the M¨ obius function, randomness and dynamics, 2011 (avail- able fromhttps://publications.ias.edu/node/506)
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:21:25.186869Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation d1612930-2fe8-4438-8cda-9b6b14756cb3 · outbound
This paper cites an unresolved cited work.
Multiple sums with the M\"obius function Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T05:21:25.051102Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation 216a22b8-e59f-4b78-baa6-c5a99bd79ef3 · outbound
This paper cites Zhan, On the representation of large odd integer as a sum of three almost equal primes, Acta Math.
Multiple sums with the M\"obius function Zhan, On the representation of large odd integer as a sum of three almost equal primes, Acta Math
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:21:24.880093Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Observation c83660e9-4956-4843-8850-c1175234878c · outbound
This paper cites Zhang, On an exponential sum related to the M¨ obius function, Proc.
Multiple sums with the M\"obius function Zhang, On an exponential sum related to the M¨ obius function, Proc
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:21:24.720193Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.
Pith citing papers
No inbound Pith citation observations are available.