Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-05-08T18:56:49.741233Z
Paper Citation Record · LEDGER
Gaps in Multiplicative Sidon Sets
As of 6 August 2026, this Paper Citation Record lists 8 of 8 outbound references and 1 inbound Pith citation observation for arXiv:2605.02064.
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 2026-08-06T06:34:29.942622+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-06-27T20:49:36.275111Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-07-02T20:17:21.303675Z
Reference resolution
8 of 8 outbound references displayed
- verified exact4
- verified fuzzy2
- unresolved1
- parse uncertain0
- malformed identifier1
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 7be9b033-6197-4646-960e-0956442964d3 · outbound
This paper cites Aristotle: IMO-level Automated Theorem Proving.
Gaps in Multiplicative Sidon Sets Aristotle: IMO-level Automated Theorem Proving
Reference 1
- Resolution
- malformed identifier
- arxiv_id, observed 2026-05-15T08:51:38.126380Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 71849e08-b3ab-409f-9ea0-0fd2fa6b41a9 · outbound
This paper cites and Harman, Glyn and Pintz, J\'anos , TITLE =.
Gaps in Multiplicative Sidon Sets and Harman, Glyn and Pintz, J\'anos , TITLE =
Reference 2
- Resolution
- verified exact
- doi, observed 2026-05-08T18:59:02.037576Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 2c96071f-4cbe-4fb9-a482-815fbc4ad249 · outbound
This paper cites an unresolved cited work.
Gaps in Multiplicative Sidon Sets Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-05-26T03:46:41.423450Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation e986eef7-e324-4883-8faa-de59900c56eb · outbound
This paper cites Erdős,On Sequences of Integers No One of Which Divides the Product of Two Others and on Some Related Problems, Mitt.
Gaps in Multiplicative Sidon Sets Erdős,On Sequences of Integers No One of Which Divides the Product of Two Others and on Some Related Problems, Mitt
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-26T03:46:41.419926Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation fb7d2863-4b47-4e07-8790-d70875907082 · outbound
This paper cites Erdős,On Some Applications of Graph Theory to Number Theoretic Problems, Publ.
Gaps in Multiplicative Sidon Sets Erdős,On Some Applications of Graph Theory to Number Theoretic Problems, Publ
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-26T03:46:41.415945Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 838a05b4-bf9d-4e15-8bfc-f52949468c3f · outbound
This paper cites Laishram and M.
Gaps in Multiplicative Sidon Sets Laishram and M
Reference 6
- Resolution
- verified exact
- arxiv_id, observed 2026-05-08T18:59:02.029432Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 44d9e762-0f25-4774-a9ed-7bc2cf65bb79 · outbound
This paper cites Liu and P.
Gaps in Multiplicative Sidon Sets Liu and P
Reference 7
- Resolution
- verified exact
- doi, observed 2026-05-08T18:59:02.041514Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Observation 5dccef37-8781-4fb1-a039-a2f7929fd6dc · outbound
This paper cites Sárközy,Unsolved Problems in Number Theory, Period.
Gaps in Multiplicative Sidon Sets Sárközy,Unsolved Problems in Number Theory, Period
Reference 8
- Resolution
- verified exact
- doi, observed 2026-05-08T18:59:02.033311Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.
Pith citing papers
Observation 835799b0-86c9-49a7-8e99-33fc57bb635f · inbound
Gaps in Multiplicative Sidon Sets II cites this paper.
Gaps in Multiplicative Sidon Sets II Gaps in Multiplicative Sidon Sets
Reference 4
- Resolution
- verified exact
- local_arxiv, observed 2026-07-02T20:17:21.304997Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.