Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T19:07:31.432066Z
Paper Citation Record · LEDGER
On divisibility relation graphs
As of 23 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 0 inbound Pith citation observations for arXiv:2507.06873.
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 2026-08-23T06:30:58.430688+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 exact0
- verified fuzzy6
- unresolved12
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 8df48898-7187-4523-9adc-640b13f4161f · outbound
This paper cites an unresolved cited work.
On divisibility relation graphs Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T19:07:35.141236Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 5aa12054-0cb4-4a3d-a3fa-79f858aef295 · outbound
This paper cites an unresolved cited work.
On divisibility relation graphs Unresolved cited work
Reference 2
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T19:07:34.921776Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 4f535118-341a-4fb6-bc3c-8e064d606dd2 · outbound
This paper cites an unresolved cited work.
On divisibility relation graphs Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T19:07:34.639364Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 606c45e6-d203-4fa3-af21-51d6abc89765 · outbound
This paper cites an unresolved cited work.
On divisibility relation graphs Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T19:07:34.324643Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 9d8a687e-0506-451a-be3d-2211ef3b98d0 · outbound
This paper cites 2, 189–198.
On divisibility relation graphs 2, 189–198
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:07:34.082957Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 7903a915-3348-4111-bba5-4fcabdec1834 · outbound
This paper cites an unresolved cited work.
On divisibility relation graphs Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T19:07:33.745950Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation abe1b344-6bd3-4e9e-8f3b-d21c1e9c7be0 · outbound
This paper cites an unresolved cited work.
On divisibility relation graphs Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T19:07:33.474191Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 8e3413d4-540a-419a-9c29-416a48c937a6 · outbound
This paper cites an unresolved cited work.
On divisibility relation graphs Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T19:07:33.147970Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 354abce2-bf47-482d-a865-36ffd3ee3be4 · outbound
This paper cites 20, Cambridge university press, 1997.
On divisibility relation graphs 20, Cambridge university press, 1997
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:07:32.864240Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation f4a458ed-f995-4f1d-98d9-1702ee0107d0 · outbound
This paper cites ,n}, European J.
On divisibility relation graphs ,n}, European J
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:07:32.583395Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 52e429b7-fc55-4fe6-a8c8-e2cfc2702e62 · outbound
This paper cites 4, 329–339.
On divisibility relation graphs 4, 329–339
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:07:32.422797Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 0a3d0b07-32eb-4692-82f9-684342339ae5 · outbound
This paper cites Merzel, J ´an Min´aˇc, Tung T.
On divisibility relation graphs Merzel, J ´an Min´aˇc, Tung T
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:07:32.295330Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 1012b451-507d-4007-9c6a-91bba623f75f · outbound
This paper cites an unresolved cited work.
On divisibility relation graphs Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T19:07:32.167424Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 0f317d16-59c2-4d93-9039-c801fd534264 · outbound
This paper cites Joins of normal matrices, their spectrum, and applications.
On divisibility relation graphs Joins of normal matrices, their spectrum, and applications
Reference 14
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T19:07:31.048177Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 995de64d-c7bc-4cda-9e91-5b5513fd1f54 · outbound
This paper cites On gcd-graphs over finite rings.
On divisibility relation graphs On gcd-graphs over finite rings
Reference 15
- Resolution
- unresolved
- no resolver link, observed 2026-08-06T19:07:31.146686Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 67bafafa-cd5a-4bb5-9c31-381c94b7d006 · outbound
This paper cites an unresolved cited work.
On divisibility relation graphs Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T19:07:31.988390Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 9f5ea80c-5ccc-49db-b87c-ca5e40598aed · outbound
This paper cites Numer40(1983), 291–304.
On divisibility relation graphs Numer40(1983), 291–304
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T19:07:31.834689Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Observation 138b6d40-3bcf-4524-bcaf-7778bd295b5d · outbound
This paper cites an unresolved cited work.
On divisibility relation graphs Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T19:07:31.663159Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.
Pith citing papers
No inbound Pith citation observations are available.