Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-12T13:42:09.385993Z
Paper Citation Record · LEDGER
Counting up-up-or-down-down permutations
As of 12 August 2026, this Paper Citation Record lists 8 of 8 outbound references and 0 inbound Pith citation observations for arXiv:2411.16113.
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 2026-08-12T06:34:41.77262+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
8 of 8 outbound references displayed
- verified exact0
- verified fuzzy4
- unresolved4
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 51ea5f24-9a23-4aac-b7e4-3244150cffe5 · outbound
This paper cites 4, 989–1034.
Counting up-up-or-down-down permutations 4, 989–1034
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T13:42:09.526155Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 6a9b5514-b6ad-4027-a2a7-0930072c48c7 · outbound
This paper cites an unresolved cited work.
Counting up-up-or-down-down permutations Unresolved cited work
Reference 2
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T13:42:09.510834Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation d300bc33-dd21-40de-a4bc-92dff9c26c34 · outbound
This paper cites Discrete Math.
Counting up-up-or-down-down permutations Discrete Math
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T13:42:09.495640Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 41c4c771-93d4-4cb0-afe5-7eb14fe2abcf · outbound
This paper cites an unresolved cited work.
Counting up-up-or-down-down permutations Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T13:42:09.479605Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 9e5bf382-f731-4306-980a-440eb2389b52 · outbound
This paper cites Knuth, The Art of Computer Programming, Volume 4, Pre-Fascicle 7a.
Counting up-up-or-down-down permutations Knuth, The Art of Computer Programming, Volume 4, Pre-Fascicle 7a
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T13:42:09.465030Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 9537af19-e40e-4142-a3fc-ccd5ed34f93d · outbound
This paper cites 306 (2006), no.
Counting up-up-or-down-down permutations 306 (2006), no
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-12T13:42:09.449772Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 764163e6-eb01-4043-bf43-09cf49a42430 · outbound
This paper cites an unresolved cited work.
Counting up-up-or-down-down permutations Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T13:42:09.435056Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Observation 95443460-40fb-428c-acfd-23d1cc653b3d · outbound
This paper cites an unresolved cited work.
Counting up-up-or-down-down permutations Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-08-12T13:42:09.419794Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.
Pith citing papers
No inbound Pith citation observations are available.