Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T13:17:55.400245Z
Paper Citation Record · LEDGER
An identity relating Catalan numbers to tangent numbers with arithmetic applications
As of 12 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2507.20965.
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
22 of 22 outbound references displayed
- verified exact2
- verified fuzzy18
- unresolved2
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation ff56c2f0-7b1e-463b-a53f-77a2aa7772ac · outbound
This paper cites Aliniaeifard and S.X.
An identity relating Catalan numbers to tangent numbers with arithmetic applications Aliniaeifard and S.X
Reference 1
- Resolution
- verified exact
- raw_fallback, observed 2026-08-06T13:17:55.574032Z
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 11aae5eb-4abf-4d60-bdf8-d24b1deac0f4 · outbound
This paper cites André, Développement desec x and tan x, C.
An identity relating Catalan numbers to tangent numbers with arithmetic applications André, Développement desec x and tan x, C
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T13:17:55.871535Z
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 38faeb0c-4489-42a8-9792-9c4911e350d0 · outbound
This paper cites Andrews and I.
An identity relating Catalan numbers to tangent numbers with arithmetic applications Andrews and I
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T13:17:55.858193Z
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 d2c08d61-54f8-4e55-ad82-12fb199aa336 · outbound
This paper cites Barsky, Congruences pour les nombres de Genocchi de deuxième espèce, Group.
An identity relating Catalan numbers to tangent numbers with arithmetic applications Barsky, Congruences pour les nombres de Genocchi de deuxième espèce, Group
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T13:17:55.843312Z
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 bdcaaf5c-ccc2-4764-97e5-ac054e2697dc · outbound
This paper cites Carlitz, The Staudt–Clausen theorem, Math.
An identity relating Catalan numbers to tangent numbers with arithmetic applications Carlitz, The Staudt–Clausen theorem, Math
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T13:17:55.829504Z
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 595918dc-e3d9-4ae0-8c7b-704203785585 · outbound
This paper cites Carlitz, A conjecture concerning Genocchi numbers, Norske Vid.
An identity relating Catalan numbers to tangent numbers with arithmetic applications Carlitz, A conjecture concerning Genocchi numbers, Norske Vid
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T13:17:55.814961Z
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 3185e28c-c423-4ac6-8475-4f0032edc011 · outbound
This paper cites Choi and H.
An identity relating Catalan numbers to tangent numbers with arithmetic applications Choi and H
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T13:17:55.799886Z
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 b35f4778-0478-4c1f-a734-630ecfd4b52e · outbound
This paper cites Foata, Further divisibility properties of theq-tangent numbers, Proc.
An identity relating Catalan numbers to tangent numbers with arithmetic applications Foata, Further divisibility properties of theq-tangent numbers, Proc
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T13:17:55.785386Z
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 4f27a29d-444d-4855-bd09-d3e1a1a746cd · outbound
This paper cites Foata and G.-N.
An identity relating Catalan numbers to tangent numbers with arithmetic applications Foata and G.-N
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T13:17:55.769956Z
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 156b604f-16b6-4e1d-8c1c-559da8cba9ee · outbound
This paper cites Foata and G.-N.
An identity relating Catalan numbers to tangent numbers with arithmetic applications Foata and G.-N
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T13:17:55.754569Z
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 24d79ad4-0127-4a0f-828e-beb8a1f8589f · outbound
This paper cites an unresolved cited work.
An identity relating Catalan numbers to tangent numbers with arithmetic applications Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T13:17:55.739944Z
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 e6ed0439-ef88-4f34-b165-ae28330532e2 · outbound
This paper cites Han and J.-Y.
An identity relating Catalan numbers to tangent numbers with arithmetic applications Han and J.-Y
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T13:17:55.725736Z
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 6c05074b-9b3a-4042-b07d-14cfa8fba5d6 · outbound
This paper cites Lin, S.-M.
An identity relating Catalan numbers to tangent numbers with arithmetic applications Lin, S.-M
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T13:17:55.711939Z
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 3c293467-5073-443d-8978-7ffd9b31a76b · outbound
This paper cites an unresolved cited work.
An identity relating Catalan numbers to tangent numbers with arithmetic applications Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T13:17:55.698093Z
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 bf3c10b7-e466-4459-b62a-4dff7cddfa25 · outbound
This paper cites Lin and J.
An identity relating Catalan numbers to tangent numbers with arithmetic applications Lin and J
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T13:17:55.684018Z
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 f0035688-65ef-48c9-b361-88562eb54934 · outbound
This paper cites Riordan and P.
An identity relating Catalan numbers to tangent numbers with arithmetic applications Riordan and P
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T13:17:55.669325Z
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 09d5fd17-8c52-4da6-8334-ce68b70a918c · outbound
This paper cites Sagan, Generalized Euler numbers and ordered set partitions, Discrete Math.,349 (2026), Article 114715.
An identity relating Catalan numbers to tangent numbers with arithmetic applications Sagan, Generalized Euler numbers and ordered set partitions, Discrete Math.,349 (2026), Article 114715
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T13:17:55.653932Z
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 71efd28b-18b2-4a77-b4f5-06b57cbc2423 · outbound
This paper cites Ordered set partition posets.
An identity relating Catalan numbers to tangent numbers with arithmetic applications Ordered set partition posets
Reference 18
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T13:17:55.448888Z
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 f306baab-62cb-40c5-a0e9-67da01492bda · outbound
This paper cites Stanley, Binomial posets, Möbius inversion, and permutation enumeration, J.
An identity relating Catalan numbers to tangent numbers with arithmetic applications Stanley, Binomial posets, Möbius inversion, and permutation enumeration, J
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T13:17:55.636903Z
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 326c6696-137f-419c-936c-87cebff6afb7 · outbound
This paper cites Stanley,Enumerative combinatorics, Vol.
An identity relating Catalan numbers to tangent numbers with arithmetic applications Stanley,Enumerative combinatorics, Vol
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T13:17:55.621472Z
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 4172efb3-9d7b-48b6-bf8a-a81da651d113 · outbound
This paper cites Stanley,Enumerative Combinatorics, Vol.
An identity relating Catalan numbers to tangent numbers with arithmetic applications Stanley,Enumerative Combinatorics, Vol
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T13:17:55.606209Z
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 03add9ae-949f-48b5-8846-01173e1dab6d · outbound
This paper cites Stanley, A Survey of Alternating Permutations, in Combinatorics and Graphs, R.A.
An identity relating Catalan numbers to tangent numbers with arithmetic applications Stanley, A Survey of Alternating Permutations, in Combinatorics and Graphs, R.A
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T13:17:55.590014Z
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.