Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T20:14:36.255676Z
Paper Citation Record · LEDGER
A q-Supercongruence Motivated by Higher-Order Generalized Lehmer-Euler Numbers
As of 15 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 0 inbound Pith citation observations for arXiv:2507.16825.
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 2026-08-14T06:32:32.682623+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 exact1
- verified fuzzy13
- unresolved4
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 29d162f6-b218-4367-884a-2c12029aa35f · outbound
This paper cites H.: Lacunary recurrence formulas for the numbers of Bernoulli and Euler.
A q-Supercongruence Motivated by Higher-Order Generalized Lehmer-Euler Numbers H.: Lacunary recurrence formulas for the numbers of Bernoulli and Euler
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:14:36.760699Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation e795cdc5-07c3-467b-a79f-178234e15016 · outbound
This paper cites and Liu G.-D.: Congruence properties of Lember-Euler number.
A q-Supercongruence Motivated by Higher-Order Generalized Lehmer-Euler Numbers and Liu G.-D.: Congruence properties of Lember-Euler number
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:14:36.738577Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 3c84c055-edd3-4f4b-b64a-80c803b2a635 · outbound
This paper cites Tamkang J.
A q-Supercongruence Motivated by Higher-Order Generalized Lehmer-Euler Numbers Tamkang J
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:14:36.716101Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 11e2002c-0964-4340-9d29-cee3b601b8fd · outbound
This paper cites an unresolved cited work.
A q-Supercongruence Motivated by Higher-Order Generalized Lehmer-Euler Numbers Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T20:14:36.693125Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 3ac6c557-f688-4e4b-90f6-631fdb306668 · outbound
This paper cites and Guo, V.J.W., Zeng J.: q-Analogues of two supercongruences of Z.-W.
A q-Supercongruence Motivated by Higher-Order Generalized Lehmer-Euler Numbers and Guo, V.J.W., Zeng J.: q-Analogues of two supercongruences of Z.-W
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:14:36.663468Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 53cd574a-b161-40a5-bd55-b2f41a979eed · outbound
This paper cites http : //math.ecnu.edu.cn/ jwguo/maths/quad.pd f(2021).
A q-Supercongruence Motivated by Higher-Order Generalized Lehmer-Euler Numbers http : //math.ecnu.edu.cn/ jwguo/maths/quad.pd f(2021)
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:14:36.633403Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 338aa8bc-1119-4819-8ca1-176c2597e96e · outbound
This paper cites and Jiang X.-T.: On the divisibility of sums of even powers of q-binomial coeffi- cients.
A q-Supercongruence Motivated by Higher-Order Generalized Lehmer-Euler Numbers and Jiang X.-T.: On the divisibility of sums of even powers of q-binomial coeffi- cients
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:14:36.614188Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 7af03dc3-eb8b-4ea1-a1f9-3c826bd98193 · outbound
This paper cites an unresolved cited work.
A q-Supercongruence Motivated by Higher-Order Generalized Lehmer-Euler Numbers Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T20:14:36.592507Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 89cdfd9d-3df1-4654-aa9f-d77463117aeb · outbound
This paper cites Rocky Mt.
A q-Supercongruence Motivated by Higher-Order Generalized Lehmer-Euler Numbers Rocky Mt
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:14:36.563134Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation c93b7023-2f15-4a34-a04e-8238c4dba0ab · outbound
This paper cites and Zhang Y.: Ageneralization of Morley’s congruence.
A q-Supercongruence Motivated by Higher-Order Generalized Lehmer-Euler Numbers and Zhang Y.: Ageneralization of Morley’s congruence
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:14:36.542706Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation e82c3b58-1bdb-4ca0-bb67-a482fbb711f2 · outbound
This paper cites an unresolved cited work.
A q-Supercongruence Motivated by Higher-Order Generalized Lehmer-Euler Numbers Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T20:14:36.523323Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 819fcc6d-bf2d-4768-a5ca-4828b0307df3 · outbound
This paper cites and Ni H.-X.: Some q-congruences arising from certain identities, Period.
A q-Supercongruence Motivated by Higher-Order Generalized Lehmer-Euler Numbers and Ni H.-X.: Some q-congruences arising from certain identities, Period
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:14:36.500644Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation fd075d24-e173-4b91-a948-88d2dcc59299 · outbound
This paper cites an unresolved cited work.
A q-Supercongruence Motivated by Higher-Order Generalized Lehmer-Euler Numbers Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-08-06T20:14:36.459947Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation cb77bc4f-8df9-40c2-938b-d2de31f0e384 · outbound
This paper cites and Qi W.-W.: Two new q-supercongruences arising from Carlitz’s identity.
A q-Supercongruence Motivated by Higher-Order Generalized Lehmer-Euler Numbers and Qi W.-W.: Two new q-supercongruences arising from Carlitz’s identity
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:14:36.435666Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 347fdb8d-b440-489b-bc07-11a27d01178c · outbound
This paper cites and Liu J.-C.: A q-congruence implying the Beukers-Van Hamme congruence.
A q-Supercongruence Motivated by Higher-Order Generalized Lehmer-Euler Numbers and Liu J.-C.: A q-congruence implying the Beukers-Van Hamme congruence
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:14:36.415162Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 273c7825-8b3e-4a33-b008-c4e750900bbf · outbound
This paper cites Acta Arith., 128, pp.
A q-Supercongruence Motivated by Higher-Order Generalized Lehmer-Euler Numbers Acta Arith., 128, pp
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:14:36.377083Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation f35a9d87-4ad5-4669-9992-df71a2ed4b80 · outbound
This paper cites and Soni R.P.: Formulas and Theorems for the Special Functions of Mathematical Physics (3rd edition), Springer, New York, 1966.
A q-Supercongruence Motivated by Higher-Order Generalized Lehmer-Euler Numbers and Soni R.P.: Formulas and Theorems for the Special Functions of Mathematical Physics (3rd edition), Springer, New York, 1966
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-06T20:14:36.346611Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Observation 4a487329-238a-43eb-b4a5-a03b6c58c41f · outbound
This paper cites Refinements of Van Hamme's (E.2) and (F.2) supercongruences and two supercongruences by Swisher.
A q-Supercongruence Motivated by Higher-Order Generalized Lehmer-Euler Numbers Refinements of Van Hamme's (E.2) and (F.2) supercongruences and two supercongruences by Swisher
Reference 18
- Resolution
- verified exact
- local_arxiv, observed 2026-08-06T20:14:36.324670Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.
Pith citing papers
No inbound Pith citation observations are available.