Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T10:30:58.283430Z
Paper Citation Record · LEDGER
Can Umbral and $q$-calculus be merged?
As of 17 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:1909.00058.
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 2026-08-16T06:30:59.297886+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
25 of 25 outbound references displayed
- verified exact1
- verified fuzzy16
- unresolved8
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 9e81b2f7-a443-4400-9f02-e84dd3e4c1e6 · outbound
This paper cites an unresolved cited work.
Can Umbral and $q$-calculus be merged? Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T10:30:59.816584Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 72fb505f-7ba2-4e10-b5d4-1fa5cddbcb2d · outbound
This paper cites The Umbral Calculus.
Can Umbral and $q$-calculus be merged? The Umbral Calculus
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T10:30:59.793985Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e35860ed-effd-45b7-ab07-83cc003dd994 · outbound
This paper cites Roman, More on the Umbral Calculus, with Emphasis on the q -Umbral Calculus , J.
Can Umbral and $q$-calculus be merged? Roman, More on the Umbral Calculus, with Emphasis on the q -Umbral Calculus , J
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T10:30:59.765935Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c35b1fd6-5c7d-48c8-9ff7-78203e625371 · outbound
This paper cites Umbral Calculus, a Different Mathematical Language.
Can Umbral and $q$-calculus be merged? Umbral Calculus, a Different Mathematical Language
Reference 4
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T10:30:58.424236Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d98360f5-e705-45cc-a54b-2a2e3249420a · outbound
This paper cites Dattoli, E.
Can Umbral and $q$-calculus be merged? Dattoli, E
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T10:30:59.726768Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6e15d94d-bad8-4fd4-8fb0-1e810b23c04a · outbound
This paper cites Babusci, G.
Can Umbral and $q$-calculus be merged? Babusci, G
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T10:30:59.702203Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4b95d1bf-a5bb-4dbb-bedf-40ad3505cb00 · outbound
This paper cites Babusci, G.
Can Umbral and $q$-calculus be merged? Babusci, G
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T10:30:59.645134Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e1a1f35a-5b4e-48a3-bb50-e977593b2bde · outbound
This paper cites Thomae, Beitrage zur Theorie der durch die Heinesche Reihe , J.
Can Umbral and $q$-calculus be merged? Thomae, Beitrage zur Theorie der durch die Heinesche Reihe , J
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T10:30:59.608476Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 0bb68505-e170-4f3e-8388-4717638e4406 · outbound
This paper cites Dattoli, E.
Can Umbral and $q$-calculus be merged? Dattoli, E
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T10:30:59.563069Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation fae98772-602e-45cd-a4e2-dec85f154a7d · outbound
This paper cites Dattoli, P.
Can Umbral and $q$-calculus be merged? Dattoli, P
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T10:30:59.478488Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation de14cdc3-5287-4431-988b-90d27e6d3922 · outbound
This paper cites an unresolved cited work.
Can Umbral and $q$-calculus be merged? Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T10:30:59.416014Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e5b843d3-8aaa-4660-b309-37d32110f9f0 · outbound
This paper cites Mez o , Duplication formulae involving Jacobi Theta functions and Gosper's q -trigonometric functions , Proceedings of the American Math.
Can Umbral and $q$-calculus be merged? Mez o , Duplication formulae involving Jacobi Theta functions and Gosper's q -trigonometric functions , Proceedings of the American Math
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T10:30:59.382793Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2b59e7bb-c019-4063-a878-3b7582294f55 · outbound
This paper cites Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics.
Can Umbral and $q$-calculus be merged? Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T10:30:59.323293Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 3152c936-6022-4c20-ac26-6e5405372741 · outbound
This paper cites an unresolved cited work.
Can Umbral and $q$-calculus be merged? Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T10:30:59.271382Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 41e155c7-156b-4d56-a2c3-d80276178f18 · outbound
This paper cites an unresolved cited work.
Can Umbral and $q$-calculus be merged? Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T10:30:59.212898Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6c25ef84-bae6-4a52-8ab6-1ac230f1c35d · outbound
This paper cites Dattoli and A.
Can Umbral and $q$-calculus be merged? Dattoli and A
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T10:30:59.166327Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 12cf75bc-a68d-4d00-9eea-4c1931236555 · outbound
This paper cites Dattoli and A.
Can Umbral and $q$-calculus be merged? Dattoli and A
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T10:30:59.121567Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 36aca212-3237-4727-bba9-d6885f1a3484 · outbound
This paper cites an unresolved cited work.
Can Umbral and $q$-calculus be merged? Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T10:30:59.020055Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 5a0054ca-3ee0-42d7-8879-1220f49c1bb7 · outbound
This paper cites Tsallis, Introduction to Nonextensive Statistical Mechanics (Springer, Berlin, 2009).
Can Umbral and $q$-calculus be merged? Tsallis, Introduction to Nonextensive Statistical Mechanics (Springer, Berlin, 2009)
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T10:30:58.951405Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 79845b42-a7a8-4af9-94f1-91a8f597774e · outbound
This paper cites an unresolved cited work.
Can Umbral and $q$-calculus be merged? Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T10:30:58.867906Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 9743389c-a4cb-4780-8ec2-f1c7e5c66eea · outbound
This paper cites Douglas et al, Tunable Tsallis Distributions in Dissipative Optical Lattices , Phys.
Can Umbral and $q$-calculus be merged? Douglas et al, Tunable Tsallis Distributions in Dissipative Optical Lattices , Phys
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T10:30:58.783222Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 0f38d656-fb1d-4a20-8cc9-692290feb533 · outbound
This paper cites Askey, The q -Gamma and q -Beta Functions , Applicable Analysis 8 (1978) 125--141.
Can Umbral and $q$-calculus be merged? Askey, The q -Gamma and q -Beta Functions , Applicable Analysis 8 (1978) 125--141
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T10:30:58.753158Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 390712c0-47ea-4933-83cd-4a71a0a8a4de · outbound
This paper cites an unresolved cited work.
Can Umbral and $q$-calculus be merged? Unresolved cited work
Reference 23
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T10:30:58.720561Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 7bd6a88f-302d-4f3b-8349-4dbef1881723 · outbound
This paper cites Encyclopedia of Mathematics and its Applications.
Can Umbral and $q$-calculus be merged? Encyclopedia of Mathematics and its Applications
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T10:30:58.614911Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c67c57f9-ac81-4746-ad19-8164b1314bb4 · outbound
This paper cites an unresolved cited work.
Can Umbral and $q$-calculus be merged? Unresolved cited work
Reference 25
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T10:30:58.508626Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Pith citing papers
No inbound Pith citation observations are available.