Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-10T13:41:58.773099Z
Paper Citation Record · LEDGER
Small gaps in the Ulam sequence
As of 12 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 0 inbound Pith citation observations for arXiv:2501.16285.
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
26 of 26 outbound references displayed
- verified exact3
- verified fuzzy20
- unresolved3
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation bdbe6f02-e126-459a-829e-8652d82e13c3 · outbound
This paper cites Distributions of Ulam Words up to Length 30.
Small gaps in the Ulam sequence Distributions of Ulam Words up to Length 30
Reference 1
- Resolution
- verified exact
- local_arxiv, observed 2026-08-10T13:41:58.853374Z
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 28146e26-ccf4-43a5-b437-2ac2577f107d · outbound
This paper cites A hidden signal in Hofstadter's $H$ sequence.
Small gaps in the Ulam sequence A hidden signal in Hofstadter's $H$ sequence
Reference 2
- Resolution
- verified exact
- local_arxiv, observed 2026-08-10T13:41:58.834653Z
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 48605163-c622-4439-8d68-5ad2abd28510 · outbound
This paper cites Bade, K., Cui, A.
Small gaps in the Ulam sequence Bade, K., Cui, A
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T13:41:59.169957Z
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 4f0457df-f61d-4bbf-a62e-9058b8440f3f · outbound
This paper cites Blondel, John N.
Small gaps in the Ulam sequence Blondel, John N
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T13:41:59.156011Z
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 5744ee03-0857-4cdc-8463-8750cc3c7250 · outbound
This paper cites Cassaigne and S.
Small gaps in the Ulam sequence Cassaigne and S
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T13:41:59.142610Z
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 582518eb-a64c-438f-ab49-80fc13468221 · outbound
This paper cites Finch, Conjectures about s-additive sequences.
Small gaps in the Ulam sequence Finch, Conjectures about s-additive sequences
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T13:41:59.128723Z
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 fca597f2-2f6e-49b9-86cf-d7b38d8be698 · outbound
This paper cites Finch, Patterns in 1-additive sequences.
Small gaps in the Ulam sequence Finch, Patterns in 1-additive sequences
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T13:41:59.115262Z
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 8258c97f-43bf-4bc9-b3b1-a5056fe74e0e · outbound
This paper cites Finch, On the regularity of certain 1-additive sequen ces.
Small gaps in the Ulam sequence Finch, On the regularity of certain 1-additive sequen ces
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T13:41:59.101603Z
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 7e2cfc4f-52ad-475f-b3ea-37ebc5725ed5 · outbound
This paper cites Finch, Are 0-Additive Sequences Always Regular? The A merican Mathematical Monthly, vol.
Small gaps in the Ulam sequence Finch, Are 0-Additive Sequences Always Regular? The A merican Mathematical Monthly, vol
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T13:41:59.088465Z
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 278a228f-76f0-44c5-8438-19e151f35a59 · outbound
This paper cites Gelfand, Normierte ringe, Rech.
Small gaps in the Ulam sequence Gelfand, Normierte ringe, Rech
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T13:41:59.074464Z
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 731805de-51af-444e-8ca6-21f19ed200ff · outbound
This paper cites Hinman, B.
Small gaps in the Ulam sequence Hinman, B
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T13:41:59.061744Z
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 ed72487d-f60b-468d-9cc6-9062c62aa118 · outbound
This paper cites Hinman, B.
Small gaps in the Ulam sequence Hinman, B
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T13:41:59.047484Z
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 3b149303-4ff7-4e67-8436-1026ed273d46 · outbound
This paper cites Kravitz and S.
Small gaps in the Ulam sequence Kravitz and S
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T13:41:59.033853Z
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 8f91af1b-3c44-4d05-a72d-e94cdea32efa · outbound
This paper cites Kuca, Structures in additive sequences, Acta Arith.
Small gaps in the Ulam sequence Kuca, Structures in additive sequences, Acta Arith
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T13:41:59.020471Z
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 c53652fa-03bc-4741-adcc-a620ebcf7c29 · outbound
This paper cites On fractal patterns in Ulam words.
Small gaps in the Ulam sequence On fractal patterns in Ulam words
Reference 15
- Resolution
- verified exact
- local_arxiv, observed 2026-08-10T13:41:58.814627Z
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 f04aaaab-b5eb-490c-b86e-50b0ca7e6007 · outbound
This paper cites an unresolved cited work.
Small gaps in the Ulam sequence Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T13:41:59.006349Z
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 bd1eb8f4-a8d0-474d-b89f-bf2597aef9a6 · outbound
This paper cites Queneau, Sur les suites s-additives.
Small gaps in the Ulam sequence Queneau, Sur les suites s-additives
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T13:41:58.991687Z
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 eafaabe4-7da8-4345-aa08-8ff20ffe783f · outbound
This paper cites Queneau, Sur les suites s-additives, J.
Small gaps in the Ulam sequence Queneau, Sur les suites s-additives, J
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T13:41:58.978545Z
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 6a99bba9-6058-4ae6-bd24-0c70a6d0c883 · outbound
This paper cites Recaman, Research Problems: Questions on a Sequence of Ulam.
Small gaps in the Ulam sequence Recaman, Research Problems: Questions on a Sequence of Ulam
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T13:41:58.965139Z
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 c6a133d9-73f5-416d-947a-59a5af47080f · outbound
This paper cites an unresolved cited work.
Small gaps in the Ulam sequence Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T13:41:58.951090Z
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 a777e980-d1f3-483d-b81e-99415e768a78 · outbound
This paper cites Schmerl and E.
Small gaps in the Ulam sequence Schmerl and E
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T13:41:58.936763Z
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 5158ed2d-3b55-4a2b-8096-d74f26a0fbf1 · outbound
This paper cites Sheydvasser, The Ulam Sequence of Linear Integer Pol ynomials.
Small gaps in the Ulam sequence Sheydvasser, The Ulam Sequence of Linear Integer Pol ynomials
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T13:41:58.921790Z
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 3d7871b8-c5d7-40b8-a143-ed0bfe5490ba · outbound
This paper cites Steinerberger, A hidden signal in the Ulam sequence.
Small gaps in the Ulam sequence Steinerberger, A hidden signal in the Ulam sequence
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T13:41:58.907935Z
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 e3aceed5-70af-4d97-9ef9-ea07487d611a · outbound
This paper cites Ulam, Ulam, On some mathematical problems connected with patterns of growth of figures.
Small gaps in the Ulam sequence Ulam, Ulam, On some mathematical problems connected with patterns of growth of figures
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T13:41:58.893400Z
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 73054107-b4f4-44c7-87be-90ef5fd16b77 · outbound
This paper cites Ulam, Combinatorial analysis in infinite sets and som e physical theories.
Small gaps in the Ulam sequence Ulam, Combinatorial analysis in infinite sets and som e physical theories
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-10T13:41:58.879787Z
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 d1c7d4a5-ace5-49c6-9e09-7d087effc465 · outbound
This paper cites an unresolved cited work.
Small gaps in the Ulam sequence Unresolved cited work
Reference 26
- Resolution
- unresolved
- raw_fallback, observed 2026-08-10T13:41:58.866935Z
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.