Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T11:31:09.652063Z
Paper Citation Record · LEDGER
When is a Puiseux monoid atomic?
As of 16 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 0 inbound Pith citation observations for arXiv:1908.09227.
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 2026-08-15T06:32:42.880941+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
43 of 43 outbound references displayed
- verified exact4
- verified fuzzy15
- unresolved24
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 58c7be09-5399-4cf3-b94c-21a04f3f0b06 · outbound
This paper cites T., Hine, N., Paixao, J.
When is a Puiseux monoid atomic? T., Hine, N., Paixao, J
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:31:10.401190Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 6e313f2e-e94a-41e7-9d91-5bb0c74ab024 · outbound
This paper cites D., Anderson, D.
When is a Puiseux monoid atomic? D., Anderson, D
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:31:10.387430Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 322fd3d2-c10d-462e-bc70-48298a1af86e · outbound
This paper cites D., Coykendall, J., Hill, L., Zafrullah, M.
When is a Puiseux monoid atomic? D., Coykendall, J., Hill, L., Zafrullah, M
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:31:10.373434Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 5901caea-4364-4460-99b3-e1d2c780883b · outbound
This paper cites an unresolved cited work.
When is a Puiseux monoid atomic? Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:31:10.359651Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 06633fb1-6711-4bf9-a87d-0242fa669d79 · outbound
This paper cites T., Kaplan, N., Reiser, D.
When is a Puiseux monoid atomic? T., Kaplan, N., Reiser, D
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:31:10.345415Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation cdbb6902-a09f-49bf-9160-358cb158ec2c · outbound
This paper cites an unresolved cited work.
When is a Puiseux monoid atomic? Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:31:10.331626Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 5529f250-27d2-4c42-9f17-e4c5d6edc967 · outbound
This paper cites an unresolved cited work.
When is a Puiseux monoid atomic? Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:31:10.318322Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 13245653-d942-41b8-b4af-8ca54f0cc734 · outbound
This paper cites T., Corrales, M., Miller, A., Miller, C., Patel, D.
When is a Puiseux monoid atomic? T., Corrales, M., Miller, A., Miller, C., Patel, D
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:31:10.304610Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 81d5f1fa-d297-4cee-95e0-d169307be5af · outbound
This paper cites T., Daigle, J., Hoyer, R., Kaplan, N.
When is a Puiseux monoid atomic? T., Daigle, J., Hoyer, R., Kaplan, N
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:31:10.290483Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 9e1da994-8189-4953-b3ec-d019ee0014ed · outbound
This paper cites T., Garc ´ ıa-Garc ´ ıa, J.
When is a Puiseux monoid atomic? T., Garc ´ ıa-Garc ´ ıa, J
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:31:10.276370Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 85bb12d3-c034-4d25-acbe-48e225ebbe0f · outbound
This paper cites T., Garc ´ ıa-S´ anchez, P.
When is a Puiseux monoid atomic? T., Garc ´ ıa-S´ anchez, P
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:31:10.262987Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 5960e46f-7484-48ee-acb6-b6bdc9418198 · outbound
This paper cites T., Gotti, F., Gotti, M.
When is a Puiseux monoid atomic? T., Gotti, F., Gotti, M
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:31:10.248962Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation af5ee6a6-e59c-416c-b36d-570f062c1430 · outbound
This paper cites T., Gotti, F., Pelayo, R.
When is a Puiseux monoid atomic? T., Gotti, F., Pelayo, R
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:31:10.235450Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 1c81babe-cf0e-4752-a529-7bc90a48068a · outbound
This paper cites T., Hoyer, R., Kaplan, N.
When is a Puiseux monoid atomic? T., Hoyer, R., Kaplan, N
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:31:10.221572Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 42f07ebd-9784-4d3c-a078-6f4e70d32e36 · outbound
This paper cites T., Holden, M., Moore, T.
When is a Puiseux monoid atomic? T., Holden, M., Moore, T
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:31:10.208259Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 1d4e26ac-c679-476c-b5c7-f3ef542d5969 · outbound
This paper cites T., Krause, U., Oeljeklaus, E.
When is a Puiseux monoid atomic? T., Krause, U., Oeljeklaus, E
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:31:10.194537Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 7ec2af19-90de-421d-8f6a-4ec216674d46 · outbound
This paper cites an unresolved cited work.
When is a Puiseux monoid atomic? Unresolved cited work
Reference 17
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:31:10.181007Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation c330e934-108a-4954-ac93-cdc0a838bedc · outbound
This paper cites an unresolved cited work.
When is a Puiseux monoid atomic? Unresolved cited work
Reference 18
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:31:10.167073Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 0da4f5a9-20be-4617-b609-5561432a3c11 · outbound
This paper cites an unresolved cited work.
When is a Puiseux monoid atomic? Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:31:10.153062Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation d2440450-eb23-43fb-a103-40a4929f442e · outbound
This paper cites an unresolved cited work.
When is a Puiseux monoid atomic? Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:31:10.139701Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 018d138d-8598-4edb-a7b4-4312a59958ce · outbound
This paper cites an unresolved cited work.
When is a Puiseux monoid atomic? Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:31:10.126421Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation bddf349d-4045-458e-bab2-e5a5c9774411 · outbound
This paper cites A., Ojeda, I., S´ anchez-R.-Navarro, A.
When is a Puiseux monoid atomic? A., Ojeda, I., S´ anchez-R.-Navarro, A
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:31:10.112117Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation ea5cd93d-dbed-41be-9e3b-9b844928b878 · outbound
This paper cites A., Rosales, J.
When is a Puiseux monoid atomic? A., Rosales, J
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:31:10.098341Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation fe02358b-40dd-4287-aea2-6c3e29aea1df · outbound
This paper cites an unresolved cited work.
When is a Puiseux monoid atomic? Unresolved cited work
Reference 24
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:31:10.084348Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 80b5a43d-a526-4c15-a585-16e9a4cfc300 · outbound
This paper cites On strongly primary monoids, with a focus on Puiseux monoids.
When is a Puiseux monoid atomic? On strongly primary monoids, with a focus on Puiseux monoids
Reference 25
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T11:31:09.857266Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 7c20ef04-3e55-4143-bfc4-0c66754ad285 · outbound
This paper cites an unresolved cited work.
When is a Puiseux monoid atomic? Unresolved cited work
Reference 26
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:31:10.070513Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 10d98a68-c094-40a2-b9ed-62ec114e9f1b · outbound
This paper cites an unresolved cited work.
When is a Puiseux monoid atomic? Unresolved cited work
Reference 27
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:31:10.056857Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 8c7ae5b0-e459-47e6-a4a2-1336c7e3b370 · outbound
This paper cites an unresolved cited work.
When is a Puiseux monoid atomic? Unresolved cited work
Reference 28
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:31:10.043484Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation b270e442-4811-421b-a4cd-8f8eda1bc0e1 · outbound
This paper cites an unresolved cited work.
When is a Puiseux monoid atomic? Unresolved cited work
Reference 29
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:31:10.029713Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 8ee3b8bb-0522-4d1d-9d30-54dce20b0caa · outbound
This paper cites Geometric and combinatorial aspects of submonoids of a finite-rank free commutative monoid.
When is a Puiseux monoid atomic? Geometric and combinatorial aspects of submonoids of a finite-rank free commutative monoid
Reference 30
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T11:31:09.836560Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 669f9603-8df6-4cfd-9e4b-b2e503cde419 · outbound
This paper cites an unresolved cited work.
When is a Puiseux monoid atomic? Unresolved cited work
Reference 31
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:31:10.015812Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation cfea9cd2-ff6a-4779-b262-2446f8db273a · outbound
This paper cites an unresolved cited work.
When is a Puiseux monoid atomic? Unresolved cited work
Reference 32
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:31:10.000923Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation f0e931ae-2e5c-4f2f-a218-c7049c8e0866 · outbound
This paper cites an unresolved cited work.
When is a Puiseux monoid atomic? Unresolved cited work
Reference 33
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:31:09.986711Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 80d45608-7d6b-4ffe-a371-11fd19821847 · outbound
This paper cites (2020) On the system of sets of lengths and the elast icity of submonoids of a finite-rank free commutative monoid.
When is a Puiseux monoid atomic? (2020) On the system of sets of lengths and the elast icity of submonoids of a finite-rank free commutative monoid
Reference 34
- Resolution
- verified exact
- doi, observed 2026-08-14T11:31:09.689569Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 7c15c345-0577-44db-9280-eb9dc0283054 · outbound
This paper cites an unresolved cited work.
When is a Puiseux monoid atomic? Unresolved cited work
Reference 35
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:31:09.971885Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 81320e98-c118-4178-9be7-b03058d0b0dd · outbound
This paper cites an unresolved cited work.
When is a Puiseux monoid atomic? Unresolved cited work
Reference 36
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:31:09.957729Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 2ce76ba9-6687-4d07-8a7f-dd00be275660 · outbound
This paper cites an unresolved cited work.
When is a Puiseux monoid atomic? Unresolved cited work
Reference 37
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:31:09.944163Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation a2bae874-3520-4cba-8aff-2a50eb8c082a · outbound
This paper cites an unresolved cited work.
When is a Puiseux monoid atomic? Unresolved cited work
Reference 38
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:31:09.930476Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation e9287063-f62f-4add-9cb7-78517513c0e0 · outbound
This paper cites an unresolved cited work.
When is a Puiseux monoid atomic? Unresolved cited work
Reference 39
- Resolution
- verified exact
- raw_fallback, observed 2026-08-14T11:31:09.815105Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 66335d10-af40-4097-888e-c47c736d2897 · outbound
This paper cites an unresolved cited work.
When is a Puiseux monoid atomic? Unresolved cited work
Reference 40
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:31:09.915811Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 65737c93-094c-477b-8df1-808527d653fc · outbound
This paper cites an unresolved cited work.
When is a Puiseux monoid atomic? Unresolved cited work
Reference 41
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:31:09.901460Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 33cf7c93-71e1-4fc2-8779-005f6abeebb1 · outbound
This paper cites an unresolved cited work.
When is a Puiseux monoid atomic? Unresolved cited work
Reference 42
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:31:09.886648Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation b936b8a8-e04a-41cc-b297-757ad6508c9c · outbound
This paper cites an unresolved cited work.
When is a Puiseux monoid atomic? Unresolved cited work
Reference 43
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:31:09.871669Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Pith citing papers
No inbound Pith citation observations are available.