Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-08T15:07:34.135705Z
Paper Citation Record · LEDGER
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties
As of 21 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 1 inbound Pith citation observation for arXiv:2502.06610.
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 2026-08-21T06:32:19.484+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-01T03:44:02.396850Z
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
29 of 29 outbound references displayed
- verified exact1
- verified fuzzy22
- unresolved6
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 581597a8-7447-4cfe-b6f4-61f99e706f40 · outbound
This paper cites an unresolved cited work.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-08-08T15:07:34.571682Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 8018c605-0f42-47d7-8972-594c1d2cc160 · outbound
This paper cites an unresolved cited work.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Unresolved cited work
Reference 2
- Resolution
- unresolved
- raw_fallback, observed 2026-08-08T15:07:34.559376Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 8afade3f-082e-481b-a2cc-8162453abd9d · outbound
This paper cites an unresolved cited work.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-08-08T15:07:34.546855Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 2c6619d4-6507-4da8-b3cf-dd0473aae6fd · outbound
This paper cites an unresolved cited work.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-08-08T15:07:34.533775Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 972cd4e0-c8c9-4124-a75b-0181f1e154fc · outbound
This paper cites Borceux, Handbook of categorical algebra 1 , Cambridge University Press, 1994.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Borceux, Handbook of categorical algebra 1 , Cambridge University Press, 1994
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T15:07:34.519207Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 43eab440-1aca-493c-8139-eb8bd48654fa · outbound
This paper cites Campanini and A.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Campanini and A
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T15:07:34.505067Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation adbd6c30-b6da-479d-b526-0277e5f63081 · outbound
This paper cites an unresolved cited work.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-08-08T15:07:34.491215Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation de870a5c-be6f-4958-b241-98c1f9f37c90 · outbound
This paper cites Cossu, Some applications of a new approach to factorization in M.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Cossu, Some applications of a new approach to factorization in M
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T15:07:34.476764Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 4b5b2265-e77a-48d0-84ce-1f552d9de416 · outbound
This paper cites Cossu and S.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Cossu and S
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T15:07:34.462908Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 9361be73-43ce-4012-9540-01b02bf3a4e8 · outbound
This paper cites Cossu and S.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Cossu and S
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T15:07:34.448682Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 8f1f484e-e7cf-4682-977a-1d8805c9f6bc · outbound
This paper cites Cossu and S.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Cossu and S
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T15:07:34.435038Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation f5c44003-4c89-4089-a468-e56151aa2d37 · outbound
This paper cites Cossu and S.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Cossu and S
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T15:07:34.420972Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation d9e1b058-6586-4938-a162-90829ad15a5a · outbound
This paper cites Coykendall and F.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Coykendall and F
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T15:07:34.406461Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 486e5a0d-d34c-49cf-9386-37381d2b2649 · outbound
This paper cites Coykendall and R.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Coykendall and R
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T15:07:34.392774Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 4b007d7b-5fec-4ada-b66d-bea32db66bc9 · outbound
This paper cites Facchini, Direct sum decomposition of modules, semilocal endomorphi sm rings, and Krull monoids , J.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Facchini, Direct sum decomposition of modules, semilocal endomorphi sm rings, and Krull monoids , J
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T15:07:34.378663Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 63e5aaeb-e7ac-406f-ab8a-34e14e609ddd · outbound
This paper cites Facchini, Semilocal Categories and Modules with Semilocal Endomorphi sm Rings , Progr.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Facchini, Semilocal Categories and Modules with Semilocal Endomorphi sm Rings , Progr
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T15:07:34.364546Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 644372fa-00b9-4a3b-b3e2-954a0db5276f · outbound
This paper cites Facchini and R.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Facchini and R
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T15:07:34.351589Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 10905288-ccca-4ba7-8e14-024569575426 · outbound
This paper cites Fan and S.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Fan and S
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T15:07:34.338859Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 14dc6e1e-5288-4e53-9bf4-3ab1d19a67de · outbound
This paper cites On monoid algebras having every nonempty subset of $\mathbb{N}_{\ge 2}$ as a length set.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties On monoid algebras having every nonempty subset of $\mathbb{N}_{\ge 2}$ as a length set
Reference 19
- Resolution
- verified exact
- local_arxiv, observed 2026-08-08T15:07:34.177315Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation f4a273d4-4ddc-47c7-a8d4-e756b3b5e284 · outbound
This paper cites Geroldinger and F.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Geroldinger and F
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T15:07:34.325479Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation d46d54d4-c3ae-428f-9b99-79ea70a50cac · outbound
This paper cites Geroldinger and Q.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Geroldinger and Q
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T15:07:34.312377Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 5e7af67e-850e-4c82-9870-64743a6ed447 · outbound
This paper cites Geroldinger and Q.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Geroldinger and Q
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T15:07:34.297541Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 226b9728-0a45-4371-a125-7c3bbdfa3c57 · outbound
This paper cites Gotti, Puiseux monoids and transfer homomorphisms , J.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Gotti, Puiseux monoids and transfer homomorphisms , J
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T15:07:34.283081Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation e3b98559-4d0c-420b-baef-cf8156353886 · outbound
This paper cites Gotti, Systems of sets of lengths of Puiseux monoids , J.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Gotti, Systems of sets of lengths of Puiseux monoids , J
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T15:07:34.268511Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 9e6936e9-e0bb-4e85-b275-92fddfc3e593 · outbound
This paper cites Gotti and B.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Gotti and B
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T15:07:34.252526Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 5ce2bd69-1d82-4b0e-bb75-70a70b40ca3d · outbound
This paper cites an unresolved cited work.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Unresolved cited work
Reference 26
- Resolution
- unresolved
- raw_fallback, observed 2026-08-08T15:07:34.237106Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation c6f12031-073b-4273-90f4-03cc350cb4c8 · outbound
This paper cites Smertnig and J.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Smertnig and J
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T15:07:34.222431Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation d696fbf5-41b9-45db-9ff6-857efccf0537 · outbound
This paper cites Tringali, An abstract factorization theorem and some applications , J.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Tringali, An abstract factorization theorem and some applications , J
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T15:07:34.207564Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 6b95c25b-c116-4bea-9890-cdf33f9575b0 · outbound
This paper cites Tringali, A characterisation of atomicity , Math.
The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties Tringali, A characterisation of atomicity , Math
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-08T15:07:34.192940Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Pith citing papers
Observation dc6cf3ff-baa2-467e-8a98-19844338050c · inbound
Categorical Algebra of Atomic Monoids: Presentability, Regularity, and Pretorsion Theories cites this paper.
Categorical Algebra of Atomic Monoids: Presentability, Regularity, and Pretorsion Theories The Category of Atomic Monoids: Universal Constructions and Arithmetic Properties
Reference 3
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T03:44:02.396850Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.