Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-11T20:28:37.682382Z
Paper Citation Record · LEDGER
On primality and atomicity of numerical power monoids
As of 13 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 3 inbound Pith citation observations for arXiv:2412.05857.
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 2026-08-13T06:32:02.005865+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-05-21T12:20:06.305556Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-05-21T12:24:10.792352Z
Reference resolution
20 of 20 outbound references displayed
- verified exact1
- verified fuzzy11
- unresolved8
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation b0ce530e-889a-4d7a-a10f-709d4af830a5 · outbound
This paper cites Almeida, Some Key Problems on Finite Semigroups , Semigroup Forum 64 (2002), 159–179.
On primality and atomicity of numerical power monoids Almeida, Some Key Problems on Finite Semigroups , Semigroup Forum 64 (2002), 159–179
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:28:38.982578Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation c7b3cfe2-e779-4fea-8c2d-e171d4bd362f · outbound
This paper cites an unresolved cited work.
On primality and atomicity of numerical power monoids Unresolved cited work
Reference 2
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:28:38.878727Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 63c7c90f-1747-4090-973d-63034d71a1e4 · outbound
This paper cites On algebraic properties of power monoids of numerical monoids.
On primality and atomicity of numerical power monoids On algebraic properties of power monoids of numerical monoids
Reference 3
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T20:28:37.480076Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7e8aca6d-6d3c-4ffe-8523-c6621f4e8d27 · outbound
This paper cites an unresolved cited work.
On primality and atomicity of numerical power monoids Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:28:38.744098Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 6966eae8-5227-4c9f-a94e-f860b42e667b · outbound
This paper cites an unresolved cited work.
On primality and atomicity of numerical power monoids Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-08-11T20:28:38.595608Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation a4572f65-54e0-4064-a476-643f7e5dda48 · outbound
This paper cites Cossu and S.
On primality and atomicity of numerical power monoids Cossu and S
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:28:38.578262Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation e5086d39-3582-4e43-9799-f9c484672ba5 · outbound
This paper cites Fan and S.
On primality and atomicity of numerical power monoids Fan and S
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:28:38.561825Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation aef18325-1243-4942-859b-86f614f90aa5 · outbound
This paper cites Geroldinger, F.
On primality and atomicity of numerical power monoids Geroldinger, F
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:28:38.544288Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 11fdd550-9e71-4249-88db-c101a76a339e · outbound
This paper cites Geroldinger and F.
On primality and atomicity of numerical power monoids Geroldinger and F
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:28:38.342708Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation e3a07c24-d4c3-4b06-af5e-080c4474effa · outbound
This paper cites Geroldinger and Q.
On primality and atomicity of numerical power monoids Geroldinger and Q
Reference 10
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T20:28:37.517141Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a5f391cd-a708-478d-acfb-642ca54f0d90 · outbound
This paper cites On the atomicity of power monoids of Puiseux monoids.
On primality and atomicity of numerical power monoids On the atomicity of power monoids of Puiseux monoids
Reference 11
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T20:28:37.523523Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5fc9c8d8-f7bc-441a-b76d-c180b6547cc8 · outbound
This paper cites Factorization of polynomials in one variable over the tropical semiring.
On primality and atomicity of numerical power monoids Factorization of polynomials in one variable over the tropical semiring
Reference 12
- Resolution
- verified exact
- local_arxiv, observed 2026-08-11T20:28:37.869384Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 1ebac805-2a44-48e4-9fac-df0f64cc997f · outbound
This paper cites an unresolved cited work.
On primality and atomicity of numerical power monoids Unresolved cited work
Reference 13
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T20:28:37.534625Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation fc827866-166e-4909-b02b-da31400e1a16 · outbound
This paper cites BG = PG: A success story.
On primality and atomicity of numerical power monoids BG = PG: A success story
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:28:38.181381Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 6beb63f1-8b39-4987-b947-1dff10212ff1 · outbound
This paper cites Algebraic Theory of Semigroups and Its Applica- tions.
On primality and atomicity of numerical power monoids Algebraic Theory of Semigroups and Its Applica- tions
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:28:38.162119Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation d251c94f-5f3e-42a5-914c-7154e2fd264a · outbound
This paper cites Shitov, How many boolean polynomials are irreducible? Int.
On primality and atomicity of numerical power monoids Shitov, How many boolean polynomials are irreducible? Int
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:28:38.098371Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 28549ef8-7d2a-49c2-872c-bc194b165fcc · outbound
This paper cites Tamura and J.
On primality and atomicity of numerical power monoids Tamura and J
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:28:38.002942Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation fbef4f6c-00a0-4327-92ac-002b1418b1fb · outbound
This paper cites On the isomorphism problem for power semigroups.
On primality and atomicity of numerical power monoids On the isomorphism problem for power semigroups
Reference 18
- Resolution
- unresolved
- no resolver link, observed 2026-08-11T20:28:37.602515Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation abff8b46-cb45-448e-b1d1-75c9071a67a5 · outbound
This paper cites Tringali and W.
On primality and atomicity of numerical power monoids Tringali and W
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:28:37.943054Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation e118ceb4-65ff-4889-b7ea-24c7cb334c90 · outbound
This paper cites Tringali and W.
On primality and atomicity of numerical power monoids Tringali and W
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-11T20:28:37.925117Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Pith citing papers
Observation eb45ee4b-77ac-40b2-b5f7-23fb21c899ad · inbound
On automorphism groups of power semigroups over numerical semigroups or over numerical monoids cites this paper.
On automorphism groups of power semigroups over numerical semigroups or over numerical monoids On primality and atomicity of numerical power monoids
Reference 1
- Resolution
- verified exact
- arxiv_id, observed 2026-05-16T22:48:38.094201Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 93d3ab2a-5e7f-4712-bed8-ab32a3cc3baf · inbound
Power monoids and their arithmetic: a survey cites this paper.
Power monoids and their arithmetic: a survey On primality and atomicity of numerical power monoids
Reference 1
- Resolution
- verified exact
- arxiv_id, observed 2026-05-21T12:24:10.794303Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 45be73a3-f249-47a1-87ea-f9d11178c1f5 · inbound
On the automorphisms of the power semigroups of a numerical semigroup cites this paper.
On the automorphisms of the power semigroups of a numerical semigroup On primality and atomicity of numerical power monoids
Reference 1
- Resolution
- verified exact
- arxiv_id, observed 2026-05-12T09:36:26.016407Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.