Paper Citation Record · LEDGER

The finite basis problem for additively idempotent semirings that relate to S_7

As of 11 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 3 inbound Pith citation observations for arXiv:2501.19049.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2501.19049 v1

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-09T21:48:49.916015Z

measured 39 of 39 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-14T18:00:13.889163Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-05-19T15:57:49.439941Z

Reference resolution

36 of 36 outbound references displayed

verified exact5
verified fuzzy27
unresolved4
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a6a6c707-b23b-492c-871c-906f611a5ae9 · outbound

This paper cites Alsulami, M.

The finite basis problem for additively idempotent semirings that relate to S_7 Alsulami, M

Reference 1

Resolution: verified exact; raw_fallback, observed 2026-08-09T21:48:50.452934Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 6983b518-e4b6-47e4-9496-30b4c844434e · outbound

This paper cites an unresolved cited work.

The finite basis problem for additively idempotent semirings that relate to S_7 Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-09T21:48:51.581176Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 61d5fcd2-91b2-4cae-863b-0ee017fabba3 · outbound

This paper cites Bonomo-Braberman, M.C.

The finite basis problem for additively idempotent semirings that relate to S_7 Bonomo-Braberman, M.C

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:48:51.547013Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation c2b7d779-780b-4e90-8c1b-b7b972432e8a · outbound

This paper cites Burris, H.P.

The finite basis problem for additively idempotent semirings that relate to S_7 Burris, H.P

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:48:51.472975Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 97b1a773-8779-4f69-aa94-59c121c1a37e · outbound

This paper cites Connes, C.

The finite basis problem for additively idempotent semirings that relate to S_7 Connes, C

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:48:51.384278Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation d5789ecb-508a-4637-bfa4-1569fc720346 · outbound

This paper cites Dolinka, A nonﬁntely based ﬁnite semiring, Internat.

The finite basis problem for additively idempotent semirings that relate to S_7 Dolinka, A nonﬁntely based ﬁnite semiring, Internat

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:48:51.301225Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation a28c9c91-4c24-42cc-acde-dc91419d3446 · outbound

This paper cites Dolinka, S.

The finite basis problem for additively idempotent semirings that relate to S_7 Dolinka, S

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:48:51.226667Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 40f7f429-f2e1-4cdc-b2c7-67a9279f675b · outbound

This paper cites Erd˝ os, A.

The finite basis problem for additively idempotent semirings that relate to S_7 Erd˝ os, A

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:48:51.190753Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation c9f708ad-a6bf-4895-99c4-acb5dee3bcf7 · outbound

This paper cites G/suppress lazek, A Guide to the Literature on Semirings and their Applications in Mathematics and Information Science, Kluwer Academic Publishers, Dord recht-Boston-London, 2001.

The finite basis problem for additively idempotent semirings that relate to S_7 G/suppress lazek, A Guide to the Literature on Semirings and their Applications in Mathematics and Information Science, Kluwer Academic Publishers, Dord recht-Boston-London, 2001

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:48:51.179776Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 174e1ed4-5f2a-4714-9527-94ec154e8ccf · outbound

This paper cites Ghosh, F.

The finite basis problem for additively idempotent semirings that relate to S_7 Ghosh, F

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:48:51.152852Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 5083c9cd-d2f2-416d-a215-efc2149386f9 · outbound

This paper cites Glasson, The Rees quotient monoid generates a variety with uncountably many subvari- eties, Semigroup Forum 109 (2024), 476–481.

The finite basis problem for additively idempotent semirings that relate to S_7 Glasson, The Rees quotient monoid generates a variety with uncountably many subvari- eties, Semigroup Forum 109 (2024), 476–481

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:48:51.141725Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 788b01db-7f27-4d00-81a9-81b84e3d39ed · outbound

This paper cites Godsil, G.

The finite basis problem for additively idempotent semirings that relate to S_7 Godsil, G

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:48:51.130347Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 060d3dc2-87e7-4dbf-ab54-17e02bc822c2 · outbound

This paper cites Golan, The Theory of Semirings with Applications in Mathematics and Theoretical Com- puter Science, Longman Scientiﬁc and Technical, Harlow, 19 92.

The finite basis problem for additively idempotent semirings that relate to S_7 Golan, The Theory of Semirings with Applications in Mathematics and Theoretical Com- puter Science, Longman Scientiﬁc and Technical, Harlow, 19 92

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:48:51.117962Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation c7d547c4-5580-46c5-a7f4-cf8c6b45129a · outbound

This paper cites Gusev, Small monoids generating varieties with uncou ntably many subvarieties, Semigroup Forum (2024), https://doi.org/10.1007/s00233-024-10499-7.

The finite basis problem for additively idempotent semirings that relate to S_7 Gusev, Small monoids generating varieties with uncou ntably many subvarieties, Semigroup Forum (2024), https://doi.org/10.1007/s00233-024-10499-7

Reference 14

Resolution: verified exact; doi, observed 2026-08-09T21:48:50.052336Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 8cc885a2-b599-4169-8241-be72259647f4 · outbound

This paper cites an unresolved cited work.

The finite basis problem for additively idempotent semirings that relate to S_7 Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-09T21:48:51.106597Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 99a70ba3-58dd-4db9-b6ab-25929d264141 · outbound

This paper cites Jackson, Flat algebras and the translation of univers al Horn logic to equational logic, J.

The finite basis problem for additively idempotent semirings that relate to S_7 Jackson, Flat algebras and the translation of univers al Horn logic to equational logic, J

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:48:51.095935Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 07e70369-a427-4cc7-91a4-7fe78cdb3e48 · outbound

This paper cites Jackson, Flexible constraint satisﬁability and a pro blem in semigroup theory, manuscript (2015), https://arxiv.org/abs/1512.03127.

The finite basis problem for additively idempotent semirings that relate to S_7 Jackson, Flexible constraint satisﬁability and a pro blem in semigroup theory, manuscript (2015), https://arxiv.org/abs/1512.03127

Reference 17

Resolution: verified exact; raw_fallback, observed 2026-08-09T21:48:50.268670Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 8e90cecc-f851-4b71-944f-984984318875 · outbound

This paper cites Jackson, E.W.H.

The finite basis problem for additively idempotent semirings that relate to S_7 Jackson, E.W.H

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:48:51.084562Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 2c4fa510-5a5f-48bd-afd7-4302ef60b04d · outbound

This paper cites Jackson, M.M.

The finite basis problem for additively idempotent semirings that relate to S_7 Jackson, M.M

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:48:51.072912Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation b5ddcce4-b863-498d-9fee-3bf99c5b0ded · outbound

This paper cites Jeˇ zek, Nonﬁnitely based three-element idempotent groupoids, Algebra Univers.

The finite basis problem for additively idempotent semirings that relate to S_7 Jeˇ zek, Nonﬁnitely based three-element idempotent groupoids, Algebra Univers

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:48:51.061382Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 87635ef0-5636-4647-8786-c2c3a17030d5 · outbound

This paper cites Lov´ asz, Kneser’s conjecture, chromatic number and h omotopy, J.

The finite basis problem for additively idempotent semirings that relate to S_7 Lov´ asz, Kneser’s conjecture, chromatic number and h omotopy, J

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:48:50.969659Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 47c18fa1-6ffc-42da-8b41-a1ed47242173 · outbound

This paper cites Lyndon, Identities in two-valued calculi, Trans.

The finite basis problem for additively idempotent semirings that relate to S_7 Lyndon, Identities in two-valued calculi, Trans

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:48:50.849144Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 3ecac1df-433b-4f4d-88fe-9c68a151c35a · outbound

This paper cites Lyndon, Identities in ﬁnite algebras, Proc.

The finite basis problem for additively idempotent semirings that relate to S_7 Lyndon, Identities in ﬁnite algebras, Proc

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:48:50.813656Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 5b6ec0e6-d5d7-461f-b6c6-60877aeb0cd5 · outbound

This paper cites Maclagan, B.

The finite basis problem for additively idempotent semirings that relate to S_7 Maclagan, B

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:48:50.802862Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation bc29126c-cb48-4653-a271-b4120348dfc3 · outbound

This paper cites Murskiˇ ı, The existence in the three-valued logic of a closed class with a ﬁnite basis having no ﬁnite complete system of identities, Soviet Math.

The finite basis problem for additively idempotent semirings that relate to S_7 Murskiˇ ı, The existence in the three-valued logic of a closed class with a ﬁnite basis having no ﬁnite complete system of identities, Soviet Math

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:48:50.792348Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 49b93ecd-b970-496c-bc2f-2c12a0e3f09b · outbound

This paper cites Pastijn, Varieties generated by ordered bands II, Order 22 (2005), no.

The finite basis problem for additively idempotent semirings that relate to S_7 Pastijn, Varieties generated by ordered bands II, Order 22 (2005), no

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:48:50.781294Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 33815094-7894-4377-889f-c568138cc67d · outbound

This paper cites Polin, Minimal varieties of semirings, Math.

The finite basis problem for additively idempotent semirings that relate to S_7 Polin, Minimal varieties of semirings, Math

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:48:50.768784Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 2940bc92-d1cf-4f7e-93bf-1edf75df100b · outbound

This paper cites The finite basis problem for additively idempotent semirings of order four, I.

The finite basis problem for additively idempotent semirings that relate to S_7 The finite basis problem for additively idempotent semirings of order four, I

Reference 28

Resolution: verified exact; local_arxiv, observed 2026-08-09T21:48:50.142809Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation f75d8831-428d-4689-aa04-d11d6cc8ae5b · outbound

This paper cites an unresolved cited work.

The finite basis problem for additively idempotent semirings that relate to S_7 Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-09T21:48:50.733571Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 326a407d-e4c5-4147-a14e-cf6a50c48ebc · outbound

This paper cites Shao, M.M.

The finite basis problem for additively idempotent semirings that relate to S_7 Shao, M.M

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:48:50.588768Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation a657933b-d897-4842-8d4f-1fa303993d52 · outbound

This paper cites Alg. Systems and their varieties.

The finite basis problem for additively idempotent semirings that relate to S_7 Alg. Systems and their varieties

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:48:50.516427Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation d55fd67b-7476-409c-b39f-d01d040d1182 · outbound

This paper cites Volkov, Semiring identities of the Brandt monoid, A lgebra Universalis 82 (2021), no.

The finite basis problem for additively idempotent semirings that relate to S_7 Volkov, Semiring identities of the Brandt monoid, A lgebra Universalis 82 (2021), no

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:48:50.504292Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 7393b043-d3f3-48ea-8d16-6215df6cd43b · outbound

This paper cites Willard, On McKenzie’s method, Period.

The finite basis problem for additively idempotent semirings that relate to S_7 Willard, On McKenzie’s method, Period

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:48:50.490327Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 091c1fe6-4d60-4895-a7a8-7b864c51f918 · outbound

This paper cites an unresolved cited work.

The finite basis problem for additively idempotent semirings that relate to S_7 Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-09T21:48:50.477481Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 2a65d171-6d3e-459f-a060-9212a552df15 · outbound

This paper cites The finite basis problem for additively idempotent semirings of order four, II.

The finite basis problem for additively idempotent semirings that relate to S_7 The finite basis problem for additively idempotent semirings of order four, II

Reference 35

Resolution: verified exact; local_arxiv, observed 2026-08-09T21:48:50.123384Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 0762a009-9113-4fbd-8a18-b6cc76cb005a · outbound

This paper cites Zhao, M.M.

The finite basis problem for additively idempotent semirings that relate to S_7 Zhao, M.M

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T21:48:50.464479Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Pith citing papers

Observation 19443d26-9b41-4692-b3c1-7577b0b9b8fe · inbound

A new limit variety of additively idempotent semirings cites this paper.

A new limit variety of additively idempotent semirings The finite basis problem for additively idempotent semirings that relate to S_7

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-05-15T12:30:00.590986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 6c097136-b28b-4a21-936f-17cc6300072b · inbound

A nonfinitely based additively idempotent semiring of order four cites this paper.

A nonfinitely based additively idempotent semiring of order four The finite basis problem for additively idempotent semirings that relate to S_7

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-05-19T15:57:49.445630Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 6927db79-3afc-4e61-97ba-afd53cc33b8d · inbound

The finite basis problem for matrix semirings $\mathbf{M}_n(S_7)$ cites this paper.

The finite basis problem for matrix semirings $\mathbf{M}_n(S_7)$ The finite basis problem for additively idempotent semirings that relate to S_7

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-14T18:00:13.889163Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.