{"as_of":"2026-08-11T17:35:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c080e42f3c89aee3052bcd6f67cd122a41900a8a3991fb1eefdfb9f393afb97d","coverage":[{"denominator":36,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":36,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-14T18:00:13.889163Z","state":"measured"},{"denominator":36,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":36,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.09677/citation-record","integrity":"/paper/2607.09677/integrity","json":"/paper/2607.09677/citation-record.json","paper":"/paper/2607.09677"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":null,"venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:95c3f932483edd2c84edac6937b64807d63a7fe527d8909f78afc2662198128d","observation_id":"d7554769-5591-4d3d-9553-eaa8109a9221","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":null,"venue":null,"work_id":null,"year":1935},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:0e8c93f3d6d80b7d31af5870aee8b4ac7d58b3a66bb3f7010ee64a926602957b","observation_id":"e534638b-3631-4bb4-82bb-69b72cf45b7c","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":"Springer, New York (1981)","venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:609a6557c7150d4c04a90b41a03515dddb6f705d8a5862a34a36f9045557b4ce","observation_id":"7d327011-b334-4431-b2b2-95336cf8982f","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":"Springer Monogr","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:8e2701531bca4ac5cae3c4fde8c0610c321e3c4ab888954aa780d0e53a155b5e","observation_id":"d3594693-f4c2-426c-8df0-ed80de2dcdf9","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":null,"venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:e0e77ad32321d2fe57303b18d8d00cedece3f569ef3d6b070ebf1f618c5d8266","observation_id":"6e7ca27c-16c1-4497-950c-150375fb9535","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:28adeb7e2d117e47f92365dbc0126cdfb5cbf5ac3d79f907c32ef60218def3f5","observation_id":"87ff692d-5e9d-41b3-8931-8459ed803918","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:f4ecbd022e06f66912807ea99982ca5db35455e292c2b8df25bd245cd1e8f4fe","observation_id":"b5cf14c8-aead-4b1f-9737-265cb737fe8c","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":"Algebra Universalis60(1), 19–35 (2009)","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:5b685f127a3406847b0421f44cb76592f9b76e102ecdc12ea6212a10ec4eed94","observation_id":"c4dd2e8a-7685-42e4-a359-c97a294c00ba","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.03709","last_updated":"2026-06-19T13:59:08Z","snapshot_observed_at":"2026-08-06T20:01:38.020842Z","submitted_at":"2025-07-04T16:48:17Z","title":"Counting finite semirings","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.03709","snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":"Preprint arXiv:2507.03709v1 (2025)","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"cited_paper":"/paper/2507.03709","citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:e5e325a8f40ce4d5ee826300a7e063f0a0a2428035c7f3efb2adab35cf1835df","observation_id":"4884c6f1-62a1-4d2b-89fc-f750e8670841","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2501.19049","last_updated":"2025-01-31T11:21:21Z","snapshot_observed_at":"2026-08-09T21:28:35.058139Z","submitted_at":"2025-01-31T11:21:21Z","title":"The finite basis problem for additively idempotent semirings that relate to S_7","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.19049","snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":"Preprint arXiv:2501.19049 (2025)","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"cited_paper":"/paper/2501.19049","citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:20240df6dd35cb248353a102a00959c4f9d19571934d4acb0b3158ef8099b018","observation_id":"6927db79-3afc-4e61-97ba-afd53cc33b8d","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":"Manuscript in preparation","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:08757bd162648c3ccbcfb91da97d93a71138e36b2eb8ae1dbcbd72a8e5630812","observation_id":"f48f9f85-f034-4d71-a2e3-15f9952540cf","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":"Kluwer Academic Publishers, Dordrecht-Boston-London (2001)","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:6c7637a031c629f47afd4d5925da4ae8f647077f838a5b36a3ff2a4e9c01b78f","observation_id":"f3b7d22d-209c-4c21-9565-28d61d0368af","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":"Longman Scientific and Technical, Harlow (1992)","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:415dc7f3959b366d1eb938bbdc0131a29ee111128980de8a2dde57688132fd1f","observation_id":"b2d88290-1f46-4a75-87fa-edfb556947ec","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:2f48a79dbd9fdb301b6b7c0b5aa23161abd5a67481977b2df58daaa2703ce1a2","observation_id":"25a4b1e9-d6a1-43a0-ab7f-770bfc979a33","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":"Semigroup Forum 106, 403–420 (2023)","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:cd6b9981dbbfe57d32eb46992b34339568916588eec9617998ed83d028ffd6fb","observation_id":"e55cefaf-c62a-407c-a459-6be2ec4531a0","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1142/s0218196726400084","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"International Journal of Algebra and Computation","work_id":"53c1a187-c520-4751-aec9-565d46fc5b1f","year":2026},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:3efab9937f116e239bca314f788a4849cee7178bab505fbcc5d8deeabc07a51d","observation_id":"11e69df8-8a5f-4b22-a0ed-e2c141addaba","resolution":{"observed_at":"2026-07-14T18:00:39.972428Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":"In preparation","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:9da1b146387533596437988aae4ce7743d3dd9cf13f58210db46e24ff68f15f8","observation_id":"49e83b8f-03e9-4f0d-8dec-142e5962ecbd","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":"Algebra Univers.79, 30 (2018)","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:e967f4d78c217898034ddc48c5a150525e428420272367dd49083cbb3bcac182","observation_id":"0b3ab32b-b2aa-46b7-8714-e6789700fcfb","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":"Linear Algebra Appl.387, 143– 165 (2004)","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:7f2b3d4663ce1c9f7641056293d6c8f54b2115465afe06cfdc23cf3dd3584c24","observation_id":"52b1298c-ef53-4eb6-bae5-c3e71024e815","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":null,"venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:8d58de7a95baefda59d633ca2fa6e5ed0ffefa6731dd1a6f18ae6983213e89f9","observation_id":"804030d2-74cd-4c99-8694-fab5e1c75051","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:b76660cfefe35b392f25d2ef28e959a0a6672795c6c505d194c6cc863b342181","observation_id":"0a8d60fc-2faf-42c4-9452-0ab8f0b74596","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":"Semigroup Forum, accepted","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:dcab31dde1fdbfb63701550fe5366d9573075b77d3ee1c391052b0d5054a79b8","observation_id":"dce7f936-8121-4cd3-9881-9cb22e56739e","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":"Semigroup Forum71(1), 27–48 (2005)","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:26719ce9a0e62e4a5eb55eaede2ec388d1d31acdb2f9e40db22a83c895c1fc44","observation_id":"f1429ae7-827b-4f2a-9d25-226514fd1daf","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:a87be9a0513ad6e5d5904c89105650f8dc2c028f66910f7f20ee128d00a89877","observation_id":"69fc09a2-ccc1-49e4-969b-ab6be58cf90a","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:0e4c9cec833a12cbe98bbc503de0ab395705212f5621a98d3d04fd15ec9a22bb","observation_id":"9d09269b-fdce-454e-89e4-69c0ba9760d3","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":"Semigroup Forum110(2), 422–457 (2025)","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:0a455a7218c337a65126a245c31602750b4d3210e4b94ac6e9faba74ec0c4670","observation_id":"92db61f1-d349-409b-b9bc-63f88b0df7fd","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":"Semigroup Forum112(2), 541–573 (2026)","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:5167f70aafc5620cda53a843814246c90f074383fef2e340a4b50f2e8186b5b4","observation_id":"bf925875-e986-476a-9c05-ba4c435822a6","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":"In preparation","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:dafb61dd7856bce1e1f91e9b9c89cd6e7902336e7e27bc6ce4d35c6d39bf93ab","observation_id":"b37f0f3b-4677-43df-b7d5-0b71d161a924","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":"Tongji Daxue Xuebao Ziran Kexue Ban24(1), 50–55 (1996) (In chinese) MR1412569","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:2a5593feccfb037960d65750c87789df3e59496c9ac8c43dcf4fe9506490650e","observation_id":"aa85bb14-5312-43b9-bea1-629827e11fd7","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":"Semigroup Forum91(1), 171–184 (2015)","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:5bb35b1d4d0e2467da60c9f877656c4ee759dc7440a321406a102150caa283cf","observation_id":"429c7f2e-d69b-4354-a452-d36fcf5d2dd1","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":"Preprint arXiv:2412.16113 (2024)","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:44b84ba159b02a570e56ce70f40618bd7f5efdd42f5f54cda764fb863fc23380","observation_id":"24c68858-a00c-4170-b917-7814e23424a3","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":"Algebra Universalis86(4), 33 (2025)","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:382ea6ab7cfb55927c9796d614d7986413f707efd6ffd45f3a770a5f3b8e09c8","observation_id":"9dece003-a1a6-473b-bc71-012eb9783cac","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":"Preprint arXiv:2603.00015 (2026)","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:2530079ee6fee0574312d7e5dd105b2c145bf438702315a10221bff88cf9b284","observation_id":"dfb4c476-4a62-4e2e-98ac-90a8e72070f5","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2605.15493","last_updated":"2026-05-15T00:17:46Z","snapshot_observed_at":"2026-08-07T12:30:22.686255Z","submitted_at":"2026-05-15T00:17:46Z","title":"A nonfinitely based additively idempotent semiring of order four","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2605.15493","snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":"Preprint arXiv:2605.15493 (2026)","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"cited_paper":"/paper/2605.15493","citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:d417d4ee958a9b7ff2c64b43c38756dcd5676a12e77a05d9b865d6c5ab5b1a76","observation_id":"3fbe3ca4-b887-499e-834e-263fdd5ce5c2","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":"Semigroup Forum108, 479–487 (2024)","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:4aa808b4725c0910bad56ec848b16567df4e06eac724168c25ebb5c472770a0b","observation_id":"955f5e2c-c7c8-4e97-a09a-20a9e094ece1","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-14T18:00:13.889163Z","title":"Ural Math","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-07-14T18:00:13.889163Z"},"links":{"citing_paper":"/paper/2607.09677"},"observation_digest":"sha256:9d2b07efa1b28d55cabec234ae054b2d8777269498a4ab6f3d6d404f69a05808","observation_id":"3acc2a2c-f09c-431e-90db-044e9c7828ae","resolution":{"observed_at":"2026-07-14T18:00:13.889163Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.09677","last_updated":"2026-06-12T03:04:14Z","latest_version":1,"primary_category":"math.RA","snapshot_observed_at":"2026-08-11T09:47:47.698852Z","submitted_at":"2026-06-12T03:04:14Z","title":"The finite basis problem for matrix semirings $\\mathbf{M}_n(S_7)$"},"reference_resolution":{"displayed":36,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":35,"verified_exact":1,"verified_fuzzy":0},"total_outbound_references":36},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2607.09677."}