{"as_of":"2026-08-08T13:37:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:8c8b402d1a1c7e2471f3ac06127f67af8b800c1b7850f1f5fca7c6189d26178e","coverage":[{"denominator":22,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":22,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T10:41:40.691281Z","state":"measured"},{"denominator":22,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":22,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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/2508.13165/citation-record","integrity":"/paper/2508.13165/integrity","json":"/paper/2508.13165/citation-record.json","paper":"/paper/2508.13165"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:41:41.530091Z","title":null,"venue":null,"work_id":"93a46ed8-57ad-46e6-bc51-ad1c8d9acf18","year":2021},"citing_paper":{"arxiv_id":"2508.13165","last_updated":"2025-07-31T14:23:28Z","snapshot_observed_at":"2026-08-06T10:41:25.152659Z","submitted_at":"2025-07-31T14:23:28Z","title":"An introduction to the algebra of rings and fields","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T10:41:40.597859Z"},"links":{"citing_paper":"/paper/2508.13165"},"observation_digest":"sha256:8f615ef1490f02bf6e3443b122c9cb61c36aeda5a0cc9c8d831ff97c65a7795a","observation_id":"00f98322-83e1-4603-acbb-64f782744908","resolution":{"observed_at":"2026-08-06T10:41:41.534523Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:41:41.446433Z","title":null,"venue":null,"work_id":"ecb983c3-4d7b-42ac-b8cf-0322e1b92497","year":1988},"citing_paper":{"arxiv_id":"2508.13165","last_updated":"2025-07-31T14:23:28Z","snapshot_observed_at":"2026-08-06T10:41:25.152659Z","submitted_at":"2025-07-31T14:23:28Z","title":"An introduction to the algebra of rings and fields","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T10:41:40.664951Z"},"links":{"citing_paper":"/paper/2508.13165"},"observation_digest":"sha256:fa70ff2cab5a687dd7228af746a758170ef6d845395a1e8b544ab09ebd1d2a6a","observation_id":"ee781808-c6b2-418e-8841-9bb156133186","resolution":{"observed_at":"2026-08-06T10:41:41.451357Z","resolver_source":"raw_fallback","status":"parse_uncertain"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:41:41.489289Z","title":"Dummit, Richard M","venue":null,"work_id":"a58e3a77-50a5-47af-9c61-02439ad147e5","year":2023},"citing_paper":{"arxiv_id":"2508.13165","last_updated":"2025-07-31T14:23:28Z","snapshot_observed_at":"2026-08-06T10:41:25.152659Z","submitted_at":"2025-07-31T14:23:28Z","title":"An introduction to the algebra of rings and fields","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T10:41:40.616259Z"},"links":{"citing_paper":"/paper/2508.13165"},"observation_digest":"sha256:cc81f760397275d7ba69e229fcc33cff457879798b98c29b6c197eb5835127a3","observation_id":"51ffaf44-4ddd-4a18-9e4f-fddcf0375d3e","resolution":{"observed_at":"2026-08-06T10:41:41.493500Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"web/2023011","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:41:41.284412Z","title":null,"venue":null,"work_id":"b7e5796d-2545-4ff3-93c5-345dceb73110","year":1907},"citing_paper":{"arxiv_id":"2508.13165","last_updated":"2025-07-31T14:23:28Z","snapshot_observed_at":"2026-08-06T10:41:25.152659Z","submitted_at":"2025-07-31T14:23:28Z","title":"An introduction to the algebra of rings and fields","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T10:41:40.635055Z"},"links":{"citing_paper":"/paper/2508.13165"},"observation_digest":"sha256:c01b12a4b7328bbcb365eae2c3441e590d065b44e13e4f60e8b623e9831396e2","observation_id":"8bd829a3-84c9-433a-ac77-eeec269522a3","resolution":{"observed_at":"2026-08-06T10:41:41.291174Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2408.07499","last_updated":"2024-08-14T12:28:40Z","snapshot_observed_at":"2026-08-07T07:10:00.085706Z","submitted_at":"2024-08-14T12:28:40Z","title":"Galois Theory","version":1},"cited_work":{"arxiv_id":"2408.07499","doi":null,"metadata_source":"pith","pith_arxiv_id":"2408.07499","snapshot_observed_at":"2026-08-06T10:41:41.205518Z","title":"Galois Theory","venue":"math.NT","work_id":"b6ba123b-46bf-482e-b097-cb70509200e5","year":2024},"citing_paper":{"arxiv_id":"2508.13165","last_updated":"2025-07-31T14:23:28Z","snapshot_observed_at":"2026-08-06T10:41:25.152659Z","submitted_at":"2025-07-31T14:23:28Z","title":"An introduction to the algebra of rings and fields","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T10:41:40.643553Z"},"links":{"cited_paper":"/paper/2408.07499","citing_paper":"/paper/2508.13165"},"observation_digest":"sha256:eac2bbb9b5d2fc35aa8d3b23b2919b85ad4d697b8765239b5b50eaabe8216caf","observation_id":"35347a73-d978-4ebe-9abf-3ccf34ccf7bf","resolution":{"observed_at":"2026-08-06T10:41:41.210103Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"web/2023030","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:41:41.103341Z","title":"McNulty, Algebra for First Year Graduate Students, 10 Jan- uary","venue":null,"work_id":"a6929416-0df5-45c7-841a-5f98b45ce7bb","year":null},"citing_paper":{"arxiv_id":"2508.13165","last_updated":"2025-07-31T14:23:28Z","snapshot_observed_at":"2026-08-06T10:41:25.152659Z","submitted_at":"2025-07-31T14:23:28Z","title":"An introduction to the algebra of rings and fields","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T10:41:40.652098Z"},"links":{"citing_paper":"/paper/2508.13165"},"observation_digest":"sha256:81baadc9b796d88d66c8d6833b801299cf13fdc8de91d7b968af9ae4940625b4","observation_id":"3c26fccf-6630-4f1b-8392-79738ba4fe99","resolution":{"observed_at":"2026-08-06T10:41:41.112043Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"web/2019052","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:41:40.929272Z","title":null,"venue":null,"work_id":"091f72da-0eea-40e9-bb07-4615961a7213","year":null},"citing_paper":{"arxiv_id":"2508.13165","last_updated":"2025-07-31T14:23:28Z","snapshot_observed_at":"2026-08-06T10:41:25.152659Z","submitted_at":"2025-07-31T14:23:28Z","title":"An introduction to the algebra of rings and fields","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T10:41:40.678176Z"},"links":{"citing_paper":"/paper/2508.13165"},"observation_digest":"sha256:2b9ac43a046123dbb1d2eb8b07def6f6849c95be39a8d3bf014f900c86e34c24","observation_id":"ce7e64bb-9f90-4838-b148-83837184a9e7","resolution":{"observed_at":"2026-08-06T10:41:40.936119Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:41:41.461294Z","title":"[KeeGui20] Patrick Keef, David Guichard, An Introduction to Higher Mathemat- ics, 13 May","venue":null,"work_id":"b17bfee2-37cd-4660-8f83-893a88b20859","year":1951},"citing_paper":{"arxiv_id":"2508.13165","last_updated":"2025-07-31T14:23:28Z","snapshot_observed_at":"2026-08-06T10:41:25.152659Z","submitted_at":"2025-07-31T14:23:28Z","title":"An introduction to the algebra of rings and fields","version":1},"reference_index":246,"source":"pdf_text","source_observed_at":"2026-08-06T10:41:40.639220Z"},"links":{"citing_paper":"/paper/2508.13165"},"observation_digest":"sha256:6e528849ff01e9b3569dde194cb7bc4a6ec24f2c62839e6a3a78eacf2d12cf43","observation_id":"38f1ab58-516c-495f-804b-945206b76252","resolution":{"observed_at":"2026-08-06T10:41:41.466285Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"math/0606547","last_updated":"2007-02-11T21:28:56Z","snapshot_observed_at":"2026-08-07T11:00:03.472177Z","submitted_at":"2006-06-22T00:23:49Z","title":"Representing Primes as x^2 + 5y^2: An Inductive Proof that Euler Missed","version":2},"cited_work":{"arxiv_id":"math/0606547","doi":null,"metadata_source":"pith","pith_arxiv_id":"math/0606547","snapshot_observed_at":"2026-08-06T10:41:40.735687Z","title":"Representing Primes as x^2 + 5y^2: An Inductive Proof that Euler Missed","venue":"math.NT","work_id":"05781a07-7818-479a-b4d3-64287b1d3002","year":2006},"citing_paper":{"arxiv_id":"2508.13165","last_updated":"2025-07-31T14:23:28Z","snapshot_observed_at":"2026-08-06T10:41:25.152659Z","submitted_at":"2025-07-31T14:23:28Z","title":"An introduction to the algebra of rings and fields","version":1},"reference_index":1986,"source":"pdf_text","source_observed_at":"2026-08-06T10:41:40.691281Z"},"links":{"cited_paper":"/paper/math/0606547","citing_paper":"/paper/2508.13165"},"observation_digest":"sha256:ef40980566cb3e4d3746b0c85129ae44f4c38c7c8c7f85728d8afb14b5421dd4","observation_id":"2fd51cc1-bd62-4a1c-afa6-2ec6f3ca3c81","resolution":{"observed_at":"2026-08-06T10:41:40.742413Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:41:41.403431Z","title":"1 (Jan., 1952), pp","venue":null,"work_id":"eb0871b6-b225-47e0-9247-27f3a15001c3","year":2023},"citing_paper":{"arxiv_id":"2508.13165","last_updated":"2025-07-31T14:23:28Z","snapshot_observed_at":"2026-08-06T10:41:25.152659Z","submitted_at":"2025-07-31T14:23:28Z","title":"An introduction to the algebra of rings and fields","version":1},"reference_index":1990,"source":"pdf_text","source_observed_at":"2026-08-06T10:41:40.687162Z"},"links":{"citing_paper":"/paper/2508.13165"},"observation_digest":"sha256:01cc909bf5cd7c9d507027e7c27aa4ff3c89aed44c462bcc6e21f1e3b2bda7fd","observation_id":"ec51d31b-e451-4078-ac04-9b7aab3f81e5","resolution":{"observed_at":"2026-08-06T10:41:41.407831Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:41:41.417201Z","title":null,"venue":null,"work_id":"8fd53f6b-3777-48e6-ba47-4a238893367d","year":2023},"citing_paper":{"arxiv_id":"2508.13165","last_updated":"2025-07-31T14:23:28Z","snapshot_observed_at":"2026-08-06T10:41:25.152659Z","submitted_at":"2025-07-31T14:23:28Z","title":"An introduction to the algebra of rings and fields","version":1},"reference_index":1996,"source":"pdf_text","source_observed_at":"2026-08-06T10:41:40.673247Z"},"links":{"citing_paper":"/paper/2508.13165"},"observation_digest":"sha256:72985f002cb2d92e3e355114aa5628b8e205016bbd85b48e64fe953b35b040ac","observation_id":"2472dc9c-31ae-43d5-bda8-e4834634a3f6","resolution":{"observed_at":"2026-08-06T10:41:41.421920Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:41:41.432204Z","title":"Rotman, Advanced Modern Algebra: Third Edition, Part 1 and Part 2 , Graduate Studies in Mathematics 165 and 180, AMS 2015 and","venue":null,"work_id":"87c0788b-f059-43ef-9f6e-18aca9406870","year":2015},"citing_paper":{"arxiv_id":"2508.13165","last_updated":"2025-07-31T14:23:28Z","snapshot_observed_at":"2026-08-06T10:41:25.152659Z","submitted_at":"2025-07-31T14:23:28Z","title":"An introduction to the algebra of rings and fields","version":1},"reference_index":2002,"source":"pdf_text","source_observed_at":"2026-08-06T10:41:40.669019Z"},"links":{"citing_paper":"/paper/2508.13165"},"observation_digest":"sha256:9cf6366f9bbd88f1fba8d30b6132f7b915e001096ff5d7e0f2703cd9d5ac26bc","observation_id":"612a44f0-3516-4b83-afb8-9ca91a8d9a87","resolution":{"observed_at":"2026-08-06T10:41:41.436872Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:41:41.475765Z","title":"[Edward22] Harold M","venue":null,"work_id":"93632c15-f1f0-4e36-a03f-3d4d929753ac","year":2022},"citing_paper":{"arxiv_id":"2508.13165","last_updated":"2025-07-31T14:23:28Z","snapshot_observed_at":"2026-08-06T10:41:25.152659Z","submitted_at":"2025-07-31T14:23:28Z","title":"An introduction to the algebra of rings and fields","version":1},"reference_index":2004,"source":"pdf_text","source_observed_at":"2026-08-06T10:41:40.621200Z"},"links":{"citing_paper":"/paper/2508.13165"},"observation_digest":"sha256:9b7d581c836e6743cb43e4050ea7e9081f489c5b2bae152b729795fb70356be5","observation_id":"dcd60727-579b-4de3-a3f3-cfa4c627382a","resolution":{"observed_at":"2026-08-06T10:41:41.480512Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:41:40.682907Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2508.13165","last_updated":"2025-07-31T14:23:28Z","snapshot_observed_at":"2026-08-06T10:41:25.152659Z","submitted_at":"2025-07-31T14:23:28Z","title":"An introduction to the algebra of rings and fields","version":1},"reference_index":2005,"source":"pdf_text","source_observed_at":"2026-08-06T10:41:40.682907Z"},"links":{"citing_paper":"/paper/2508.13165"},"observation_digest":"sha256:488694120aa4b8769f031814a66dc92f992cf7eedd80a3da53c2ae48b083f53c","observation_id":"4d4c288e-7d20-40de-89ec-1e8379fb9349","resolution":{"observed_at":"2026-08-06T10:41:40.682907Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2212.13624","last_updated":"2023-11-16T00:51:29Z","snapshot_observed_at":"2026-07-06T14:35:21.868173Z","submitted_at":"2022-12-27T21:27:49Z","title":"On an identity of Sylvester","version":2},"cited_work":{"arxiv_id":"2212.13624","doi":null,"metadata_source":"pith","pith_arxiv_id":"2212.13624","snapshot_observed_at":"2026-08-06T10:41:40.950234Z","title":"On an identity of Sylvester","venue":"math.CO","work_id":"a8b460be-b2fc-47d2-abdf-56256a633b4c","year":2022},"citing_paper":{"arxiv_id":"2508.13165","last_updated":"2025-07-31T14:23:28Z","snapshot_observed_at":"2026-08-06T10:41:25.152659Z","submitted_at":"2025-07-31T14:23:28Z","title":"An introduction to the algebra of rings and fields","version":1},"reference_index":2007,"source":"pdf_text","source_observed_at":"2026-08-06T10:41:40.660355Z"},"links":{"cited_paper":"/paper/2212.13624","citing_paper":"/paper/2508.13165"},"observation_digest":"sha256:ac014a0e1e2c18f731e3236037af8bae3bf0c52641ac4bb7adb648ded31951a6","observation_id":"44de2221-d711-4a67-ba2c-c2f95044589a","resolution":{"observed_at":"2026-08-06T10:41:40.955676Z","resolver_source":"local_arxiv","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T10:41:40.611741Z","title":"Cox, Galois Theory, 2nd edition, Wiley","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2508.13165","last_updated":"2025-07-31T14:23:28Z","snapshot_observed_at":"2026-08-06T10:41:25.152659Z","submitted_at":"2025-07-31T14:23:28Z","title":"An introduction to the algebra of rings and fields","version":1},"reference_index":2015,"source":"pdf_text","source_observed_at":"2026-08-06T10:41:40.611741Z"},"links":{"citing_paper":"/paper/2508.13165"},"observation_digest":"sha256:a1d83015be87d93407957af393b2f196e15be8d5d2e3dfeb3835f357387f7fb3","observation_id":"e8a6abe6-773f-4da9-8d45-a0b6a394a066","resolution":{"observed_at":"2026-08-06T10:41:40.611741Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2008.09862","last_updated":"2022-09-15T13:18:32Z","snapshot_observed_at":"2026-07-06T09:49:19.769284Z","submitted_at":"2020-08-22T16:06:22Z","title":"Notes on the combinatorial fundamentals of algebra","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2008.09862","snapshot_observed_at":"2026-08-06T10:41:40.629900Z","title":"dir/algebrabook.html [Grinbe15] Darij Grinberg, Notes on the combinatorial fundamentals of algebra , 15 September 2022, arXiv:2008.09862v3","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2508.13165","last_updated":"2025-07-31T14:23:28Z","snapshot_observed_at":"2026-08-06T10:41:25.152659Z","submitted_at":"2025-07-31T14:23:28Z","title":"An introduction to the algebra of rings and fields","version":1},"reference_index":2016,"source":"pdf_text","source_observed_at":"2026-08-06T10:41:40.629900Z"},"links":{"cited_paper":"/paper/2008.09862","citing_paper":"/paper/2508.13165"},"observation_digest":"sha256:f243d02201dba66e809fbda0dd1ff32c71fceb0202eb9b727beb14c2e4ec62e6","observation_id":"34fac1a5-06d9-4c41-a5ca-514ec0e23032","resolution":{"observed_at":"2026-08-06T10:41:40.629900Z","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":"web/2022113","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:41:41.386146Z","title":"Gallian, Contemporary Abstract Algebra, 10th edition, CRC Press","venue":null,"work_id":"aa8623e4-e313-4593-9399-e7c5466fa28d","year":null},"citing_paper":{"arxiv_id":"2508.13165","last_updated":"2025-07-31T14:23:28Z","snapshot_observed_at":"2026-08-06T10:41:25.152659Z","submitted_at":"2025-07-31T14:23:28Z","title":"An introduction to the algebra of rings and fields","version":1},"reference_index":2019,"source":"pdf_text","source_observed_at":"2026-08-06T10:41:40.625607Z"},"links":{"citing_paper":"/paper/2508.13165"},"observation_digest":"sha256:8be6ae845e35d09d5eb6edc5c55ace81541f69535fee82a07f31ea1fa257dde3","observation_id":"5c041b25-d22d-494e-80e9-04fda193a46c","resolution":{"observed_at":"2026-08-06T10:41:41.393943Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"web/2023081","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:41:41.184902Z","title":null,"venue":null,"work_id":"592b38c7-2c6d-48ff-b7d4-85d7cb0cd920","year":2023},"citing_paper":{"arxiv_id":"2508.13165","last_updated":"2025-07-31T14:23:28Z","snapshot_observed_at":"2026-08-06T10:41:25.152659Z","submitted_at":"2025-07-31T14:23:28Z","title":"An introduction to the algebra of rings and fields","version":1},"reference_index":2020,"source":"pdf_text","source_observed_at":"2026-08-06T10:41:40.648044Z"},"links":{"citing_paper":"/paper/2508.13165"},"observation_digest":"sha256:43ab5e2d105fc3edcb8c584aeb0f30bbf63551efdfd56054c0448cc6bdf9034e","observation_id":"d49e2c81-e82a-4919-adde-3b6f4d8611a7","resolution":{"observed_at":"2026-08-06T10:41:41.191557Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:41:41.502862Z","title":"4 (April 2011), pp","venue":null,"work_id":"d1f9cc1b-f8f3-44b4-b1c7-14996c0dbde6","year":2011},"citing_paper":{"arxiv_id":"2508.13165","last_updated":"2025-07-31T14:23:28Z","snapshot_observed_at":"2026-08-06T10:41:25.152659Z","submitted_at":"2025-07-31T14:23:28Z","title":"An introduction to the algebra of rings and fields","version":1},"reference_index":2021,"source":"pdf_text","source_observed_at":"2026-08-06T10:41:40.607143Z"},"links":{"citing_paper":"/paper/2508.13165"},"observation_digest":"sha256:26b1c63f904cfa1332fe49700c58940b69fb109456684c4c65cb3c693bd38164","observation_id":"0f99754d-3555-46bf-9f56-f186384e891b","resolution":{"observed_at":"2026-08-06T10:41:41.507241Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2411.17602","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:41:41.033745Z","title":"[MulMum07] Gary L","venue":null,"work_id":"57f845ba-2a39-487f-b495-d2fb140994fb","year":null},"citing_paper":{"arxiv_id":"2508.13165","last_updated":"2025-07-31T14:23:28Z","snapshot_observed_at":"2026-08-06T10:41:25.152659Z","submitted_at":"2025-07-31T14:23:28Z","title":"An introduction to the algebra of rings and fields","version":1},"reference_index":2023,"source":"pdf_text","source_observed_at":"2026-08-06T10:41:40.656320Z"},"links":{"citing_paper":"/paper/2508.13165"},"observation_digest":"sha256:282129c7ef272ba02c30f9e3c65dcb52825472cdfb185fd0369d32f6629e6e20","observation_id":"d454c6e0-446c-4d84-aa3f-22435b740f43","resolution":{"observed_at":"2026-08-06T10:41:41.040314Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T10:41:41.516291Z","title":"https://www.cip.ifi.lmu.de/~grinberg/t/21w/ [Aluffi16] Paolo Aluffi, Algebra: Chapter 0 , Graduate Studies in Mathematics 104, 2nd printing, AMS","venue":null,"work_id":"472f1008-2209-422f-af27-10e0f8883edc","year":2021},"citing_paper":{"arxiv_id":"2508.13165","last_updated":"2025-07-31T14:23:28Z","snapshot_observed_at":"2026-08-06T10:41:25.152659Z","submitted_at":"2025-07-31T14:23:28Z","title":"An introduction to the algebra of rings and fields","version":1},"reference_index":2025,"source":"pdf_text","source_observed_at":"2026-08-06T10:41:40.602476Z"},"links":{"citing_paper":"/paper/2508.13165"},"observation_digest":"sha256:aaf50bb9a2a7774ccbd5b89692d82c43c2c57a302298305a4d310fa4dc2fb253","observation_id":"9d9310c1-cf6d-45ea-8d5d-0ec3b11dc6fe","resolution":{"observed_at":"2026-08-06T10:41:41.520916Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2508.13165","last_updated":"2025-07-31T14:23:28Z","latest_version":1,"primary_category":"math.RA","snapshot_observed_at":"2026-08-06T10:41:25.152659Z","submitted_at":"2025-07-31T14:23:28Z","title":"An introduction to the algebra of rings and fields"},"reference_resolution":{"displayed":22,"state_counts":{"malformed_identifier":0,"metadata_mismatch":2,"parse_uncertain":1,"unresolved":5,"verified_exact":7,"verified_fuzzy":7},"total_outbound_references":22},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2508.13165."}