{"as_of":"2026-08-16T08:35:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:bdb762f0eec5f19a39c800b8560fe28b9717962d6c03da8a5dfd516cf14adffc","coverage":[{"denominator":11,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":11,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T12:43:19.266014Z","state":"measured"},{"denominator":11,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":11,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+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/1908.06811/citation-record","integrity":"/paper/1908.06811/integrity","json":"/paper/1908.06811/citation-record.json","paper":"/paper/1908.06811"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:43:19.429456Z","title":"Alsaody, Composition algebras and outer automorphisms of algebraic groups via triality , Comm","venue":null,"work_id":"41ec2e33-cb99-44a1-b1a5-70a71b9672a7","year":2017},"citing_paper":{"arxiv_id":"1908.06811","last_updated":"2019-08-19T14:05:46Z","snapshot_observed_at":"2026-08-14T12:31:45.549977Z","submitted_at":"2019-08-19T14:05:46Z","title":"On Four-Dimensional Unital Division Algebras over Fields of Characteristic not 2","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T12:43:19.220977Z"},"links":{"citing_paper":"/paper/1908.06811"},"observation_digest":"sha256:3b1e1527356f0f3e7d05d74ef4ce0c9dbd7697bbeea085fc044042e9e432e78e","observation_id":"b041a825-ba87-4f1f-876f-48e77cb185e6","resolution":{"observed_at":"2026-08-14T12:43:19.433937Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:43:19.417238Z","title":"Bani-Ata, S","venue":null,"work_id":"b50f97a0-032a-4aea-926e-00483d13d420","year":2015},"citing_paper":{"arxiv_id":"1908.06811","last_updated":"2019-08-19T14:05:46Z","snapshot_observed_at":"2026-08-14T12:31:45.549977Z","submitted_at":"2019-08-19T14:05:46Z","title":"On Four-Dimensional Unital Division Algebras over Fields of Characteristic not 2","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T12:43:19.225654Z"},"links":{"citing_paper":"/paper/1908.06811"},"observation_digest":"sha256:6e9247384dce7d2e05c28a9e593c0fe3e46b32b5691f592eb1cff438dd9fbb70","observation_id":"ec21ee2b-9006-4b46-8299-2a486d31a6a6","resolution":{"observed_at":"2026-08-14T12:43:19.421352Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:43:19.402381Z","title":"Curtis, I","venue":null,"work_id":"5e01490a-bb9b-4b5c-9ac5-71ba1f7ac514","year":1962},"citing_paper":{"arxiv_id":"1908.06811","last_updated":"2019-08-19T14:05:46Z","snapshot_observed_at":"2026-08-14T12:31:45.549977Z","submitted_at":"2019-08-19T14:05:46Z","title":"On Four-Dimensional Unital Division Algebras over Fields of Characteristic not 2","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T12:43:19.229843Z"},"links":{"citing_paper":"/paper/1908.06811"},"observation_digest":"sha256:ddb0aa3ad6f4df926629e9baa9c42b53ab5e950a8294423d56a1d880cbf805ff","observation_id":"3c9df2e8-b63e-4300-9d71-2d052c68945a","resolution":{"observed_at":"2026-08-14T12:43:19.406242Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:43:19.390323Z","title":"Dieterich, Classification, automorphism groups and categorical struc- ture of the two-dimensional real division algebras , J","venue":null,"work_id":"edd1cddb-285e-4905-8854-63c2fd505063","year":2005},"citing_paper":{"arxiv_id":"1908.06811","last_updated":"2019-08-19T14:05:46Z","snapshot_observed_at":"2026-08-14T12:31:45.549977Z","submitted_at":"2019-08-19T14:05:46Z","title":"On Four-Dimensional Unital Division Algebras over Fields of Characteristic not 2","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T12:43:19.234030Z"},"links":{"citing_paper":"/paper/1908.06811"},"observation_digest":"sha256:f3ba61c6d70eea573f11de6fb997301be0f0e58223218f673dba23cd581443ba","observation_id":"7bfac9f2-bec7-4115-a013-b359e2abcc49","resolution":{"observed_at":"2026-08-14T12:43:19.394118Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:43:19.378921Z","title":"Dieterich, A general approach to finite-dimensional division algebras , Colloq","venue":null,"work_id":"6beca75f-9831-4f5a-a9a8-4b477bdab193","year":2012},"citing_paper":{"arxiv_id":"1908.06811","last_updated":"2019-08-19T14:05:46Z","snapshot_observed_at":"2026-08-14T12:31:45.549977Z","submitted_at":"2019-08-19T14:05:46Z","title":"On Four-Dimensional Unital Division Algebras over Fields of Characteristic not 2","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T12:43:19.238357Z"},"links":{"citing_paper":"/paper/1908.06811"},"observation_digest":"sha256:4782fab55e5d62e87c20eddf0f6989a34de89a28489f0794efc7d9dd1afd8408","observation_id":"233943e8-f80c-4c87-87e9-ae9cbb873a19","resolution":{"observed_at":"2026-08-14T12:43:19.383053Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:43:19.365852Z","title":"Gabriel, Matrizen, Geometrie, Lineare Algebra , Birkh¨ auser Advan- ced Texts, Birkh¨ auser Verlag 1996","venue":null,"work_id":"3e35c68e-27b6-446d-b2b5-206528e78005","year":1996},"citing_paper":{"arxiv_id":"1908.06811","last_updated":"2019-08-19T14:05:46Z","snapshot_observed_at":"2026-08-14T12:31:45.549977Z","submitted_at":"2019-08-19T14:05:46Z","title":"On Four-Dimensional Unital Division Algebras over Fields of Characteristic not 2","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T12:43:19.243928Z"},"links":{"citing_paper":"/paper/1908.06811"},"observation_digest":"sha256:863f6819b374ed851a7d88d648ba7dae201325da10ebcb4a7d63657a05f7a794","observation_id":"6e88e5b0-a6de-4601-8e66-6fefcb76987e","resolution":{"observed_at":"2026-08-14T12:43:19.370345Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:43:19.353891Z","title":"Gabriel, A.V","venue":null,"work_id":"192dd7f7-16e4-485b-b893-64c6145e9af2","year":1992},"citing_paper":{"arxiv_id":"1908.06811","last_updated":"2019-08-19T14:05:46Z","snapshot_observed_at":"2026-08-14T12:31:45.549977Z","submitted_at":"2019-08-19T14:05:46Z","title":"On Four-Dimensional Unital Division Algebras over Fields of Characteristic not 2","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T12:43:19.248589Z"},"links":{"citing_paper":"/paper/1908.06811"},"observation_digest":"sha256:c18bb3480de469433b725c37bba3ad545c1f94902905659ec41cda5bdc37637b","observation_id":"4b437c97-88ba-4fba-9d4e-308f552564c7","resolution":{"observed_at":"2026-08-14T12:43:19.357956Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:43:19.340960Z","title":"Grillet, Abstract algebra, Second Edition, Graduate Texts in Ma- thematics 242, Springer 2007","venue":null,"work_id":"2af88397-5867-4980-bb56-6a0dbfb89c0e","year":2007},"citing_paper":{"arxiv_id":"1908.06811","last_updated":"2019-08-19T14:05:46Z","snapshot_observed_at":"2026-08-14T12:31:45.549977Z","submitted_at":"2019-08-19T14:05:46Z","title":"On Four-Dimensional Unital Division Algebras over Fields of Characteristic not 2","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T12:43:19.253372Z"},"links":{"citing_paper":"/paper/1908.06811"},"observation_digest":"sha256:0c692aa494761573ec559b14d545c81aba62d273dce5fa82365c6ee0e18d9f5b","observation_id":"4d622aff-4841-4814-a497-c23c8557d624","resolution":{"observed_at":"2026-08-14T12:43:19.345265Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1802.08507","last_updated":"2018-02-23T12:53:32Z","snapshot_observed_at":"2026-08-14T19:42:55.258531Z","submitted_at":"2018-02-23T12:53:32Z","title":"On the classification of rational four-dimensional unital division algebras","version":1},"cited_work":{"arxiv_id":"1802.08507","doi":null,"metadata_source":"pith","pith_arxiv_id":"1802.08507","snapshot_observed_at":"2026-08-14T12:43:19.297360Z","title":"On the classification of rational four-dimensional unital division algebras","venue":"math.RA","work_id":"24d82c01-6aa6-45e7-9035-94ce8bbc358e","year":2018},"citing_paper":{"arxiv_id":"1908.06811","last_updated":"2019-08-19T14:05:46Z","snapshot_observed_at":"2026-08-14T12:31:45.549977Z","submitted_at":"2019-08-19T14:05:46Z","title":"On Four-Dimensional Unital Division Algebras over Fields of Characteristic not 2","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T12:43:19.257792Z"},"links":{"cited_paper":"/paper/1802.08507","citing_paper":"/paper/1908.06811"},"observation_digest":"sha256:fac8a659e22a49879bd42475d04aed0086265e1848f2bd7bdc93962dc5bba304","observation_id":"1dc48a1a-ac53-4524-8714-da3f40909f8d","resolution":{"observed_at":"2026-08-14T12:43:19.304301Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:43:19.327286Z","title":"Reiner, Maximal orders, L.M.S","venue":null,"work_id":"d53cb7b4-51b7-4dc7-9a89-b4b1a88505b9","year":1975},"citing_paper":{"arxiv_id":"1908.06811","last_updated":"2019-08-19T14:05:46Z","snapshot_observed_at":"2026-08-14T12:31:45.549977Z","submitted_at":"2019-08-19T14:05:46Z","title":"On Four-Dimensional Unital Division Algebras over Fields of Characteristic not 2","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T12:43:19.262121Z"},"links":{"citing_paper":"/paper/1908.06811"},"observation_digest":"sha256:a03b5b858ab684465d14dc5d1475f58f2d29095d3402baf3bc0ca8bf23d35a7e","observation_id":"ad0114d9-1f87-4b41-aa7a-de7ea1702bec","resolution":{"observed_at":"2026-08-14T12:43:19.331433Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T12:43:19.313893Z","title":"Springer, F.D","venue":null,"work_id":"670a2ec0-b56e-4840-a287-37c50075b96d","year":2000},"citing_paper":{"arxiv_id":"1908.06811","last_updated":"2019-08-19T14:05:46Z","snapshot_observed_at":"2026-08-14T12:31:45.549977Z","submitted_at":"2019-08-19T14:05:46Z","title":"On Four-Dimensional Unital Division Algebras over Fields of Characteristic not 2","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T12:43:19.266014Z"},"links":{"citing_paper":"/paper/1908.06811"},"observation_digest":"sha256:799f284f4f337e0f5f03946611af145c51325b8f348bdf5dbd56fc370b11dd56","observation_id":"628c9888-9387-4890-8675-702931c3077b","resolution":{"observed_at":"2026-08-14T12:43:19.318868Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1908.06811","last_updated":"2019-08-19T14:05:46Z","latest_version":1,"primary_category":"math.RA","snapshot_observed_at":"2026-08-14T12:31:45.549977Z","submitted_at":"2019-08-19T14:05:46Z","title":"On Four-Dimensional Unital Division Algebras over Fields of Characteristic not 2"},"reference_resolution":{"displayed":11,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":1,"verified_fuzzy":10},"total_outbound_references":11},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 11 of 11 outbound references and 0 inbound Pith citation observations for arXiv:1908.06811."}