{"as_of":"2026-08-16T18:21:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:903e902f595ad5446ffc5033bdb9bef00415d8a3b926fec945856014beada1b7","coverage":[{"denominator":9,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":9,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T14:58:29.272434Z","state":"measured"},{"denominator":9,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":9,"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/1908.02318/citation-record","integrity":"/paper/1908.02318/integrity","json":"/paper/1908.02318/citation-record.json","paper":"/paper/1908.02318"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T14:58:29.863067Z","title":null,"venue":null,"work_id":"89e11537-e33e-41fc-8d9c-75b2ead24f0d","year":2008},"citing_paper":{"arxiv_id":"1908.02318","last_updated":"2019-08-06T18:36:30Z","snapshot_observed_at":"2026-08-16T05:23:14.843405Z","submitted_at":"2019-08-06T18:36:30Z","title":"An introduction to $\\Gamma$-number fields","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T14:58:29.027657Z"},"links":{"citing_paper":"/paper/1908.02318"},"observation_digest":"sha256:f2bd45a4cc9b10550a3e9452c70d0246ca05524321a90d36119f02e1e097c690","observation_id":"45e11f46-e773-4fd7-8cdc-de70aac4f2a3","resolution":{"observed_at":"2026-08-14T14:58:29.869105Z","resolver_source":"raw_fallback","status":"unresolved"},"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":"1904.10080","last_updated":"2020-03-21T20:58:06Z","snapshot_observed_at":"2026-08-14T16:42:58.274770Z","submitted_at":"2019-04-22T22:26:58Z","title":"The trace form over cyclic number fields","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1904.10080","snapshot_observed_at":"2026-08-14T14:58:29.035506Z","title":"Bola˜ nos, G","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"1908.02318","last_updated":"2019-08-06T18:36:30Z","snapshot_observed_at":"2026-08-16T05:23:14.843405Z","submitted_at":"2019-08-06T18:36:30Z","title":"An introduction to $\\Gamma$-number fields","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T14:58:29.035506Z"},"links":{"cited_paper":"/paper/1904.10080","citing_paper":"/paper/1908.02318"},"observation_digest":"sha256:5465d0ca3be17fd313b6e3d524e58baac7c6e116d5713158eff93b443679ba2b","observation_id":"34b49f76-fea1-4f1b-9c96-fe81de1bdb9a","resolution":{"observed_at":"2026-08-14T14:58:29.035506Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T14:58:29.845867Z","title":"Jones, D","venue":null,"work_id":"227310b4-bdaa-4f36-8f46-e3a68b150242","year":2014},"citing_paper":{"arxiv_id":"1908.02318","last_updated":"2019-08-06T18:36:30Z","snapshot_observed_at":"2026-08-16T05:23:14.843405Z","submitted_at":"2019-08-06T18:36:30Z","title":"An introduction to $\\Gamma$-number fields","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T14:58:29.041900Z"},"links":{"citing_paper":"/paper/1908.02318"},"observation_digest":"sha256:fa867ec55e482c3e43aa3f575a03d19d80c90c247f1b6f23907a3c0c88f025da","observation_id":"36407dd7-1f6a-4e8c-85cc-7c7159b44e8e","resolution":{"observed_at":"2026-08-14T14:58:29.851359Z","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":"2026-08-14T14:58:29.829078Z","title":"Mantilla-Soler, The Spinor Genus of the integral trace , Transactions of the Amer- ican Mathematical Society 369 (2017) , 1547-1577","venue":null,"work_id":"ffe79879-eb99-45d8-89e8-c9bcb7852219","year":2017},"citing_paper":{"arxiv_id":"1908.02318","last_updated":"2019-08-06T18:36:30Z","snapshot_observed_at":"2026-08-16T05:23:14.843405Z","submitted_at":"2019-08-06T18:36:30Z","title":"An introduction to $\\Gamma$-number fields","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T14:58:29.047525Z"},"links":{"citing_paper":"/paper/1908.02318"},"observation_digest":"sha256:60001bf11f82962dbfc94899d58c118401bf98de2a62dd88a008708ea16e0498","observation_id":"ccf4b7b0-5102-4e11-a861-428433586ec7","resolution":{"observed_at":"2026-08-14T14:58:29.834265Z","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":"2026-08-14T14:58:29.584193Z","title":"Mantilla-Soler","venue":null,"work_id":"14bb3143-fa2a-4ea6-a6c5-a32cf8214bcd","year":2015},"citing_paper":{"arxiv_id":"1908.02318","last_updated":"2019-08-06T18:36:30Z","snapshot_observed_at":"2026-08-16T05:23:14.843405Z","submitted_at":"2019-08-06T18:36:30Z","title":"An introduction to $\\Gamma$-number fields","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T14:58:29.052445Z"},"links":{"citing_paper":"/paper/1908.02318"},"observation_digest":"sha256:6b979d52dba48af54162ad5f32e059caad25b4c410f91c5ee78ab40d8739b442","observation_id":"6ee67e25-f64c-4fde-ba0f-750b7b2a35fb","resolution":{"observed_at":"2026-08-14T14:58:29.682025Z","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":"1812.03133","last_updated":"2022-04-13T04:28:57Z","snapshot_observed_at":"2026-08-16T09:13:39.756899Z","submitted_at":"2018-12-07T17:48:08Z","title":"The integral trace form as a complete invariant for real $S_n$ number fields","version":6},"cited_work":{"arxiv_id":"1812.03133","doi":null,"metadata_source":"pith","pith_arxiv_id":"1812.03133","snapshot_observed_at":"2026-08-14T14:58:29.336341Z","title":"The integral trace form as a complete invariant for real $S_n$ number fields","venue":"math.NT","work_id":"66a69275-6cac-4c9e-90a0-eaeb2fef8609","year":2018},"citing_paper":{"arxiv_id":"1908.02318","last_updated":"2019-08-06T18:36:30Z","snapshot_observed_at":"2026-08-16T05:23:14.843405Z","submitted_at":"2019-08-06T18:36:30Z","title":"An introduction to $\\Gamma$-number fields","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T14:58:29.058610Z"},"links":{"cited_paper":"/paper/1812.03133","citing_paper":"/paper/1908.02318"},"observation_digest":"sha256:8c010d513a60fdd20ec31db7d0e7e09042cbe1f4f3df3e6f3e6873dd168b828f","observation_id":"e5e9b592-4bfb-497e-ae6a-3f0e7ae91a8d","resolution":{"observed_at":"2026-08-14T14:58:29.356160Z","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":{"arxiv_id":"1906.04254","last_updated":"2019-06-10T20:00:58Z","snapshot_observed_at":"2026-08-14T16:17:51.769029Z","submitted_at":"2019-06-10T20:00:58Z","title":"The $(\\alpha, \\beta)-$ramification invariants of a number field","version":1},"cited_work":{"arxiv_id":"1906.04254","doi":null,"metadata_source":"pith","pith_arxiv_id":"1906.04254","snapshot_observed_at":"2026-08-14T14:58:29.310397Z","title":"The $(\\alpha, \\beta)-$ramification invariants of a number field","venue":"math.NT","work_id":"ee44ee67-fd07-48a0-9f36-4e1a48eeacfb","year":2019},"citing_paper":{"arxiv_id":"1908.02318","last_updated":"2019-08-06T18:36:30Z","snapshot_observed_at":"2026-08-16T05:23:14.843405Z","submitted_at":"2019-08-06T18:36:30Z","title":"An introduction to $\\Gamma$-number fields","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T14:58:29.104069Z"},"links":{"cited_paper":"/paper/1906.04254","citing_paper":"/paper/1908.02318"},"observation_digest":"sha256:10dd9501874d49bc465a2b9e8a67a5b638fce65326cfed39355598c16bb4b2c6","observation_id":"8208fbee-93e1-4113-8db2-12228870bdb1","resolution":{"observed_at":"2026-08-14T14:58:29.317853Z","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":"2026-08-14T14:58:29.566527Z","title":"Serre, Local fields , Graduate Texts in Mathematics, 67","venue":null,"work_id":"f4e3c711-1cc0-400f-a9c1-e695dd591ee3","year":1979},"citing_paper":{"arxiv_id":"1908.02318","last_updated":"2019-08-06T18:36:30Z","snapshot_observed_at":"2026-08-16T05:23:14.843405Z","submitted_at":"2019-08-06T18:36:30Z","title":"An introduction to $\\Gamma$-number fields","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T14:58:29.176829Z"},"links":{"citing_paper":"/paper/1908.02318"},"observation_digest":"sha256:b9b79ddf6ac2124b9d0d00f947eed055302b03d4a4e12167bd5ac0dfb7472708","observation_id":"d3fc9471-973f-4850-aa19-3a52b3d6b56a","resolution":{"observed_at":"2026-08-14T14:58:29.571715Z","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":"2026-08-14T14:58:29.507916Z","title":"Taussky, The discriminant matrix of a number field , J","venue":null,"work_id":"f7b02ad1-4544-419a-9a01-72bbe1222d06","year":1968},"citing_paper":{"arxiv_id":"1908.02318","last_updated":"2019-08-06T18:36:30Z","snapshot_observed_at":"2026-08-16T05:23:14.843405Z","submitted_at":"2019-08-06T18:36:30Z","title":"An introduction to $\\Gamma$-number fields","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T14:58:29.272434Z"},"links":{"citing_paper":"/paper/1908.02318"},"observation_digest":"sha256:5593b0df30a13cd99f52ef57be6868b65553a26222f0b4192701bca709c606dc","observation_id":"db66f847-fcb2-4dd6-8847-e3d7c696c9ae","resolution":{"observed_at":"2026-08-14T14:58:29.554679Z","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":"1908.02318","last_updated":"2019-08-06T18:36:30Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-08-16T05:23:14.843405Z","submitted_at":"2019-08-06T18:36:30Z","title":"An introduction to $\\Gamma$-number fields"},"reference_resolution":{"displayed":9,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":2,"verified_exact":2,"verified_fuzzy":5},"total_outbound_references":9},"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 9 of 9 outbound references and 0 inbound Pith citation observations for arXiv:1908.02318."}