{"as_of":"2026-08-20T06:15:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:895d0125e46e3d0730fa7c8287dd710f398fc11899ed97cff04a082bc2121853","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":"2026-08-15T15:26:55.988159Z","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":"2026-08-19T06:32:44.657259+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/2608.00387/citation-record","integrity":"/paper/2608.00387/integrity","json":"/paper/2608.00387/citation-record.json","paper":"/paper/2608.00387"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:26:55.870221Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.870221Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:f8978f33ffe70d59ac60c06f925d619848e5d10bc2d3cb1553a66852898204cc","observation_id":"0fdd2231-b31f-4333-8640-fb06ae2e0b7b","resolution":{"observed_at":"2026-08-15T15:26:55.870221Z","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":"2026-08-15T15:26:56.526168Z","title":null,"venue":null,"work_id":"06722c47-306c-4c8f-9084-a936bfb3f2ab","year":2022},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.874114Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:2280f2aefc922bb61ece79d144c99e7d9d4f7923f887f7c502dfdb28bd740094","observation_id":"f42d23e9-ced3-4c6a-816e-5414744e1657","resolution":{"observed_at":"2026-08-15T15:26:56.529574Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T15:26:56.515998Z","title":"Cohen, H","venue":null,"work_id":"0f4b44ac-946c-4a13-845b-007c4d3bf980","year":1983},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.877883Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:3ce100acce7ebabb65a9145b464d0bdda0908a79298c9d9628651bad0b4f8625","observation_id":"0960e8bb-4069-4dc8-847b-0e06385d491d","resolution":{"observed_at":"2026-08-15T15:26:56.519696Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T15:26:56.506779Z","title":"Cohen, J","venue":null,"work_id":"6d949505-a113-452c-9c9f-c05ae65474d9","year":1990},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.881571Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:6f91c77a902363d7fd27b72d2f0b0ad6a2de09aeef3e04aec4d4440eb1d27484","observation_id":"85f53c2d-5c6e-47d0-b354-ed13593c91fb","resolution":{"observed_at":"2026-08-15T15:26:56.510163Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T15:26:56.496718Z","title":"Erdős, M","venue":null,"work_id":"feed3669-709e-4afd-9750-497846ee936f","year":1940},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.885207Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:9d5b8f6a452d93e7f20513ed8986771fd0d0f99d405d77dabb2764e43ca76f59","observation_id":"fd4181bd-c946-43ba-ab7c-13e3830a08be","resolution":{"observed_at":"2026-08-15T15:26:56.500231Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.5802/jtnb.1220","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:26:56.153400Z","title":"Fouvry, P","venue":null,"work_id":"1c0fadd9-cdb8-4a6a-9949-b870d9bbcffb","year":2022},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.888636Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:892e174534404f7300a8eb9f5e90fdf8c917c624a6553682fe5e3ee435bf9541","observation_id":"ade0d14b-e369-4342-85cb-d8e7578abf60","resolution":{"observed_at":"2026-08-15T15:26:56.156799Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T15:26:56.485730Z","title":"Fouvry, J","venue":null,"work_id":"be140c39-8b63-4593-a175-83f6948134c2","year":2007},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.892316Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:d57f4f10723a1c8f5b3f813f36446ec6623980f2b3db3e74b72576212f21d08d","observation_id":"818f8606-a67b-4fcb-9706-5d07493834f5","resolution":{"observed_at":"2026-08-15T15:26:56.489532Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T15:26:56.474822Z","title":"Fouvry, J","venue":null,"work_id":"d2d9df4e-e807-4e72-83b6-13d0952a9d9c","year":2010},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.895426Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:f48ec82c3de6e97198738a68ed16c1026e28d239233f56bfe81260504dba7074","observation_id":"c5a57cd3-9851-4168-ba00-470ae0c2e444","resolution":{"observed_at":"2026-08-15T15:26:56.478373Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1017/s1474748020000651","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:26:56.143020Z","title":"Fouvry, P","venue":null,"work_id":"f71a3918-904e-4e08-897d-ce799a5e6029","year":2022},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.898552Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:6abe49c538d56ad192c381f8a5bc0fbd250602ce025352e6927db48cd056894b","observation_id":"a90fa76d-0017-4156-9dba-4b3bfb3b223e","resolution":{"observed_at":"2026-08-15T15:26:56.146475Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T15:26:56.460724Z","title":"Fröhlich, Central Extensions, Galois Groups, and Ideal Class Groups of Number Fields , Contemp","venue":null,"work_id":"1da9a282-21b2-4b6a-a3c0-754026b5d7e7","year":1983},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.901975Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:d2ad5b7c48200c4902ce5931f0707182f1e756b79b0b92c758b7cd98d35a32b4","observation_id":"5df2abe2-c8e8-49cd-99cb-0846893fbf09","resolution":{"observed_at":"2026-08-15T15:26:56.465086Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T15:26:56.448124Z","title":"Gerth III, The 4-class ranks of quadratic fields , Invent","venue":null,"work_id":"0473634d-abbf-459f-91f7-3519108853c5","year":1984},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.905104Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:70c5a032a9e759c043b4bcc8bbb24c4fe199f6e81abd68363797be79153fea1d","observation_id":"ff7749de-b20f-418a-bdd1-07f253179158","resolution":{"observed_at":"2026-08-15T15:26:56.452008Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T15:26:56.435430Z","title":"Gerth III, Extension of conjectures of Cohen and Lenstra , Expo","venue":null,"work_id":"5dd5c06b-ea9f-4b9d-b6ad-742d1138fdd1","year":1987},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.908516Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:beefe47cad7a64c968b383c3a2e73431cc414c2f0ea327bac9ed776e800aa43d","observation_id":"80ff027a-1f81-4ff0-8d78-cdaa732ee86b","resolution":{"observed_at":"2026-08-15T15:26:56.439129Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T15:26:56.418837Z","title":"Granville, Prime divisors are Poisson distributed , Int","venue":null,"work_id":"a33f02d9-0190-4df5-81cb-a574c4e9438a","year":2007},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.911843Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:338922e1bdb66be513d034822ba99cc0c8e67e00c0966b5ace550f80c9a81599","observation_id":"6a139af5-dced-4819-a2c3-ddbbcd0e7d07","resolution":{"observed_at":"2026-08-15T15:26:56.423077Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1093/imrn/rnaa196","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:26:56.132930Z","title":"Koymans, C","venue":null,"work_id":"384f9875-aba5-4269-82f9-ce94de945f5c","year":2022},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.914976Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:670058ad312cb0fd464d8ec690517af3fa44ccff59c25b5dd57cd45a3e2c8789","observation_id":"8a4631c1-d7d8-4d27-b0d3-548650a36c76","resolution":{"observed_at":"2026-08-15T15:26:56.136424Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1515/forum-2023-0131","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:26:56.123077Z","title":null,"venue":null,"work_id":"89181a07-4779-46ea-a3dd-45cd56e21c48","year":2024},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.918207Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:a019cf057ff95158b2300823149d10c68162ba49692cfa2dea5747515c26dc7b","observation_id":"e6ca9ce3-a2e1-4e2c-b750-44c97e7b78cc","resolution":{"observed_at":"2026-08-15T15:26:56.126401Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2101.03407","last_updated":"2021-01-09T18:43:02Z","snapshot_observed_at":"2026-08-16T18:53:19.961352Z","submitted_at":"2021-01-09T18:43:02Z","title":"The $4$-rank of class groups of $K(\\sqrt{n})$","version":1},"cited_work":{"arxiv_id":"2101.03407","doi":null,"metadata_source":"pith","pith_arxiv_id":"2101.03407","snapshot_observed_at":"2026-08-15T15:26:56.370452Z","title":"The $4$-rank of class groups of $K(\\sqrt{n})$","venue":"math.NT","work_id":"4ece3a48-66af-4901-b36b-2cc5245039f9","year":2021},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.921308Z"},"links":{"cited_paper":"/paper/2101.03407","citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:a094b56da60f736d27a0f03403cc8855ee4e1efe89ec6eb77edbf3dfbc4df778","observation_id":"5cf4697e-43cf-4b07-9adc-329195ff3282","resolution":{"observed_at":"2026-08-15T15:26:56.374793Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4064/aa230318-4-1","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:26:56.111956Z","title":"Koymans, C","venue":null,"work_id":"ccfb92d3-b84a-4419-a780-4f2d678641f8","year":2024},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.924665Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:a45c4211f4954ffcd17ae1046b8ff68b6fca89c237015e4433ebf6d164a4d26b","observation_id":"b1a9a5a8-beff-41eb-a827-3be8ebe21ceb","resolution":{"observed_at":"2026-08-15T15:26:56.115701Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2201.13424","last_updated":"2022-01-31T18:35:03Z","snapshot_observed_at":"2026-08-16T17:24:36.300698Z","submitted_at":"2022-01-31T18:35:03Z","title":"On Stevenhagen's conjecture","version":1},"cited_work":{"arxiv_id":"2201.13424","doi":null,"metadata_source":"pith","pith_arxiv_id":"2201.13424","snapshot_observed_at":"2026-08-15T15:26:56.348971Z","title":"On Stevenhagen's conjecture","venue":"math.NT","work_id":"f0fc554e-c0d2-487d-a08c-07e2aaa1989b","year":2022},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.927631Z"},"links":{"cited_paper":"/paper/2201.13424","citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:75ea2c1763bfb2145fe481b1c2d10f03a180082f9f82de0f3defd6fdfc18b84c","observation_id":"207b2b8c-ca2e-4a7f-8051-9ef4cebd7880","resolution":{"observed_at":"2026-08-15T15:26:56.354433Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T15:26:55.931232Z","title":"Koymans, Y","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.931232Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:1e81e54747ae84795f417a4346f612c4acef7748afb0a4964f0bc332dbac13b0","observation_id":"b8fa7e14-6e39-43cd-b1c8-c26d1a459831","resolution":{"observed_at":"2026-08-15T15:26:55.931232Z","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":"2026-08-15T15:26:56.408306Z","title":"Koymans, The 16-rank of Q(√−p), Algebra Number Theory 14 (2020), no","venue":null,"work_id":"fc8a1a8d-87ea-45d0-a794-e6472d3c0c19","year":2020},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.934367Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:c2d755ba4d79f95bc3d161ce282bb79f81b0e0bbf4b099dcb9c4a3efcecf405a","observation_id":"5ab8fe71-829e-4376-86b7-e085efe80026","resolution":{"observed_at":"2026-08-15T15:26:56.411767Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1093/imrn/rny010","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:26:56.101774Z","title":"Koymans, D","venue":null,"work_id":"c20a98af-c62c-45ae-910e-7e047c3eeecc","year":2019},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.937584Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:d859cbbec104f2923f972dc861a95349197b6cc5b42436c74d03ff15c6f0bd8e","observation_id":"9387ee01-e86e-4fd7-b312-d0425f5c4bbd","resolution":{"observed_at":"2026-08-15T15:26:56.105284Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T15:26:55.940687Z","title":"Koymans, D","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.940687Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:3c755497a438c265985acef195e7f8a3136c69eb27cdf51e31f506df4848c2da","observation_id":"d3d6c429-6715-497a-b7e2-04c8332e19d2","resolution":{"observed_at":"2026-08-15T15:26:55.940687Z","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":"10.1515/forum-2022-0209","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:26:56.084219Z","title":"Lee, Joint distribution of the cokernels of random p-adic matrices , Forum Math","venue":null,"work_id":"5b93982b-a2ee-4374-b47a-6e7cb237bec3","year":2023},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.943790Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:f30453e614050a1926c7ed02a0c8b00a67ba9d5294f757137c9db7af076c8aa0","observation_id":"1ebda4fa-1fff-4754-a5b0-6197f6def51c","resolution":{"observed_at":"2026-08-15T15:26:56.088318Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jalgebra.2023.10.038","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:26:56.073177Z","title":"Lee, Mixed moments and the joint distribution of random groups , J","venue":null,"work_id":"9ccd48a7-00a6-4421-a343-edf0abbf21b8","year":2024},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.946937Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:a76849bedf1c4d1eb619d2ad27d0b8797764a712045d44d03229cf0124c6d920","observation_id":"67627c01-62a3-49b4-bae7-fc33e756b2c9","resolution":{"observed_at":"2026-08-15T15:26:56.076721Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4064/aa-66-3-245-","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:26:56.063045Z","title":"Lemmermeyer, Kuroda’s class number formula , Acta Arith","venue":null,"work_id":"06db1c51-4428-4ed4-9c4d-9bb244ba987f","year":1994},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.950509Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:e14c25205215468bf4086e61dc63718e7f5a65b1d277dc2f046b46b087a0b656","observation_id":"785b6a41-bb52-4379-a953-ffe54940cbc3","resolution":{"observed_at":"2026-08-15T15:26:56.066469Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4153/cjm-1997-014-2","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:26:56.052666Z","title":null,"venue":null,"work_id":"d08c26df-881e-404d-bfd6-2bac6b09f9b6","year":1997},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.953821Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:c2b1f1d3bef3c3c7b563b2de89ec073fe688c2b2acac2e9d33075d66d8ffa588","observation_id":"325a7da8-b85f-44ac-8a6c-2a6a789d0e0b","resolution":{"observed_at":"2026-08-15T15:26:56.056378Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2001.07213","last_updated":"2020-01-20T18:58:58Z","snapshot_observed_at":"2026-07-06T08:51:39.054038Z","submitted_at":"2020-01-20T18:58:58Z","title":"On Hasse's Unit Index","version":1},"cited_work":{"arxiv_id":"2001.07213","doi":null,"metadata_source":"pith","pith_arxiv_id":"2001.07213","snapshot_observed_at":"2026-08-15T15:26:56.277582Z","title":"On Hasse's Unit Index","venue":"math.NT","work_id":"6ab2d142-76bc-4099-b0fb-ab18b5ea3cb4","year":2020},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.957159Z"},"links":{"cited_paper":"/paper/2001.07213","citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:bafbf44bbfa9bca2f3c5529620032a198eb94032682d71f0c212ad21eb7fcdcb","observation_id":"bf99befc-1fc7-4b87-89b8-3f8a726c825e","resolution":{"observed_at":"2026-08-15T15:26:56.282136Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1710.07587","last_updated":"2017-10-20T16:02:38Z","snapshot_observed_at":"2026-08-14T20:21:49.339400Z","submitted_at":"2017-10-20T16:02:38Z","title":"4-ranks and the general model for statistics of ray class groups of imaginary quadratic number fields","version":1},"cited_work":{"arxiv_id":"1710.07587","doi":null,"metadata_source":"pith","pith_arxiv_id":"1710.07587","snapshot_observed_at":"2026-08-15T15:26:56.259747Z","title":"4-ranks and the general model for statistics of ray class groups of imaginary quadratic number fields","venue":"math.NT","work_id":"42164c60-7b47-4a5d-b4e0-f9361dc4aabd","year":2017},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.960538Z"},"links":{"cited_paper":"/paper/1710.07587","citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:38a316c4e45192da95eddd2ec86200a10d02070e509a1341cd5572d3cc059fff","observation_id":"aa401f4b-c6f9-45b6-bd61-a7d66367b07f","resolution":{"observed_at":"2026-08-15T15:26:56.264395Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T15:26:56.396669Z","title":"Rédei, H","venue":null,"work_id":"66d42d89-46ba-4b64-914e-70fce8f62b2b","year":1934},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.964297Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:83b1d60dee0562e8d528a84500b3d9307eb9adb884d31664aa4d35d609e34d41","observation_id":"370a9231-85a2-4262-b1a9-d9cd8398816b","resolution":{"observed_at":"2026-08-15T15:26:56.400531Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T15:26:56.382987Z","title":"Selberg, Note on a paper by L","venue":null,"work_id":"e31f1552-6094-4f33-97ec-9835c2b41faf","year":1954},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.967670Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:3f24e04b27ecda649daf6615a6288c9df1399d5f60f8bb5a5fd3e8316d90ab2c","observation_id":"7814f906-0323-4dd5-a786-d78abfea5ae9","resolution":{"observed_at":"2026-08-15T15:26:56.387610Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1702.02325","last_updated":"2017-06-07T00:58:17Z","snapshot_observed_at":"2026-08-14T21:17:28.415830Z","submitted_at":"2017-02-08T08:42:41Z","title":"$2^\\infty$-Selmer groups, $2^\\infty$-class groups, and Goldfeld's conjecture","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1702.02325","snapshot_observed_at":"2026-08-15T15:26:55.970895Z","title":"Smith, 2∞-Selmer groups, 2∞-class groups, and Goldfeld’s conjecture , arXiv:1702.02325v2, 7 June 2017","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.970895Z"},"links":{"cited_paper":"/paper/1702.02325","citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:77fe9c23af309d3ff1593fd114890e1a0cc090d9c9a3d08fe365e30edbd89a57","observation_id":"6d98228b-9ccc-41ce-b18a-3ad87a2b657b","resolution":{"observed_at":"2026-08-15T15:26:55.970895Z","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":"10.1090/jams/1062","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:26:56.042170Z","title":"Smith, The distribution of ℓ∞-Selmer groups in degree ℓ twist families I , J","venue":null,"work_id":"184df38f-3b28-492b-af4f-82276fd10c3b","year":2026},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.974700Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:277ce3cb3e697ecfc1de974acc04ebbd8c17f6b1eb77e2f96a242825109c1a40","observation_id":"b83352ba-a1f5-492b-a7ed-55cd47faaf83","resolution":{"observed_at":"2026-08-15T15:26:56.045771Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1090/jams/1063","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:26:56.031677Z","title":"Smith, The distribution of ℓ∞-Selmer groups in degree ℓ twist families II , J","venue":null,"work_id":"69b1e855-80cc-41ef-9d8c-edcd97040d7e","year":2026},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.978315Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:aab220d574c97583133c57de05e2c6da27f9bdc56f3e61008b12d0ee81d07ea0","observation_id":"025ea4e0-60e5-401f-abd8-e09c9fcdab82","resolution":{"observed_at":"2026-08-15T15:26:56.035602Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-15T15:26:55.981656Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.981656Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:f1768bc98284f97ff7930c35c47803549a5b473e39f970420f92c898c6b2074d","observation_id":"373db785-df11-46fb-8e69-4369240e4438","resolution":{"observed_at":"2026-08-15T15:26:55.981656Z","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":"2026-08-15T15:26:55.985110Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.985110Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:7ee2023ca30f4e5ea4f7a2e1c34ecb0109e105cbf56103e5241d7d32da24ef28","observation_id":"9feede7c-9446-473d-81a5-d5dcf8f26ad1","resolution":{"observed_at":"2026-08-15T15:26:55.985110Z","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":"10.1007/s11425-024-2455-y","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:26:56.013687Z","title":null,"venue":null,"work_id":"33c820dd-1024-4e29-9f08-f1495624ce8d","year":2026},"citing_paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-15T15:26:55.988159Z"},"links":{"citing_paper":"/paper/2608.00387"},"observation_digest":"sha256:b4e1ef78e23ba50fae4b298e4cf094acb3404747a390b68dea006117de2ac92d","observation_id":"86df1fa9-2540-4aab-a197-4e0f78a5e1f4","resolution":{"observed_at":"2026-08-15T15:26:56.017880Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2608.00387","last_updated":"2026-08-01T01:55:26Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-08-17T14:11:12.224496Z","submitted_at":"2026-08-01T01:55:26Z","title":"Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields"},"reference_resolution":{"displayed":36,"state_counts":{"malformed_identifier":3,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":6,"verified_exact":16,"verified_fuzzy":11},"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":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 20 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 0 inbound Pith citation observations for arXiv:2608.00387."}