{"as_of":"2026-08-20T07:27:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:156bc008d6bbcdb4abaf8ddde87b80d6d430112b761b9da6310f466c68fae982","coverage":[{"denominator":15,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":15,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T15:51:24.429166Z","state":"measured"},{"denominator":15,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":15,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-20T06:33:59.587034+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.27364/citation-record","integrity":"/paper/2607.27364/integrity","json":"/paper/2607.27364/citation-record.json","paper":"/paper/2607.27364"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/0-8176-4417-2_7","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-17T11:03:46.409680Z","title":"Ellenberg and Akshay Venkatesh","venue":"Birkhäuser-Verlag eBooks","work_id":"07411c58-6dcb-4480-98d5-efe40c2566d3","year":2005},"citing_paper":{"arxiv_id":"2607.27364","last_updated":"2026-07-29T18:15:36Z","snapshot_observed_at":"2026-08-18T16:24:24.139561Z","submitted_at":"2026-07-29T18:15:36Z","title":"Multivariate counting of wild abelian extensions","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-15T15:51:24.338511Z"},"links":{"citing_paper":"/paper/2607.27364"},"observation_digest":"sha256:b63b4050227f532f520fe03eaabab1a0fb48cd73760d2bd9e9132424dc497daf","observation_id":"bf638945-2b01-475a-b078-3940f98aaf2c","resolution":{"observed_at":"2026-08-15T15:51:24.565364Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T15:51:24.345625Z","title":"Analytic combinatorics","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.27364","last_updated":"2026-07-29T18:15:36Z","snapshot_observed_at":"2026-08-18T16:24:24.139561Z","submitted_at":"2026-07-29T18:15:36Z","title":"Multivariate counting of wild abelian extensions","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-15T15:51:24.345625Z"},"links":{"citing_paper":"/paper/2607.27364"},"observation_digest":"sha256:ef6c552eb058176b3790d51df06c93f0bc53ff896af54340bde30d0b322e7898","observation_id":"c8365e90-37cd-41a3-bb18-a569f0e468f2","resolution":{"observed_at":"2026-08-15T15:51:24.345625Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.18207","last_updated":"2025-02-25T13:49:48Z","snapshot_observed_at":"2026-08-16T12:55:21.576984Z","submitted_at":"2025-02-25T13:49:48Z","title":"Counting two-step nilpotent wildly ramified extensions of function fields","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.18207","snapshot_observed_at":"2026-08-15T15:51:24.351486Z","title":"Counting two-step nilpotent wildly ramified extensions of function fields, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.27364","last_updated":"2026-07-29T18:15:36Z","snapshot_observed_at":"2026-08-18T16:24:24.139561Z","submitted_at":"2026-07-29T18:15:36Z","title":"Multivariate counting of wild abelian extensions","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-15T15:51:24.351486Z"},"links":{"cited_paper":"/paper/2502.18207","citing_paper":"/paper/2607.27364"},"observation_digest":"sha256:c35a3b3d91ade5e4ab23234210f7337775077c5d77ef05f30fb99806445ce11d","observation_id":"0b19a364-3e85-47cb-bd67-7ef2686beee6","resolution":{"observed_at":"2026-08-15T15:51:24.351486Z","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":"2603.15544","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:51:24.803845Z","title":"Lifts of unramified twists and local-global principles, 2026","venue":null,"work_id":"6b9b1316-1dba-4336-a643-c6f40a25b04f","year":2026},"citing_paper":{"arxiv_id":"2607.27364","last_updated":"2026-07-29T18:15:36Z","snapshot_observed_at":"2026-08-18T16:24:24.139561Z","submitted_at":"2026-07-29T18:15:36Z","title":"Multivariate counting of wild abelian extensions","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-15T15:51:24.357294Z"},"links":{"citing_paper":"/paper/2607.27364"},"observation_digest":"sha256:b37b12e784eca973183b26c00c731a8b39a18e75db65c2c3ea108e174de67527","observation_id":"f82add40-289d-4eba-ab2c-db8a755f9713","resolution":{"observed_at":"2026-08-15T15:51:24.812609Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2211.16698","last_updated":"2022-11-30T02:39:53Z","snapshot_observed_at":"2026-08-16T16:12:13.379177Z","submitted_at":"2022-11-30T02:39:53Z","title":"Malle's conjecture with multiple invariants","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2211.16698","snapshot_observed_at":"2026-08-15T15:51:24.363437Z","title":"Malle's conjecture with multiple invariants, 2022","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.27364","last_updated":"2026-07-29T18:15:36Z","snapshot_observed_at":"2026-08-18T16:24:24.139561Z","submitted_at":"2026-07-29T18:15:36Z","title":"Multivariate counting of wild abelian extensions","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-15T15:51:24.363437Z"},"links":{"cited_paper":"/paper/2211.16698","citing_paper":"/paper/2607.27364"},"observation_digest":"sha256:821cee16d242f5b9da83c837a251785dc8710a8109aec25941677ad5cd00aba9","observation_id":"65fdfa27-d627-442f-8ebe-04fafd1a6fd3","resolution":{"observed_at":"2026-08-15T15:51:24.363437Z","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/proc/17440","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-15T15:51:24.530227Z","title":"Counting abelian extensions by A rtin- S chreier conductor","venue":null,"work_id":"bc78ab97-9ec7-4bd4-82c8-a9eb8907cab7","year":2026},"citing_paper":{"arxiv_id":"2607.27364","last_updated":"2026-07-29T18:15:36Z","snapshot_observed_at":"2026-08-18T16:24:24.139561Z","submitted_at":"2026-07-29T18:15:36Z","title":"Multivariate counting of wild abelian extensions","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-15T15:51:24.369561Z"},"links":{"citing_paper":"/paper/2607.27364"},"observation_digest":"sha256:315a8aa9338276d219cc3a2e626b6ff4b9759557db555d6b99c057fa8876e0aa","observation_id":"1aad32e4-5669-4ab2-8e80-2f760f14b24d","resolution":{"observed_at":"2026-08-15T15:51:24.537646Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2607.16079","last_updated":"2026-07-20T10:27:13Z","snapshot_observed_at":"2026-08-15T08:24:02.223470Z","submitted_at":"2026-07-17T16:07:01Z","title":"Equidistribution for abelian extensions of global fields","version":2},"cited_work":{"arxiv_id":"2607.16079","doi":null,"metadata_source":"pith","pith_arxiv_id":"2607.16079","snapshot_observed_at":"2026-08-15T15:51:24.604326Z","title":"Equidistribution for abelian extensions of global fields","venue":"math.NT","work_id":"09d6ab95-203f-45d8-be22-d0ce7a0635b8","year":2026},"citing_paper":{"arxiv_id":"2607.27364","last_updated":"2026-07-29T18:15:36Z","snapshot_observed_at":"2026-08-18T16:24:24.139561Z","submitted_at":"2026-07-29T18:15:36Z","title":"Multivariate counting of wild abelian extensions","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-15T15:51:24.376005Z"},"links":{"cited_paper":"/paper/2607.16079","citing_paper":"/paper/2607.27364"},"observation_digest":"sha256:a127c09a92768a067d8cb6bbdcd58163bf38299c3e16c1b8fefda435db214e2a","observation_id":"1e94854a-7e8c-475e-82d7-f043ad05edba","resolution":{"observed_at":"2026-08-15T15:51:24.613443Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+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":"2026-08-15T15:51:24.384362Z","title":"Distribution of A rtin- S chreier extensions","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2607.27364","last_updated":"2026-07-29T18:15:36Z","snapshot_observed_at":"2026-08-18T16:24:24.139561Z","submitted_at":"2026-07-29T18:15:36Z","title":"Multivariate counting of wild abelian extensions","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-15T15:51:24.384362Z"},"links":{"citing_paper":"/paper/2607.27364"},"observation_digest":"sha256:b13a22a51adb178b29a56121ffa149f1082f3548e3489d8f489ba1a3c4dee4aa","observation_id":"00e00581-3c80-4c1f-a19e-e30f9c5068ec","resolution":{"observed_at":"2026-08-15T15:51:24.384362Z","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":"2026-08-15T15:51:24.391029Z","title":"Distribution of A rtin- S chreier- W itt extensions","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.27364","last_updated":"2026-07-29T18:15:36Z","snapshot_observed_at":"2026-08-18T16:24:24.139561Z","submitted_at":"2026-07-29T18:15:36Z","title":"Multivariate counting of wild abelian extensions","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-15T15:51:24.391029Z"},"links":{"citing_paper":"/paper/2607.27364"},"observation_digest":"sha256:69512cd968f1241616b7e47c3ac4684b83f1f710b4a0d80085386f99715d3923","observation_id":"8b01991b-1058-4ed9-8fc4-596d8587cfc6","resolution":{"observed_at":"2026-08-15T15:51:24.391029Z","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":"2026-08-15T15:51:24.396393Z","title":"Commutative ring theory , volume 8 of Cambridge Studies in Advanced Mathematics","venue":null,"work_id":null,"year":1986},"citing_paper":{"arxiv_id":"2607.27364","last_updated":"2026-07-29T18:15:36Z","snapshot_observed_at":"2026-08-18T16:24:24.139561Z","submitted_at":"2026-07-29T18:15:36Z","title":"Multivariate counting of wild abelian extensions","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-15T15:51:24.396393Z"},"links":{"citing_paper":"/paper/2607.27364"},"observation_digest":"sha256:ec6c660cc108cb981b8df3e78786078e901db855bde5f468df416d4dd40b1d25","observation_id":"8ec50d6e-45b6-4062-8ef1-fe6ceee34d76","resolution":{"observed_at":"2026-08-15T15:51:24.396393Z","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":"2026-08-15T15:51:24.401967Z","title":"On the asymptotics of elementary-abelian extensions of local and global function fields","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.27364","last_updated":"2026-07-29T18:15:36Z","snapshot_observed_at":"2026-08-18T16:24:24.139561Z","submitted_at":"2026-07-29T18:15:36Z","title":"Multivariate counting of wild abelian extensions","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-15T15:51:24.401967Z"},"links":{"citing_paper":"/paper/2607.27364"},"observation_digest":"sha256:2b563b56d6089bf041bdac46300021e32592e5cdb81c3d8d85793254fe662755","observation_id":"e6e66eec-9917-40fd-a763-5a8909422a74","resolution":{"observed_at":"2026-08-15T15:51:24.401967Z","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":"2026-08-15T15:51:24.409171Z","title":"The stacks project","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.27364","last_updated":"2026-07-29T18:15:36Z","snapshot_observed_at":"2026-08-18T16:24:24.139561Z","submitted_at":"2026-07-29T18:15:36Z","title":"Multivariate counting of wild abelian extensions","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-15T15:51:24.409171Z"},"links":{"citing_paper":"/paper/2607.27364"},"observation_digest":"sha256:597aa9a766f4b040ec331c33d1374bce8573325140b1dad17a43a40c5365b34f","observation_id":"40f60b89-b20c-4ce0-bc7e-4c85006367c5","resolution":{"observed_at":"2026-08-15T15:51:24.409171Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.00448","last_updated":"2025-07-01T06:00:49Z","snapshot_observed_at":"2026-08-20T03:11:41.214893Z","submitted_at":"2025-07-01T06:00:49Z","title":"Counting abelian number fields with restricted ramification type","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.00448","snapshot_observed_at":"2026-08-15T15:51:24.416452Z","title":"Counting abelian number fields with restricted ramification type, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.27364","last_updated":"2026-07-29T18:15:36Z","snapshot_observed_at":"2026-08-18T16:24:24.139561Z","submitted_at":"2026-07-29T18:15:36Z","title":"Multivariate counting of wild abelian extensions","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-15T15:51:24.416452Z"},"links":{"cited_paper":"/paper/2507.00448","citing_paper":"/paper/2607.27364"},"observation_digest":"sha256:e80b3514d3084a827355269c5e834f470390736d15f186f414ae4b4e5ada820e","observation_id":"3c02861b-ba19-4b74-bffd-c9a83bac9ce2","resolution":{"observed_at":"2026-08-15T15:51:24.416452Z","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":"2026-08-15T15:51:24.422709Z","title":"On the probabilities of local behaviors in abelian field extensions","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.27364","last_updated":"2026-07-29T18:15:36Z","snapshot_observed_at":"2026-08-18T16:24:24.139561Z","submitted_at":"2026-07-29T18:15:36Z","title":"Multivariate counting of wild abelian extensions","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-15T15:51:24.422709Z"},"links":{"citing_paper":"/paper/2607.27364"},"observation_digest":"sha256:4ee044881025460c0ccd8c1daeac233a7d4787c3594536cdd5452f47274b575f","observation_id":"88ecfa04-5b35-4cb8-8352-bc15f6d47859","resolution":{"observed_at":"2026-08-15T15:51:24.422709Z","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":"2026-08-15T15:51:24.429166Z","title":null,"venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2607.27364","last_updated":"2026-07-29T18:15:36Z","snapshot_observed_at":"2026-08-18T16:24:24.139561Z","submitted_at":"2026-07-29T18:15:36Z","title":"Multivariate counting of wild abelian extensions","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-15T15:51:24.429166Z"},"links":{"citing_paper":"/paper/2607.27364"},"observation_digest":"sha256:94b9b1f859ffc48b95e2edc22077a069faf5f566aa648ef9adcf4fe36af3ca1b","observation_id":"9cf714cb-23c6-4fa6-8921-6c585e27a4c3","resolution":{"observed_at":"2026-08-15T15:51:24.429166Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.27364","last_updated":"2026-07-29T18:15:36Z","latest_version":1,"primary_category":"math.NT","snapshot_observed_at":"2026-08-18T16:24:24.139561Z","submitted_at":"2026-07-29T18:15:36Z","title":"Multivariate counting of wild abelian extensions"},"reference_resolution":{"displayed":15,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":11,"verified_exact":4,"verified_fuzzy":0},"total_outbound_references":15},"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":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"thesis":"As of 20 August 2026, this Paper Citation Record lists 15 of 15 outbound references and 0 inbound Pith citation observations for arXiv:2607.27364."}