{"as_of":"2026-08-16T21:07:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:33f09c2160baaa5ff86a61ebfcd7b75ac5ca970c417b9cde87932bd6a4cf4648","coverage":[{"denominator":13,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":13,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T14:59:06.191152Z","state":"measured"},{"denominator":13,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":13,"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/1908.02394/citation-record","integrity":"/paper/1908.02394/integrity","json":"/paper/1908.02394/citation-record.json","paper":"/paper/1908.02394"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T14:59:06.623183Z","title":null,"venue":null,"work_id":"384d4018-df99-48c3-87b8-e9d806bf9eb3","year":1995},"citing_paper":{"arxiv_id":"1908.02394","last_updated":"2019-10-03T17:03:15Z","snapshot_observed_at":"2026-08-16T10:45:34.102599Z","submitted_at":"2019-08-06T22:56:32Z","title":"An Unconditional Improvement to the Running Time of the Quadratic Frobenius Test","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T14:59:06.075788Z"},"links":{"citing_paper":"/paper/1908.02394"},"observation_digest":"sha256:9bcabe3744a63c677a8b3c67ffdce89f9fb060a356283fb1b552e2e66c445a37","observation_id":"87d3e1d2-d068-48dd-a470-a62bd7fea9b8","resolution":{"observed_at":"2026-08-14T14:59:06.631901Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T14:59:06.594180Z","title":"Baillie and S","venue":null,"work_id":"10d26d19-841b-4007-b33d-06af92d6ef0a","year":1980},"citing_paper":{"arxiv_id":"1908.02394","last_updated":"2019-10-03T17:03:15Z","snapshot_observed_at":"2026-08-16T10:45:34.102599Z","submitted_at":"2019-08-06T22:56:32Z","title":"An Unconditional Improvement to the Running Time of the Quadratic Frobenius Test","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T14:59:06.083792Z"},"links":{"citing_paper":"/paper/1908.02394"},"observation_digest":"sha256:31ff62764f35f44df4a1e9c941fc2dce2e62a16f2252d476e42e21d6e770d990","observation_id":"16090430-b114-4eba-b80d-e365693a3889","resolution":{"observed_at":"2026-08-14T14:59:06.603707Z","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":"2026-08-14T14:59:06.573062Z","title":null,"venue":null,"work_id":"1097a521-59f2-4817-b199-c2c0cb561bf7","year":2008},"citing_paper":{"arxiv_id":"1908.02394","last_updated":"2019-10-03T17:03:15Z","snapshot_observed_at":"2026-08-16T10:45:34.102599Z","submitted_at":"2019-08-06T22:56:32Z","title":"An Unconditional Improvement to the Running Time of the Quadratic Frobenius Test","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T14:59:06.092151Z"},"links":{"citing_paper":"/paper/1908.02394"},"observation_digest":"sha256:be9b6251521968ca1b9cb4b3ddd7482837c1830386cec5a6acb0ee7d8eb9f90b","observation_id":"448f6e8f-daae-4fdf-bc76-83c9e836f772","resolution":{"observed_at":"2026-08-14T14:59:06.579869Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T14:59:06.542622Z","title":null,"venue":null,"work_id":"dffbb290-8b7a-42b4-be63-f75e8293a393","year":1986},"citing_paper":{"arxiv_id":"1908.02394","last_updated":"2019-10-03T17:03:15Z","snapshot_observed_at":"2026-08-16T10:45:34.102599Z","submitted_at":"2019-08-06T22:56:32Z","title":"An Unconditional Improvement to the Running Time of the Quadratic Frobenius Test","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T14:59:06.099419Z"},"links":{"citing_paper":"/paper/1908.02394"},"observation_digest":"sha256:20c5745caa3b16583a92d9adf2d2fe9f7a6ffa0b43f785008399c9dc882dbbb1","observation_id":"675cda3b-8b9f-4aed-9729-54825c03cf71","resolution":{"observed_at":"2026-08-14T14:59:06.550711Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T14:59:06.518910Z","title":null,"venue":null,"work_id":"a117659f-b571-47b6-a2d1-7a733293238e","year":2006},"citing_paper":{"arxiv_id":"1908.02394","last_updated":"2019-10-03T17:03:15Z","snapshot_observed_at":"2026-08-16T10:45:34.102599Z","submitted_at":"2019-08-06T22:56:32Z","title":"An Unconditional Improvement to the Running Time of the Quadratic Frobenius Test","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T14:59:06.105249Z"},"links":{"citing_paper":"/paper/1908.02394"},"observation_digest":"sha256:f07fe2d7e3d108ccc116da0939ac371f37eab0e6dee2b45b056886787078a485","observation_id":"5721274b-842f-4032-9b83-4976f1583db4","resolution":{"observed_at":"2026-08-14T14:59:06.525401Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T14:59:06.488725Z","title":"Grantham, A probable prime test with high confidence, J","venue":null,"work_id":"560df48d-8d9c-4b36-9266-4d4c243cb40c","year":1998},"citing_paper":{"arxiv_id":"1908.02394","last_updated":"2019-10-03T17:03:15Z","snapshot_observed_at":"2026-08-16T10:45:34.102599Z","submitted_at":"2019-08-06T22:56:32Z","title":"An Unconditional Improvement to the Running Time of the Quadratic Frobenius Test","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T14:59:06.116318Z"},"links":{"citing_paper":"/paper/1908.02394"},"observation_digest":"sha256:ab7d5ae21aaa1a29431f782fb38ded516fb4a878b5673be70e019e06b84f6bac","observation_id":"35abfc55-f3ea-4187-b1d8-09458a19c9a6","resolution":{"observed_at":"2026-08-14T14:59:06.501397Z","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":"2026-08-14T14:59:06.461025Z","title":"Granville and K","venue":null,"work_id":"cc5563f5-1d88-4e50-98be-d75751f828c3","year":2018},"citing_paper":{"arxiv_id":"1908.02394","last_updated":"2019-10-03T17:03:15Z","snapshot_observed_at":"2026-08-16T10:45:34.102599Z","submitted_at":"2019-08-06T22:56:32Z","title":"An Unconditional Improvement to the Running Time of the Quadratic Frobenius Test","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T14:59:06.125729Z"},"links":{"citing_paper":"/paper/1908.02394"},"observation_digest":"sha256:fd44436cb5b5e21a2a89ca550320cf86ee41439b61c765e8fcb11e4a7ad5ea7c","observation_id":"d29cc13a-203c-4296-81ac-18cc5c20b0ee","resolution":{"observed_at":"2026-08-14T14:59:06.467457Z","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":"2026-08-14T14:59:06.429047Z","title":"Monier, Evaluation and comparison of two efficient probabilistic p rimal- ity testing algorithms, Theoret","venue":null,"work_id":"63f93f99-3028-4cf7-bf4c-9bdc20937ccf","year":1980},"citing_paper":{"arxiv_id":"1908.02394","last_updated":"2019-10-03T17:03:15Z","snapshot_observed_at":"2026-08-16T10:45:34.102599Z","submitted_at":"2019-08-06T22:56:32Z","title":"An Unconditional Improvement to the Running Time of the Quadratic Frobenius Test","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T14:59:06.136405Z"},"links":{"citing_paper":"/paper/1908.02394"},"observation_digest":"sha256:6187d6cfa9599e363c7f4830039bd691a2c1c323bcc4f3e5900df5b18875ccb9","observation_id":"8e6b3f07-ba48-4a0b-b569-e1038a9ef94f","resolution":{"observed_at":"2026-08-14T14:59:06.438169Z","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":"2026-08-14T14:59:06.394608Z","title":"M¨ uller, A probable prime test with very high confidence for n ≡ 1 mod 4, in Advances in cryptology—ASIACRYPT 2001 (Gold Coast) , Lecture Notes in Comput","venue":null,"work_id":"a9274884-f847-4624-88d6-52a038aaae44","year":2001},"citing_paper":{"arxiv_id":"1908.02394","last_updated":"2019-10-03T17:03:15Z","snapshot_observed_at":"2026-08-16T10:45:34.102599Z","submitted_at":"2019-08-06T22:56:32Z","title":"An Unconditional Improvement to the Running Time of the Quadratic Frobenius Test","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T14:59:06.152229Z"},"links":{"citing_paper":"/paper/1908.02394"},"observation_digest":"sha256:b352fc1a4da66d9b7e1c41b0e56efd7d0065564bae62f492aee30c9e99f24047","observation_id":"4d4a56ac-7eef-4e55-9cef-711be92e275c","resolution":{"observed_at":"2026-08-14T14:59:06.406046Z","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":"2026-08-14T14:59:06.360981Z","title":"Cryptology 16 (2003) 117–139","venue":null,"work_id":"d85d01a0-e9d3-4248-ad58-29c3adfc0f52","year":2003},"citing_paper":{"arxiv_id":"1908.02394","last_updated":"2019-10-03T17:03:15Z","snapshot_observed_at":"2026-08-16T10:45:34.102599Z","submitted_at":"2019-08-06T22:56:32Z","title":"An Unconditional Improvement to the Running Time of the Quadratic Frobenius Test","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T14:59:06.166455Z"},"links":{"citing_paper":"/paper/1908.02394"},"observation_digest":"sha256:7f3b89433fdc854f554ad8ac85a36c64a76e3e5889caf3275bb39bc7ca2eca0a","observation_id":"c9eccec5-3d96-4414-b220-9452d37163f2","resolution":{"observed_at":"2026-08-14T14:59:06.368558Z","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":"2026-08-14T14:59:06.318926Z","title":"Pomerance, J","venue":null,"work_id":"c561fcaa-3c65-40fb-b1c7-e4af473d2e4b","year":1980},"citing_paper":{"arxiv_id":"1908.02394","last_updated":"2019-10-03T17:03:15Z","snapshot_observed_at":"2026-08-16T10:45:34.102599Z","submitted_at":"2019-08-06T22:56:32Z","title":"An Unconditional Improvement to the Running Time of the Quadratic Frobenius Test","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T14:59:06.174031Z"},"links":{"citing_paper":"/paper/1908.02394"},"observation_digest":"sha256:12139ff0585b89438d3a662313e0b1688b30d66113cd0c11990b5ca1873f3a29","observation_id":"1c85b0bc-6fd3-47ce-a16b-190197174643","resolution":{"observed_at":"2026-08-14T14:59:06.328344Z","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":"2026-08-14T14:59:06.283394Z","title":null,"venue":null,"work_id":"e7f707fa-5ff9-49de-b704-ae46d2908d70","year":1980},"citing_paper":{"arxiv_id":"1908.02394","last_updated":"2019-10-03T17:03:15Z","snapshot_observed_at":"2026-08-16T10:45:34.102599Z","submitted_at":"2019-08-06T22:56:32Z","title":"An Unconditional Improvement to the Running Time of the Quadratic Frobenius Test","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T14:59:06.182962Z"},"links":{"citing_paper":"/paper/1908.02394"},"observation_digest":"sha256:35640073bb70fe0f68808229bfbc4a0224bf5d74c147b740a8f83126ff8cb2ab","observation_id":"1fad5cdc-16c5-4093-ad0e-96cf3f80e2c1","resolution":{"observed_at":"2026-08-14T14:59:06.294408Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T14:59:06.245930Z","title":"Zhang, A one-parameter quadratic-base version of the Ba illie-PSW prob- able prime test, Math","venue":null,"work_id":"d6507e32-668b-4302-8051-0ef637b9bf43","year":2002},"citing_paper":{"arxiv_id":"1908.02394","last_updated":"2019-10-03T17:03:15Z","snapshot_observed_at":"2026-08-16T10:45:34.102599Z","submitted_at":"2019-08-06T22:56:32Z","title":"An Unconditional Improvement to the Running Time of the Quadratic Frobenius Test","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T14:59:06.191152Z"},"links":{"citing_paper":"/paper/1908.02394"},"observation_digest":"sha256:57ee8bc77a4fa1f25e12cc499ba784cdcace037690e012bc976ce6319a38289f","observation_id":"6d588566-fc33-4027-9213-3f97aa4b31f8","resolution":{"observed_at":"2026-08-14T14:59:06.263361Z","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":"1908.02394","last_updated":"2019-10-03T17:03:15Z","latest_version":2,"primary_category":"math.NT","snapshot_observed_at":"2026-08-16T10:45:34.102599Z","submitted_at":"2019-08-06T22:56:32Z","title":"An Unconditional Improvement to the Running Time of the Quadratic Frobenius Test"},"reference_resolution":{"displayed":13,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":0,"verified_fuzzy":8},"total_outbound_references":13},"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 13 of 13 outbound references and 0 inbound Pith citation observations for arXiv:1908.02394."}