{"as_of":"2026-08-14T07:26:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:2549908c80a797310d08c032dca69572d3c8929cac510afd2876b59fe4c5c415","coverage":[{"denominator":23,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":23,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T16:31:14.000446Z","state":"measured"},{"denominator":23,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":23,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+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/2411.13486/citation-record","integrity":"/paper/2411.13486/integrity","json":"/paper/2411.13486/citation-record.json","paper":"/paper/2411.13486"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T16:31:15.040131Z","title":"Krygin, An example of a cylindrical cascade with ano malous metric properties, Moscow State University Bulletin, ser","venue":null,"work_id":"c3392646-b5b8-4a37-865d-dd549123ba47","year":1975},"citing_paper":{"arxiv_id":"2411.13486","last_updated":"2024-12-04T11:26:14Z","snapshot_observed_at":"2026-08-13T05:56:45.036993Z","submitted_at":"2024-11-20T17:35:26Z","title":"Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-12T16:31:13.761447Z"},"links":{"citing_paper":"/paper/2411.13486"},"observation_digest":"sha256:fb0eda9b0c08828b0f07a61ff5e540d865ccdb756da9e89f51a05192f462907c","observation_id":"808fe95a-cbe5-47f6-932e-b903ec363922","resolution":{"observed_at":"2026-08-12T16:31:15.047369Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T16:31:14.982359Z","title":"Shneiberg, Zeros of integrals along trajectories of ergodic systems, Funct","venue":null,"work_id":"7fc28602-e86e-42ab-918f-d12f265419ed","year":1985},"citing_paper":{"arxiv_id":"2411.13486","last_updated":"2024-12-04T11:26:14Z","snapshot_observed_at":"2026-08-13T05:56:45.036993Z","submitted_at":"2024-11-20T17:35:26Z","title":"Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-12T16:31:13.783065Z"},"links":{"citing_paper":"/paper/2411.13486"},"observation_digest":"sha256:8d72ccb12829867ef4d65fc7656f661ce15a13d5b8bc427175e84c94fa86359a","observation_id":"c8729cbf-f817-42fa-a332-80aa52d49260","resolution":{"observed_at":"2026-08-12T16:31:14.990190Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T16:31:14.943579Z","title":null,"venue":null,"work_id":"1c468f6c-6076-45f8-b6b6-efec259cf94e","year":2023},"citing_paper":{"arxiv_id":"2411.13486","last_updated":"2024-12-04T11:26:14Z","snapshot_observed_at":"2026-08-13T05:56:45.036993Z","submitted_at":"2024-11-20T17:35:26Z","title":"Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-12T16:31:13.792391Z"},"links":{"citing_paper":"/paper/2411.13486"},"observation_digest":"sha256:279f7acb2a58a0af75ce9bbf6f68a1e77e92e529580eb4a8c0003e82e48b6fc7","observation_id":"a3d0e799-924e-422f-bb58-e71c1d70f025","resolution":{"observed_at":"2026-08-12T16:31:14.954296Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T16:31:14.907910Z","title":"Ryzhikov, Recurrence of integral zeros on trajecto ries of ergodic ﬂow","venue":null,"work_id":"f486cfd2-221c-462d-a1f3-61c56c98e280","year":2024},"citing_paper":{"arxiv_id":"2411.13486","last_updated":"2024-12-04T11:26:14Z","snapshot_observed_at":"2026-08-13T05:56:45.036993Z","submitted_at":"2024-11-20T17:35:26Z","title":"Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-12T16:31:13.801554Z"},"links":{"citing_paper":"/paper/2411.13486"},"observation_digest":"sha256:4de297b48250250d22486e35493300d6ecf9634cea3451db2402a83ea639cb0a","observation_id":"7c6844d7-5fb5-4450-88da-d1202c700889","resolution":{"observed_at":"2026-08-12T16:31:14.915590Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T16:31:14.871118Z","title":"Moshchevitin, Recurrence of the integral of a smoot h three-frequency conditionally periodic function, Math","venue":null,"work_id":"ea9d02db-5ea3-48d2-a23a-2371f82832e1","year":1995},"citing_paper":{"arxiv_id":"2411.13486","last_updated":"2024-12-04T11:26:14Z","snapshot_observed_at":"2026-08-13T05:56:45.036993Z","submitted_at":"2024-11-20T17:35:26Z","title":"Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-12T16:31:13.812873Z"},"links":{"citing_paper":"/paper/2411.13486"},"observation_digest":"sha256:7670de9c8e540f04f489e7419b3ecb36da5b06d9ea0fc00f550b62390bbe3186","observation_id":"31ea0d43-a399-41b6-a151-343b2c594c55","resolution":{"observed_at":"2026-08-12T16:31:14.882837Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T16:31:14.849964Z","title":"Konyagin, Recurrence of the integral of an odd condi tionally periodic function, Math","venue":null,"work_id":"458d85b5-da05-4efe-a51b-a9ddb0e628c9","year":1997},"citing_paper":{"arxiv_id":"2411.13486","last_updated":"2024-12-04T11:26:14Z","snapshot_observed_at":"2026-08-13T05:56:45.036993Z","submitted_at":"2024-11-20T17:35:26Z","title":"Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-12T16:31:13.819927Z"},"links":{"citing_paper":"/paper/2411.13486"},"observation_digest":"sha256:ce0e2bcb54c75bf38d512f32648cf477c9b3140e1d7416f1220024c7bd3bc7cb","observation_id":"bc3a0da8-063f-4e28-83f1-61f1cb8a1571","resolution":{"observed_at":"2026-08-12T16:31:14.857507Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T16:31:14.812992Z","title":null,"venue":null,"work_id":"0cc83806-5860-4d6d-a4a9-163f3fe39047","year":2000},"citing_paper":{"arxiv_id":"2411.13486","last_updated":"2024-12-04T11:26:14Z","snapshot_observed_at":"2026-08-13T05:56:45.036993Z","submitted_at":"2024-11-20T17:35:26Z","title":"Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-12T16:31:13.828861Z"},"links":{"citing_paper":"/paper/2411.13486"},"observation_digest":"sha256:ddc8b0a81e654b49af07f1238b92ce5e26a7d5711eccc5e6706c33288fb79bce","observation_id":"0a23dcbe-fc42-41da-92d0-1059c37c96fc","resolution":{"observed_at":"2026-08-12T16:31:14.831773Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T16:31:14.774857Z","title":"Kochergin, On the Growth of Birkhoﬀ Sums over a Rotat ion of the Circle, Math","venue":null,"work_id":"b29f6bd6-fb36-4c3e-b8f5-45050aced6f7","year":2023},"citing_paper":{"arxiv_id":"2411.13486","last_updated":"2024-12-04T11:26:14Z","snapshot_observed_at":"2026-08-13T05:56:45.036993Z","submitted_at":"2024-11-20T17:35:26Z","title":"Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-12T16:31:13.840138Z"},"links":{"citing_paper":"/paper/2411.13486"},"observation_digest":"sha256:da196ae046dc69176ebf5c11c4f4dbb72e46668f7949e996be6ad6b9e31afa5b","observation_id":"5912365b-4666-41ef-af3a-a9eafd730ce6","resolution":{"observed_at":"2026-08-12T16:31:14.781140Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T16:31:14.740115Z","title":"Ryzhikov, Polymorphisms, joinings, and the tenso r simplicity of dynamical systems, Funct","venue":null,"work_id":"fac2abe4-37f8-483e-b15b-a2900182ea32","year":1997},"citing_paper":{"arxiv_id":"2411.13486","last_updated":"2024-12-04T11:26:14Z","snapshot_observed_at":"2026-08-13T05:56:45.036993Z","submitted_at":"2024-11-20T17:35:26Z","title":"Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-12T16:31:13.856145Z"},"links":{"citing_paper":"/paper/2411.13486"},"observation_digest":"sha256:aecbe53078dbc894ca38234d4eb50b61c0152295a2c8cb6b25ea21b509cbbd80","observation_id":"7d160dd8-a2a1-4609-91c6-2b7d2434a0fa","resolution":{"observed_at":"2026-08-12T16:31:14.748869Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T16:31:14.702945Z","title":"Ryzhikov, Self-joinings and generic extensions o f ergodic systems, Funct","venue":null,"work_id":"5e9f8ee6-61f0-42e8-934a-f32ff2401661","year":2023},"citing_paper":{"arxiv_id":"2411.13486","last_updated":"2024-12-04T11:26:14Z","snapshot_observed_at":"2026-08-13T05:56:45.036993Z","submitted_at":"2024-11-20T17:35:26Z","title":"Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-12T16:31:13.867561Z"},"links":{"citing_paper":"/paper/2411.13486"},"observation_digest":"sha256:dc06b32ce5decb230f88ba7028396d7d56d00ca1bc8228065a70fffe3796a902","observation_id":"a5bbb63d-a32b-471f-a3cd-afd414ddc59a","resolution":{"observed_at":"2026-08-12T16:31:14.712732Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"0342.60049","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T16:31:14.279115Z","title":"Weiss, Single orbit dynamics","venue":null,"work_id":"55deb8d7-a363-46d1-9063-4286adca5d73","year":2000},"citing_paper":{"arxiv_id":"2411.13486","last_updated":"2024-12-04T11:26:14Z","snapshot_observed_at":"2026-08-13T05:56:45.036993Z","submitted_at":"2024-11-20T17:35:26Z","title":"Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-12T16:31:13.882533Z"},"links":{"citing_paper":"/paper/2411.13486"},"observation_digest":"sha256:efe806532720f5e7eac4d1ff4f78e548754a2773a468327dfae6edc8a307a956","observation_id":"cc292d43-6cab-439c-bfff-1ffb6af9f437","resolution":{"observed_at":"2026-08-12T16:31:14.302439Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T16:31:14.667221Z","title":"Krygin, An example of a cylindrical cascade with ano malous metric properties, Moscow State University Bulletin, ser","venue":null,"work_id":"04c167ab-019d-4a3f-8e44-7005acd24b3a","year":1975},"citing_paper":{"arxiv_id":"2411.13486","last_updated":"2024-12-04T11:26:14Z","snapshot_observed_at":"2026-08-13T05:56:45.036993Z","submitted_at":"2024-11-20T17:35:26Z","title":"Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-12T16:31:13.897436Z"},"links":{"citing_paper":"/paper/2411.13486"},"observation_digest":"sha256:793327ca9d1576ed58739ef5c66fe6e9f9804a4757a775937bc2f343df072413","observation_id":"1bbddfcb-2bc6-4256-bcc7-d565a939f258","resolution":{"observed_at":"2026-08-12T16:31:14.676182Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T16:31:13.905470Z","title":"Atkinson, Reccurence of co-cycles and random walks, J","venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2411.13486","last_updated":"2024-12-04T11:26:14Z","snapshot_observed_at":"2026-08-13T05:56:45.036993Z","submitted_at":"2024-11-20T17:35:26Z","title":"Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-12T16:31:13.905470Z"},"links":{"citing_paper":"/paper/2411.13486"},"observation_digest":"sha256:fc8e9b6853c78ea4ce7c575626a20e6f567a3356b1eefa841b98047b9d83fea8","observation_id":"0a20c635-f52a-4064-87a5-b7ceb98a4c53","resolution":{"observed_at":"2026-08-12T16:31:13.905470Z","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":"2026-08-12T16:31:14.638487Z","title":"Shneiberg, Zeros of integrals along trajectories of ergodic systems, Funct","venue":null,"work_id":"e1768042-b2da-4237-8cd0-7d74c5c4206c","year":1985},"citing_paper":{"arxiv_id":"2411.13486","last_updated":"2024-12-04T11:26:14Z","snapshot_observed_at":"2026-08-13T05:56:45.036993Z","submitted_at":"2024-11-20T17:35:26Z","title":"Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-12T16:31:13.912561Z"},"links":{"citing_paper":"/paper/2411.13486"},"observation_digest":"sha256:c2befffdd802602915d1548b14de7f9395a9f9e48b4879df74ed01964b5f37a1","observation_id":"48dbd095-b5b2-4e3f-a390-f84433181eb8","resolution":{"observed_at":"2026-08-12T16:31:14.646408Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T16:31:14.599927Z","title":null,"venue":null,"work_id":"56e12724-8dcd-4819-a430-54690b5dbd60","year":2023},"citing_paper":{"arxiv_id":"2411.13486","last_updated":"2024-12-04T11:26:14Z","snapshot_observed_at":"2026-08-13T05:56:45.036993Z","submitted_at":"2024-11-20T17:35:26Z","title":"Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-12T16:31:13.922890Z"},"links":{"citing_paper":"/paper/2411.13486"},"observation_digest":"sha256:71b43ac70c820264f7c464e48ce1e619bf01889e0007147eb7ef1079bd30d8e0","observation_id":"b4a09b6d-b5c5-4494-bedc-8e06da209d21","resolution":{"observed_at":"2026-08-12T16:31:14.611287Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T16:31:14.562423Z","title":"Ryzhikov, Recurrence of integral zeros on trajecto ries of ergodic ﬂow","venue":null,"work_id":"3795b1dc-f5b7-456c-8fb8-f028ab59072b","year":2024},"citing_paper":{"arxiv_id":"2411.13486","last_updated":"2024-12-04T11:26:14Z","snapshot_observed_at":"2026-08-13T05:56:45.036993Z","submitted_at":"2024-11-20T17:35:26Z","title":"Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-12T16:31:13.932447Z"},"links":{"citing_paper":"/paper/2411.13486"},"observation_digest":"sha256:c74874cff3ea913c789b8f444035a3512973a765260c4ff8cfa3ba1dc63a4632","observation_id":"112042a6-4f1c-4173-9051-e60d7ecffea9","resolution":{"observed_at":"2026-08-12T16:31:14.569843Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T16:31:14.536528Z","title":"Мощевитин, О возвращаемости интеграла гладкой тре хчастотной условнопериодической функции, Матем","venue":null,"work_id":"9eda0ced-c98c-4e93-9a02-d5ac8d7c22d3","year":1995},"citing_paper":{"arxiv_id":"2411.13486","last_updated":"2024-12-04T11:26:14Z","snapshot_observed_at":"2026-08-13T05:56:45.036993Z","submitted_at":"2024-11-20T17:35:26Z","title":"Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-12T16:31:13.945395Z"},"links":{"citing_paper":"/paper/2411.13486"},"observation_digest":"sha256:628a283de006859830d7578f87bfab7666833e92a52134baa79701a7677c8d2e","observation_id":"f2b1f63d-ab6b-4cec-a1b9-217962b0281c","resolution":{"observed_at":"2026-08-12T16:31:14.545438Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T16:31:14.499212Z","title":"Конягин, О возвращаемости интеграла нечетной усло внопериодической функции, Матем","venue":null,"work_id":"d94da6d2-0220-435e-b731-48da49177890","year":1997},"citing_paper":{"arxiv_id":"2411.13486","last_updated":"2024-12-04T11:26:14Z","snapshot_observed_at":"2026-08-13T05:56:45.036993Z","submitted_at":"2024-11-20T17:35:26Z","title":"Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-12T16:31:13.953652Z"},"links":{"citing_paper":"/paper/2411.13486"},"observation_digest":"sha256:b01180d893ad201eac679c0319ebec00e71e48c5465b558441150ffbe9c0cb9e","observation_id":"52be4cdb-e75d-4f25-9ff3-eb2b69674769","resolution":{"observed_at":"2026-08-12T16:31:14.512960Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T16:31:14.444338Z","title":"Козлов, Методы качественного анализа в динамике тв ердого тела, РХД, Ижевск, 2000 V","venue":null,"work_id":"9ddddae2-4135-461f-88e8-396c97496607","year":2000},"citing_paper":{"arxiv_id":"2411.13486","last_updated":"2024-12-04T11:26:14Z","snapshot_observed_at":"2026-08-13T05:56:45.036993Z","submitted_at":"2024-11-20T17:35:26Z","title":"Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-12T16:31:13.963047Z"},"links":{"citing_paper":"/paper/2411.13486"},"observation_digest":"sha256:f0815eaf39437324c3f8e60faec7928d99c1fd06b73ec426e9319f81069a846b","observation_id":"fb0903bc-ed70-4fa0-9c0b-52629a44a808","resolution":{"observed_at":"2026-08-12T16:31:14.466671Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T16:31:14.409009Z","title":"Кочергин, О росте сумм Биркгофа над поворотом окруж ности, Матем","venue":null,"work_id":"afd07f2e-badf-4ab0-9f6e-e8a7e1828ddf","year":2023},"citing_paper":{"arxiv_id":"2411.13486","last_updated":"2024-12-04T11:26:14Z","snapshot_observed_at":"2026-08-13T05:56:45.036993Z","submitted_at":"2024-11-20T17:35:26Z","title":"Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-12T16:31:13.973068Z"},"links":{"citing_paper":"/paper/2411.13486"},"observation_digest":"sha256:689a8eda73fa57fb7c7b20ff77bad44f0beda7d441ffbae5907c3e8c88a8d0be","observation_id":"191eedc9-6057-43e2-b0ea-a33834c8d125","resolution":{"observed_at":"2026-08-12T16:31:14.415340Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T16:31:14.382602Z","title":null,"venue":null,"work_id":"b7a8e422-3255-4465-b6f7-144e8178f255","year":1997},"citing_paper":{"arxiv_id":"2411.13486","last_updated":"2024-12-04T11:26:14Z","snapshot_observed_at":"2026-08-13T05:56:45.036993Z","submitted_at":"2024-11-20T17:35:26Z","title":"Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-12T16:31:13.981081Z"},"links":{"citing_paper":"/paper/2411.13486"},"observation_digest":"sha256:1a6774aaa8bca51f1290604fe2b17e332df760a9bfb32f47f140644c3c8b0e53","observation_id":"e631d319-9a7d-4574-9761-46fe5e273be0","resolution":{"observed_at":"2026-08-12T16:31:14.388753Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T16:31:14.349109Z","title":"Ryzhikov, Self-joinings and generic extensions o f ergodic systems, Funct","venue":null,"work_id":"85cb7a02-e05c-4b40-9ff6-c36bb2b9992c","year":2023},"citing_paper":{"arxiv_id":"2411.13486","last_updated":"2024-12-04T11:26:14Z","snapshot_observed_at":"2026-08-13T05:56:45.036993Z","submitted_at":"2024-11-20T17:35:26Z","title":"Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-12T16:31:13.993003Z"},"links":{"citing_paper":"/paper/2411.13486"},"observation_digest":"sha256:613d3b2f2fd901df415b4437db226401b7096eb39600d0850bdbcb567b50768a","observation_id":"486afcad-b470-4998-9263-03205cb91280","resolution":{"observed_at":"2026-08-12T16:31:14.363050Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-12T16:31:14.320590Z","title":"Weiss, Single orbit dynamics","venue":null,"work_id":"6e514e6e-8e0e-4e60-adef-72f4d5b78a76","year":2000},"citing_paper":{"arxiv_id":"2411.13486","last_updated":"2024-12-04T11:26:14Z","snapshot_observed_at":"2026-08-13T05:56:45.036993Z","submitted_at":"2024-11-20T17:35:26Z","title":"Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-12T16:31:14.000446Z"},"links":{"citing_paper":"/paper/2411.13486"},"observation_digest":"sha256:3164d7bcb31db58641c93cc5719c9e0080a7747dbf3a7420488dc5e168450df5","observation_id":"292bdf33-407f-4577-b842-7d3c7b41e9d9","resolution":{"observed_at":"2026-08-12T16:31:14.327048Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2411.13486","last_updated":"2024-12-04T11:26:14Z","latest_version":2,"primary_category":"math.DS","snapshot_observed_at":"2026-08-13T05:56:45.036993Z","submitted_at":"2024-11-20T17:35:26Z","title":"Around Krygin-Atkinson, Shneiberg theorems, the recurrence with zero integrals"},"reference_resolution":{"displayed":23,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":1,"verified_fuzzy":17},"total_outbound_references":23},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 0 inbound Pith citation observations for arXiv:2411.13486."}