{"as_of":"2026-08-13T11:23:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:6cefe99a0563128dcf75a90908cb3bc507b1e9fbd2e587abb705ff78519effca","coverage":[{"denominator":45,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":45,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T15:45:44.124835Z","state":"measured"},{"denominator":45,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":45,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+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/2508.19636/citation-record","integrity":"/paper/2508.19636/integrity","json":"/paper/2508.19636/citation-record.json","paper":"/paper/2508.19636"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.2307/1970053","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Auslander and M","venue":"Annals of Mathematics","work_id":"aa3e7753-1823-4974-a942-35a7f77451d4","year":1957},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:37.644823Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:43098472e568af87e5f82277dc85464d9c10ba9d81eeb8a2837404e86a6a1f02","observation_id":"d78da058-650a-48f0-81e4-5b9790347514","resolution":{"observed_at":"2026-08-05T15:45:46.677101Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T15:45:49.863592Z","title":null,"venue":null,"work_id":"bab5f52b-95fe-46ea-aa94-69ca6d270cee","year":null},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:37.797911Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:c152eba5b9e4eb1c8beb2eb04945bb7030852f568ab04b959dcfa1b1861a22be","observation_id":"9fa41184-5c31-4e64-ba3a-cb841baa67b1","resolution":{"observed_at":"2026-08-05T15:45:49.914846Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T15:45:38.034843Z","title":null,"venue":null,"work_id":null,"year":1969},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:38.034843Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:88adddd62f479a29dd7282415e5de081a000072c400b40beecba28def387b78f","observation_id":"ce498bad-bec1-4ea3-8561-c51a37a90e7e","resolution":{"observed_at":"2026-08-05T15:45:38.034843Z","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":"2026-08-05T15:45:49.696360Z","title":null,"venue":null,"work_id":"2aee0e94-42f1-4dd9-87c8-a46c2f7808e6","year":1966},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:38.302457Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:4b70e4bb25f8ae6c485403fecf020cdcf77c17b0c14ee290b01f90677f415cc3","observation_id":"8224e174-17a9-4214-a735-d90fc3ea16d2","resolution":{"observed_at":"2026-08-05T15:45:49.742782Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T15:45:49.594818Z","title":"Feshchenko","venue":null,"work_id":"d7df03f9-9017-455d-9fe3-359c835f9d73","year":2015},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:38.394874Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:11cbc64d680388af1be186f70499ab91e9fe195628bda13fcdc66c095ed563ec","observation_id":"50facc80-4f19-4c9d-add3-54cdb076059a","resolution":{"observed_at":"2026-08-05T15:45:49.634982Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1804.08966","last_updated":"2018-04-24T11:46:51Z","snapshot_observed_at":"2026-08-13T03:23:28.482473Z","submitted_at":"2018-04-24T11:46:51Z","title":"Deformations of smooth function on $2$-torus whose KR-graph is a tree","version":1},"cited_work":{"arxiv_id":"1804.08966","doi":"10.48550/arxiv.1804.08966","metadata_source":"pith","pith_arxiv_id":"1804.08966","snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Deformations of smooth function on $2$-torus whose KR-graph is a tree","venue":"math.AT","work_id":"7580efd9-e492-42c3-bce4-cf049cbf2cfc","year":2018},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:38.564748Z"},"links":{"cited_paper":"/paper/1804.08966","citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:d0e8c0d5bfc8cc6c8897c9b42f65d51ff24b168884c502efa98c73b8753cbffd","observation_id":"d9cad1fb-2097-4735-9797-c8bc8276e1b3","resolution":{"observed_at":"2026-08-05T15:45:46.495253Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T15:45:49.304870Z","title":"Feshchenko","venue":null,"work_id":"8cb9a5c0-0499-4b7c-aafd-7a5305460083","year":2016},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:38.689521Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:97ed07c4eca59c4c26104e683c6259d21fea77ac025539d8eafc76393e8b4a18","observation_id":"a50bc467-3267-4057-9951-90177eba8b11","resolution":{"observed_at":"2026-08-05T15:45:49.354744Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.15673/tmgc.v12i3.1528","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Feshchenko","venue":"Proceedings of the International Geometry Center","work_id":"3882f0f2-75a4-4807-9beb-8c72329f6982","year":2019},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:38.813129Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:ff63575178efbb064296ef21cf271be425f17739517bfbd9b109474d905e60e0","observation_id":"928a0264-82e2-4207-a7f2-f7d54ad44caa","resolution":{"observed_at":"2026-08-05T15:45:46.398967Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.15673/tmgc.v14i2.2008","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Feshchenko","venue":"Proceedings of the International Geometry Center","work_id":"c5b327d6-b40f-4e74-a1fe-2884d4d4ad6d","year":2021},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:38.965449Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:4f472be9f3055785d7de475da5ae875f746babc828ce5822ba9b7a4d96cb0f30","observation_id":"7affe5a6-deee-47d0-882d-55f7c57cbdef","resolution":{"observed_at":"2026-08-05T15:45:46.368648Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T15:45:49.164853Z","title":"Groups acting on the circle","venue":null,"work_id":"69f862a1-a115-4fe9-a303-e35ece533060","year":2001},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:39.084844Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:36e3a3ff69aa9a24f10123ab5359856204eda08c774cac78282925c8caa7b6d4","observation_id":"bf6da8cb-60e4-4cc3-88b2-c6a76fbfe364","resolution":{"observed_at":"2026-08-05T15:45:49.204745Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0711.4859","last_updated":"2008-02-19T16:04:03Z","snapshot_observed_at":"2026-07-06T01:32:55.493041Z","submitted_at":"2007-11-30T02:43:15Z","title":"Higher string topology operations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0711.4859","snapshot_observed_at":"2026-08-05T15:45:39.176139Z","title":"Higher string topology operations","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:39.176139Z"},"links":{"cited_paper":"/paper/0711.4859","citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:687041c57ddb4150a927d8841f998048abd3876b4d7ae8546e9f8c11c164d469","observation_id":"dcfcdf67-4a63-4eae-a66d-d00ae6e81164","resolution":{"observed_at":"2026-08-05T15:45:39.176139Z","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":"10.24033/asens.1242","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Le type d’homotopie du groupe des diff´ eomorphismes d’une surface compacte","venue":"Annales Scientifiques de l École Normale Supérieure","work_id":"5c19d7d7-6c8f-4502-b6d4-cb6418a61368","year":1973},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:39.288114Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:35f0f942a5f92917f686c6fd8ca36205cf1afda8b287a1fbbe4238a1a8926fd3","observation_id":"b1e03c48-9377-477a-94d4-44ae4915c950","resolution":{"observed_at":"2026-08-05T15:45:46.325121Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.indag.2019.12.004","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Khokhliuk and S","venue":"Indagationes Mathematicae","work_id":"6fbe1d0f-4369-424a-918d-a742f7bc02fb","year":2020},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:39.454825Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:582373358fe0f0a7e95e25757d2dc7d2262544694d4f1995e88e09a566504f4d","observation_id":"f4cd242a-034a-4baa-a403-a3db767714b1","resolution":{"observed_at":"2026-08-05T15:45:46.297491Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T15:45:49.024749Z","title":"Khokhliuk and S","venue":null,"work_id":"f43cb7d4-e565-46b9-bed6-c3a17412b41d","year":null},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:39.636876Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:11206dd54155442b17f78b20eb11b72e6d0a7d690af4e231444aa9bce1786049","observation_id":"07e255f7-0d86-440d-a61f-7ec993998545","resolution":{"observed_at":"2026-08-05T15:45:49.058089Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T15:45:48.886353Z","title":"Kravchenko and B","venue":null,"work_id":"5f5c06fe-94bb-4936-9023-1690d254a5aa","year":2020},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:39.791518Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:2844ad0fb81ce49007fa2184b4227c01f1397cbd285e3b35562600c2d1479229","observation_id":"ac16f153-0962-45fe-91cc-a60d8a2b1cb0","resolution":{"observed_at":"2026-08-05T15:45:48.932092Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.3103/s0027132212010019","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Kudryavtseva","venue":"Moscow University Mathematics Bulletin","work_id":"436cf7f2-cb9a-4318-9f24-ceb70831a30e","year":2012},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:39.976699Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:2d8a04fb3a743c255c8d1f0cbc02af1caf7bbd6b9678c7723fee8c9df8ffeb40","observation_id":"f84e9ea0-2f5e-4b2c-b99e-6b729fa4637f","resolution":{"observed_at":"2026-08-05T15:45:46.241450Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.3103/s0027132212040031","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Kudryavtseva","venue":"Moscow University Mathematics Bulletin","work_id":"1513a97f-4cde-4f88-bf67-cf64e52fff64","year":2012},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:40.200478Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:f570b8676a4dcefc6dd1a6b960ca4993c92ea05e1d6fbc37e144c7f8d0b9e1a1","observation_id":"d3b4048c-77e3-43a6-a134-a6d48de72ef7","resolution":{"observed_at":"2026-08-05T15:45:46.204745Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T15:45:48.737045Z","title":"Kudryavtseva","venue":null,"work_id":"17a7ff1f-b434-4796-b41e-75582a39cdfc","year":null},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:40.342985Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:0843d4c15633b1dac70ee1c712c624f19f1b963b72388b88acfbc761f55bb067","observation_id":"eafaf47a-4609-400e-94a4-7ed3053afb0f","resolution":{"observed_at":"2026-08-05T15:45:48.784750Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1070/sm2013v204n01abeh004292","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Kudryavtseva","venue":"Sbornik Mathematics","work_id":"813108fa-54d1-40d1-8b76-02175cd8a866","year":2013},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:40.587132Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:e946a6c15633b5e44681ec8d8e4921ec23f33244906be8c828d7376413d562e4","observation_id":"da05c403-1acd-4fe1-b76b-b890f15fb014","resolution":{"observed_at":"2026-08-05T15:45:46.094250Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T15:45:48.594745Z","title":"Kudryavtseva","venue":null,"work_id":"15feaa18-c29b-4686-af51-1124b944c127","year":2016},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:40.790445Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:ca511618d06329eeeb542b335a84078b9873dde483a8657f4ad7cee0ed611b8a","observation_id":"d266f401-5503-419d-bd4c-8187a1d268ad","resolution":{"observed_at":"2026-08-05T15:45:48.644744Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2106.03017","last_updated":"2021-06-06T03:09:12Z","snapshot_observed_at":"2026-07-06T11:16:19.955258Z","submitted_at":"2021-06-06T03:09:12Z","title":"Topology of spaces of smooth functions and gradient-like flows with prescribed singularities on surfaces","version":1},"cited_work":{"arxiv_id":"2106.03017","doi":"10.48550/arxiv.2106.03017","metadata_source":"pith","pith_arxiv_id":"2106.03017","snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Topology of spaces of smooth functions and gradient-like flows with prescribed singularities on surfaces","venue":"math.GT","work_id":"8d548888-7c98-46ed-a8ea-c8472a7e3d66","year":2021},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:40.919656Z"},"links":{"cited_paper":"/paper/2106.03017","citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:4e944462098753111adcc8a7131bf1560834ec42d61ae69b8d9cd5df4edb940e","observation_id":"326e5af5-071b-4ae5-8d42-48aef736c2ae","resolution":{"observed_at":"2026-08-05T15:45:46.013043Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.37863/umzh.v73i2.2383","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Kuznietsova and Yu","venue":"Ukrains’kyi Matematychnyi Zhurnal","work_id":"7b115d3e-78fa-40b6-af68-45077713cff3","year":2021},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:41.044747Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:e5e1ba820f0f25d219c9380f22cc80f390ccd2356566f5e85cf4240d59c8c9d6","observation_id":"737a7378-f8bc-4df8-ac21-be4ab1a97b08","resolution":{"observed_at":"2026-08-05T15:45:45.915513Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.15673/tmgc.v13i4.1953","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Maksymenko","venue":"Proceedings of the International Geometry Center","work_id":"de45a0de-af0e-449f-a8df-73a2f6b617fb","year":2020},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:41.187886Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:63c1e0d6e9e9b2934e3ee83803593692ff3be0baf666cfb7d4190653d470a866","observation_id":"3815383d-bf35-463b-b999-c0ddc11f80e5","resolution":{"observed_at":"2026-08-05T15:45:45.861941Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.12775/tmna.2024.022","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Deformational symmetries of smooth functions on non- orientable surfaces","venue":"Topological Methods in Nonlinear Analysis","work_id":"db1c4c65-a516-4c88-8522-d16c8545cc9c","year":2025},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:41.290192Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:e2f9b626f8a0df5c4a3c5f7ef2d3361ee840b2f938f195700173ad8a7b92ed3b","observation_id":"3b3fd1f1-62d2-40fd-b004-3efab42e970c","resolution":{"observed_at":"2026-08-05T15:45:45.803278Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1017/s0305004100036926","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Mathematical Proceedings of the Cambridge Philosophical Society","work_id":"054722fe-b54c-4b6c-b499-77d6da0d78c5","year":1963},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:41.436787Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:c74cb0aaf43054eafc0e70bcb849f2285761d279875a926533f1422406e207b7","observation_id":"800f576a-f8a8-4452-9082-a1ac5cd5064d","resolution":{"observed_at":"2026-08-05T15:45:45.705743Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10455-005-9012-6","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Maksymenko","venue":"Annals of Global Analysis and Geometry","work_id":"bceb512f-8f33-4f9b-8713-130eb8f64f87","year":2006},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:41.583340Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:eb1e78a0e6b0fde17a1509f8027278ad2800520e3e0e472b31a49ecd81c72e42","observation_id":"782692f5-4d17-4777-a369-e203e31c0233","resolution":{"observed_at":"2026-08-05T15:45:45.498465Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0710.4437","last_updated":"2015-12-24T13:12:01Z","snapshot_observed_at":"2026-07-06T01:31:37.701334Z","submitted_at":"2007-10-24T11:40:44Z","title":"Homotopy dimension of orbits of Morse functions on surfaces","version":3},"cited_work":{"arxiv_id":"0710.4437","doi":null,"metadata_source":"pith","pith_arxiv_id":"0710.4437","snapshot_observed_at":"2026-08-05T15:45:47.584962Z","title":"Homotopy dimension of orbits of Morse functions on surfaces","venue":"math.AT","work_id":"d35d6cb5-7cd0-4538-9372-af22bbad1a22","year":2007},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:41.647667Z"},"links":{"cited_paper":"/paper/0710.4437","citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:66a1363df5615bf82d06301e2e83e2a4fa2ca36ea58a8fcca55e37fa6f63bc12","observation_id":"eae1f337-fa9d-4b70-82c9-56365816d37d","resolution":{"observed_at":"2026-08-05T15:45:47.601665Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T15:45:48.414749Z","title":"Maksymenko","venue":null,"work_id":"41d1b9a4-d708-4d8c-afe4-58e22e0c6872","year":2010},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:41.754523Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:6e303d4e9ba617097075fde91c8d9af23bd4685319d52fab59788c7a093bcb17","observation_id":"794ef07b-363c-43bc-affc-e542c252a767","resolution":{"observed_at":"2026-08-05T15:45:48.454741Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0806.4704","last_updated":"2009-12-17T13:20:20Z","snapshot_observed_at":"2026-07-06T01:39:35.270236Z","submitted_at":"2008-06-28T16:40:33Z","title":"Functions with isolated singularities on surfaces","version":2},"cited_work":{"arxiv_id":"0806.4704","doi":null,"metadata_source":"pith","pith_arxiv_id":"0806.4704","snapshot_observed_at":"2026-08-05T15:45:47.512379Z","title":"Functions with isolated singularities on surfaces","venue":"math.GT","work_id":"81dc2187-7851-4347-8459-6089756914e5","year":2008},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:41.886755Z"},"links":{"cited_paper":"/paper/0806.4704","citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:effd7dac5a890451b203c5abc8bb1c25978993f4dc7533e53ae2a6eda6017a5e","observation_id":"3b0a8899-0af2-4848-af91-26702ac9f77f","resolution":{"observed_at":"2026-08-05T15:45:47.526281Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0806.1502","last_updated":"2015-12-24T13:20:27Z","snapshot_observed_at":"2026-07-06T01:40:48.319992Z","submitted_at":"2008-06-09T17:36:44Z","title":"Local inverses of shift maps along orbits of flows","version":4},"cited_work":{"arxiv_id":"0806.1502","doi":null,"metadata_source":"pith","pith_arxiv_id":"0806.1502","snapshot_observed_at":"2026-08-05T15:45:47.423414Z","title":"Local inverses of shift maps along orbits of flows","venue":"math.DS","work_id":"de4a67c2-0205-433f-b2f6-4a22833ee412","year":2008},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:41.975116Z"},"links":{"cited_paper":"/paper/0806.1502","citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:4cfc3ff217814aa7a701cb08e35aeb8ea60d322809d6a3f6defa5cee9f88d348","observation_id":"01cc5b98-e634-4103-8208-dbda25aee306","resolution":{"observed_at":"2026-08-05T15:45:47.448737Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1205.4196","last_updated":"2012-05-18T16:50:24Z","snapshot_observed_at":"2026-07-06T02:48:21.680156Z","submitted_at":"2012-05-18T16:50:24Z","title":"Functions with isolated singularities on surfaces, II","version":1},"cited_work":{"arxiv_id":"1205.4196","doi":null,"metadata_source":"pith","pith_arxiv_id":"1205.4196","snapshot_observed_at":"2026-08-05T15:45:47.341691Z","title":"Functions with isolated singularities on surfaces, II","venue":"math.GT","work_id":"c700cf4e-4994-4aa7-b98d-3e761cdcc31e","year":2012},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:42.132613Z"},"links":{"cited_paper":"/paper/1205.4196","citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:3737c3df38fe4d7cda1383ced8ac25c3cf196de45fb0d542fc642803cafa187f","observation_id":"3c360dfc-f906-4e7d-8417-ccc42f904d4d","resolution":{"observed_at":"2026-08-05T15:45:47.367574Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T15:45:48.270156Z","title":"Maksymenko","venue":null,"work_id":"e5ae67ef-2e66-48b8-b6f2-8345def52e1b","year":2020},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:42.326519Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:6a5ed8295177b9d761a2881f27c3cb38c3090913f718fa93643163189c06ddcc","observation_id":"6dd13494-2177-40ca-acff-0ffd1855f549","resolution":{"observed_at":"2026-08-05T15:45:48.304130Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T15:45:42.526065Z","title":"Maksymenko","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:42.526065Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:d8948429d22b8b23a57b2bc1570e29066886a004e3711198dcc00fc946fbf1dc","observation_id":"15ace046-74a2-4483-9c4b-3e1ec9c27b96","resolution":{"observed_at":"2026-08-05T15:45:42.526065Z","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":"10.15330/ms.44.1.67-83","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Maksymenko and B","venue":"Matematychni Studii","work_id":"ac752d5e-fab2-44dd-916c-fc6bc72cdae7","year":2015},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:42.734892Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:0968f2acdd537b1f25ef963713b04a7d18c01f4c223a7e2262fc06e24f12b287","observation_id":"bf9efde8-d7ad-43d9-b990-874a7316d8b1","resolution":{"observed_at":"2026-08-05T15:45:45.146967Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T15:45:48.211458Z","title":"Maksymenko and B","venue":null,"work_id":"3e30d678-ac1d-425a-83f7-d8ae04b84e1b","year":2015},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:42.904827Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:5c15fc60a0857b3e88d9bde492114d60bd47655c8676985f3e7bcd669c419677","observation_id":"9fa337d1-689b-4e2f-b6bc-2ced0fa28c3c","resolution":{"observed_at":"2026-08-05T15:45:48.240183Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s11253-015-1014-3","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Ukrainian Mathematical Journal","work_id":"6312fe89-c627-48b4-95c7-5f6f13a4b11a","year":2015},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:43.074752Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:ab23e073e18a6a8c87ecd1501b74ba4ab78de35a9862527eb08f2a7c8c8bee50","observation_id":"255f1cc6-03ca-4d3e-9498-c91e69798412","resolution":{"observed_at":"2026-08-05T15:45:44.914743Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T15:45:48.125101Z","title":"Topological actions of wreath products","venue":null,"work_id":"d8f73c92-2a15-4ef5-8cc0-5f1646d8c1bb","year":null},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:43.234918Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:acc63f6eb56d789a2cf643639493c5a65cfc69e7c8cd7c3d2c1390c3d30ba76a","observation_id":"69350246-eae8-42ec-b7ea-7c18fdc92c84","resolution":{"observed_at":"2026-08-05T15:45:48.149786Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2024.10218","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T15:45:46.869410Z","title":"Vector bundle automorphisms preserving Morse-Bott foliations","venue":null,"work_id":"f1a234c2-d6be-44bf-b228-f3ba41f5b211","year":2024},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:43.464338Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:3d7f8141ee9aa5fa9df3929e73118073151945b3d351aecf46c7cc42574c4c30","observation_id":"f401c7fe-58f3-4fd4-accf-20379b7eaf38","resolution":{"observed_at":"2026-08-05T15:45:46.995904Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T15:45:48.027716Z","title":"The Sullivan conjecture on maps from classifying spaces","venue":null,"work_id":"354c599b-6895-441d-b390-cf07f6da5c85","year":null},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:43.574828Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:95687a71ce8411ecaedf0f3f0a0e525b35cf498d53d1a94f2103dedd508b1c38","observation_id":"4f3500a9-4879-4448-b5d9-0d8f8d44af7c","resolution":{"observed_at":"2026-08-05T15:45:48.059335Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.24033/asens.1239","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Un th´ eor` eme de fonctions implicites sur certains espaces de Fr´ echet et quelques applications","venue":"Annales Scientifiques de l École Normale Supérieure","work_id":"8b9561a6-98ab-4e6e-8ed5-67b7d4d259b1","year":1972},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:43.724850Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:e9c3d090f7a882d14d1d7b0d3c8fd91e70184aea2ab2aa6f90bb0baf33d5edea","observation_id":"ed721b1c-a2d4-46d6-8d24-a53a93c58e64","resolution":{"observed_at":"2026-08-05T15:45:44.414065Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T15:45:47.943462Z","title":"Diffeomorphisms of the 2-sphere","venue":null,"work_id":"13af6d43-08e6-43e2-9963-c00e2bf6a1b8","year":1959},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:43.890479Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:122ff3d82856b9f29a525b3c170622d42633f5461b3ebc521a8346a5606ebfd4","observation_id":"58442723-783d-476b-8e70-d3939574421b","resolution":{"observed_at":"2026-08-05T15:45:47.956657Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+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":"2026-08-05T15:45:44.124835Z","title":null,"venue":null,"work_id":null,"year":1970},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:44.124835Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:3c25b11a5357f67d59d5ca647709da8a2eb4fd562eb25032edfe00806b1769fe","observation_id":"48794d6a-0fa4-490f-b551-30739a0d2075","resolution":{"observed_at":"2026-08-05T15:45:44.124835Z","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":"2026-08-05T15:45:37.904761Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":1986,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:37.904761Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:b1a2dd926eb791b1088ac31a1039cf7e33652836f0345af0cf3a0ab937b79b1d","observation_id":"a7121726-8718-47ed-ae0c-32095861a94b","resolution":{"observed_at":"2026-08-05T15:45:37.904761Z","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":"10.1134/s0001434612070243","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Zametki 92 (2012), no","venue":"Mathematical Notes","work_id":"b6308e6a-7f2c-41b5-af98-7c6465e10034","year":2012},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":2012,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:40.484824Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:6d1b387df33457948705a57da33abadd817d6a24f1dd87c94e1c18d08db4a6b1","observation_id":"e64ae570-775c-4145-a690-46a9ea124291","resolution":{"observed_at":"2026-08-05T15:45:46.132663Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s40879-024-00732-6","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"European Journal of Mathematics","work_id":"ec7d45c7-1740-4477-8ae5-7cb4f4eac60b","year":null},"citing_paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands","version":1},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-05T15:45:43.374749Z"},"links":{"citing_paper":"/paper/2508.19636"},"observation_digest":"sha256:e6cc56623ecc01296677347d58ae5f75dd04ad0773c84509d7f61daeb4f87cbe","observation_id":"fc02dc43-47d4-4911-a53d-1f15f3af9c6b","resolution":{"observed_at":"2026-08-05T15:45:44.694768Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2508.19636","last_updated":"2025-08-27T07:25:12Z","latest_version":1,"primary_category":"math.GT","snapshot_observed_at":"2026-08-13T10:03:35.239019Z","submitted_at":"2025-08-27T07:25:12Z","title":"Smooth functions that split a Klein bottle into two M\\\"obius bands"},"reference_resolution":{"displayed":45,"state_counts":{"malformed_identifier":1,"metadata_mismatch":1,"parse_uncertain":0,"unresolved":6,"verified_exact":24,"verified_fuzzy":13},"total_outbound_references":45},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 45 of 45 outbound references and 0 inbound Pith citation observations for arXiv:2508.19636."}