{"as_of":"2026-08-18T18:47:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:2eb6fcbb38b45ad95dd225c89b920572af5135146b457fbda620d751aaa88eab","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":12,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":12,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+00:00","state":"measured"},{"denominator":12,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":12,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T19:11:30.201632Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-07-01T14:15:47.303940Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1902.08841","last_updated":"2021-07-27T09:55:56Z","snapshot_observed_at":"2026-08-14T17:12:17.730537Z","submitted_at":"2019-02-23T19:55:38Z","title":"On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1902.08841","snapshot_observed_at":"2026-08-14T13:57:08.816445Z","title":"Kitazawa, On Reeb graphs induced from smooth functions on 3-dimensional closed ori- entable manifolds with ﬁnitely many singular values , accepted for publication in Topol","venue":null,"work_id":null,"year":1902},"citing_paper":{"arxiv_id":"1908.04340","last_updated":"2022-03-25T10:19:39Z","snapshot_observed_at":"2026-08-18T12:13:26.849343Z","submitted_at":"2019-08-12T19:11:23Z","title":"On Reeb graphs induced from smooth functions on closed or open manifolds","version":8},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T13:57:08.816445Z"},"links":{"cited_paper":"/paper/1902.08841","citing_paper":"/paper/1908.04340"},"observation_digest":"sha256:de28136b0dd3b2247d68571e7cde908c82de2062cc855e19495ff4eaaaec795f","observation_id":"30d79fc1-6401-4975-8d40-d8972e409e84","resolution":{"observed_at":"2026-08-14T13:57:08.816445Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1902.08841","last_updated":"2021-07-27T09:55:56Z","snapshot_observed_at":"2026-08-14T17:12:17.730537Z","submitted_at":"2019-02-23T19:55:38Z","title":"On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1902.08841","snapshot_observed_at":"2026-08-12T13:48:56.169772Z","title":"Kitazawa, On Reeb graphs induced from smooth functions on 3-dimensional closed ori- entable manifolds with ﬁnitely many singular values , Topol","venue":null,"work_id":null,"year":1902},"citing_paper":{"arxiv_id":"2411.15943","last_updated":"2024-11-27T01:04:12Z","snapshot_observed_at":"2026-08-16T20:12:33.989941Z","submitted_at":"2024-11-24T18:10:20Z","title":"On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-12T13:48:56.169772Z"},"links":{"cited_paper":"/paper/1902.08841","citing_paper":"/paper/2411.15943"},"observation_digest":"sha256:cfb8f3c6309d9a8c487e4ad752db822e9868caabde10c1054a05481fa0ea2415","observation_id":"eeb2240b-1c9c-499e-b0cd-c836f8304340","resolution":{"observed_at":"2026-08-12T13:48:56.169772Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1902.08841","last_updated":"2021-07-27T09:55:56Z","snapshot_observed_at":"2026-08-14T17:12:17.730537Z","submitted_at":"2019-02-23T19:55:38Z","title":"On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1902.08841","snapshot_observed_at":"2026-08-11T22:14:58.014737Z","title":"Kitazawa, On Reeb graphs induced from smooth functions on 3-dimensional closed ori- entable manifolds with ﬁnitely many singular values , Topol","venue":null,"work_id":null,"year":1902},"citing_paper":{"arxiv_id":"2412.03846","last_updated":"2025-01-21T01:40:16Z","snapshot_observed_at":"2026-08-17T08:53:09.994306Z","submitted_at":"2024-12-05T03:23:58Z","title":"Arrangements of small circles for Morse-Bott functions","version":3},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T22:14:58.014737Z"},"links":{"cited_paper":"/paper/1902.08841","citing_paper":"/paper/2412.03846"},"observation_digest":"sha256:52a32c77e061f746eed114973d03391ec2c60f371710919d8387627a27a742e5","observation_id":"e62d9810-9768-49b0-8b5e-e41dcb2d6eee","resolution":{"observed_at":"2026-08-11T22:14:58.014737Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1902.08841","last_updated":"2021-07-27T09:55:56Z","snapshot_observed_at":"2026-08-14T17:12:17.730537Z","submitted_at":"2019-02-23T19:55:38Z","title":"On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1902.08841","snapshot_observed_at":"2026-08-15T19:11:30.201632Z","title":"Kitazawa,On Reeb graphs induced from smooth functions on3-dimensional closed ori- entable manifolds with finitely many singular values, Topol","venue":null,"work_id":null,"year":1902},"citing_paper":{"arxiv_id":"2506.17791","last_updated":"2025-06-21T19:02:46Z","snapshot_observed_at":"2026-08-16T21:26:47.600163Z","submitted_at":"2025-06-21T19:02:46Z","title":"Moment-like maps and real algebraic functions with prescribed preimages","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:30.201632Z"},"links":{"cited_paper":"/paper/1902.08841","citing_paper":"/paper/2506.17791"},"observation_digest":"sha256:f81c0d360e5f44e9122599e4c11d9e1dbe6c1904cd362aa7b669a98650f80d3f","observation_id":"699cc41b-50fe-40dc-ae76-3f67db7db286","resolution":{"observed_at":"2026-08-15T19:11:30.201632Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1902.08841","last_updated":"2021-07-27T09:55:56Z","snapshot_observed_at":"2026-08-14T17:12:17.730537Z","submitted_at":"2019-02-23T19:55:38Z","title":"On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1902.08841","snapshot_observed_at":"2026-08-06T18:03:32.594906Z","title":"Kitazawa, On Reeb graphs induced from smooth functions on 3-dimensional closed ori- entable manifolds with finitely many singular values, Topol","venue":null,"work_id":null,"year":1902},"citing_paper":{"arxiv_id":"2507.09467","last_updated":"2025-07-20T04:17:54Z","snapshot_observed_at":"2026-08-18T02:28:35.696314Z","submitted_at":"2025-07-13T03:03:37Z","title":"Reconstruction of real algebraic functions into curves with prescribed Reeb graphs","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T18:03:32.594906Z"},"links":{"cited_paper":"/paper/1902.08841","citing_paper":"/paper/2507.09467"},"observation_digest":"sha256:d0d2371d4fb0e8631904eb345391fcbe410694de56b6f7700062ce00b7cba721","observation_id":"6a0d15d7-77b9-4f8c-a1ad-c28e75683a6f","resolution":{"observed_at":"2026-08-06T18:03:32.594906Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1902.08841","last_updated":"2021-07-27T09:55:56Z","snapshot_observed_at":"2026-08-14T17:12:17.730537Z","submitted_at":"2019-02-23T19:55:38Z","title":"On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1902.08841","snapshot_observed_at":"2026-08-06T06:13:19.276948Z","title":"Kitazawa, On Reeb graphs induced from smooth functions on 3-dimensional closed ori- entable manifolds with ﬁnitely many singular values , Topol","venue":null,"work_id":null,"year":1902},"citing_paper":{"arxiv_id":"2508.00729","last_updated":"2025-08-05T17:33:44Z","snapshot_observed_at":"2026-08-09T21:11:34.278507Z","submitted_at":"2025-08-01T15:51:54Z","title":"Graphs with tree decompositions of small graphs and realizing them as the Reeb graphs of real algebraic functions","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T06:13:19.276948Z"},"links":{"cited_paper":"/paper/1902.08841","citing_paper":"/paper/2508.00729"},"observation_digest":"sha256:55ead95c6a236496d45484b1828297229062375c08a95ae707b41a27cd66caba","observation_id":"ae4d211e-bc67-4088-9cce-467ca09b406f","resolution":{"observed_at":"2026-08-06T06:13:19.276948Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1902.08841","last_updated":"2021-07-27T09:55:56Z","snapshot_observed_at":"2026-08-14T17:12:17.730537Z","submitted_at":"2019-02-23T19:55:38Z","title":"On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values","version":5},"cited_work":{"arxiv_id":"1902.08841","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1902.08841","snapshot_observed_at":"2026-07-01T14:15:47.303940Z","title":"Kitazawa,On Reeb graphs induced from smooth functions on3-dimensional closed ori- entable manifolds with finitely many singular values, Topol","venue":null,"work_id":"d03d4bcf-25af-4a0c-9428-9aa596fa7573","year":1902},"citing_paper":{"arxiv_id":"2604.04910","last_updated":"2026-04-06T17:54:06Z","snapshot_observed_at":"2026-08-10T01:26:20.389326Z","submitted_at":"2026-04-06T17:54:06Z","title":"Morse functions with regular level sets consisting of $2$-dimensional spheres, $2$-dimensional tori, or Klein Bottles","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-10T18:57:35.894279Z"},"links":{"cited_paper":"/paper/1902.08841","citing_paper":"/paper/2604.04910"},"observation_digest":"sha256:26b3955e4cc893a0a7bb03615894fc51ea147301affc9a6dc120637c61e689a5","observation_id":"f8102f00-8464-48aa-a201-25432ca0a7c0","resolution":{"observed_at":"2026-05-10T23:40:51.410258Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1902.08841","last_updated":"2021-07-27T09:55:56Z","snapshot_observed_at":"2026-08-14T17:12:17.730537Z","submitted_at":"2019-02-23T19:55:38Z","title":"On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values","version":5},"cited_work":{"arxiv_id":"1902.08841","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1902.08841","snapshot_observed_at":"2026-07-01T14:15:47.303940Z","title":"Kitazawa,On Reeb graphs induced from smooth functions on3-dimensional closed ori- entable manifolds with finitely many singular values, Topol","venue":null,"work_id":"d03d4bcf-25af-4a0c-9428-9aa596fa7573","year":1902},"citing_paper":{"arxiv_id":"2605.12219","last_updated":"2026-07-06T01:13:23Z","snapshot_observed_at":"2026-08-06T06:00:01.931555Z","submitted_at":"2026-05-12T14:57:08Z","title":"Representations of Reeb spaces via simplified graphs and examples","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-13T04:42:51.554526Z"},"links":{"cited_paper":"/paper/1902.08841","citing_paper":"/paper/2605.12219"},"observation_digest":"sha256:f7658a9de5acda0e17035ba1781a61bee03a5b5b106d058f6350b8c5f2787c1a","observation_id":"3785e6f2-4a83-4c7b-a924-d2ccc9813f0d","resolution":{"observed_at":"2026-05-13T05:12:18.421798Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1902.08841","last_updated":"2021-07-27T09:55:56Z","snapshot_observed_at":"2026-08-14T17:12:17.730537Z","submitted_at":"2019-02-23T19:55:38Z","title":"On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values","version":5},"cited_work":{"arxiv_id":"1902.08841","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1902.08841","snapshot_observed_at":"2026-07-01T14:15:47.303940Z","title":"Kitazawa,On Reeb graphs induced from smooth functions on3-dimensional closed ori- entable manifolds with finitely many singular values, Topol","venue":null,"work_id":"d03d4bcf-25af-4a0c-9428-9aa596fa7573","year":1902},"citing_paper":{"arxiv_id":"2605.12219","last_updated":"2026-07-06T01:13:23Z","snapshot_observed_at":"2026-08-06T06:00:01.931555Z","submitted_at":"2026-05-12T14:57:08Z","title":"Representations of Reeb spaces via simplified graphs and examples","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-30T22:09:11.987811Z"},"links":{"cited_paper":"/paper/1902.08841","citing_paper":"/paper/2605.12219"},"observation_digest":"sha256:818118ee15effb62c858e6c400afa79d585c1daa773ab7d9db2fbf43724a2497","observation_id":"416567e7-500b-4f03-b22a-b84eeca80f60","resolution":{"observed_at":"2026-07-01T14:15:47.305520Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1902.08841","last_updated":"2021-07-27T09:55:56Z","snapshot_observed_at":"2026-08-14T17:12:17.730537Z","submitted_at":"2019-02-23T19:55:38Z","title":"On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1902.08841","snapshot_observed_at":"2026-07-11T17:12:07.354182Z","title":"Kitazawa,On Reeb graphs induced from smooth functions on3-dimensional closed ori- entable manifolds with finitely many singular values, Topol","venue":null,"work_id":null,"year":1902},"citing_paper":{"arxiv_id":"2607.04565","last_updated":"2026-07-06T00:32:58Z","snapshot_observed_at":"2026-08-13T09:23:51.408608Z","submitted_at":"2026-07-06T00:32:58Z","title":"Compactifying real analytic functions and resulting Reeb spaces","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-11T17:12:07.354182Z"},"links":{"cited_paper":"/paper/1902.08841","citing_paper":"/paper/2607.04565"},"observation_digest":"sha256:12c4ef732d932f5d3b230a226587f530a1cdac0e0eeb2efb0c9930b3c85164e1","observation_id":"a5bce9ca-573b-4dff-8b3b-fe3a43a6e403","resolution":{"observed_at":"2026-07-11T17:12:07.354182Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1902.08841","last_updated":"2021-07-27T09:55:56Z","snapshot_observed_at":"2026-08-14T17:12:17.730537Z","submitted_at":"2019-02-23T19:55:38Z","title":"On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1902.08841","snapshot_observed_at":"2026-08-01T18:58:34.787122Z","title":"Kitazawa, On Reeb graphs induced from smooth functions on 3-dimensional closed ori- entable manifolds with ﬁnitely many singular values , Topol","venue":null,"work_id":null,"year":1902},"citing_paper":{"arxiv_id":"2607.17180","last_updated":"2026-07-27T08:31:17Z","snapshot_observed_at":"2026-08-05T19:57:55.637664Z","submitted_at":"2026-07-19T10:35:38Z","title":"Regions represented as foliated forms and natural smooth maps onto them","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:34.787122Z"},"links":{"cited_paper":"/paper/1902.08841","citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:5f0b28d57d0ceba5db3842d1672db40cffde07b348337d041f669b1b2dfef89f","observation_id":"4897cac8-5107-49a7-96d4-14a24b2e021f","resolution":{"observed_at":"2026-08-01T18:58:34.787122Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1902.08841","last_updated":"2021-07-27T09:55:56Z","snapshot_observed_at":"2026-08-14T17:12:17.730537Z","submitted_at":"2019-02-23T19:55:38Z","title":"On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1902.08841","snapshot_observed_at":"2026-08-05T00:54:16.202466Z","title":"Kitazawa, On Reeb graphs induced from smooth functions on 3-dimensional closed ori- entable manifolds with ﬁnitely many singular values , Topol","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2608.00556","last_updated":"2026-08-01T09:21:36Z","snapshot_observed_at":"2026-08-10T00:06:11.727871Z","submitted_at":"2026-08-01T09:21:36Z","title":"Fundamental examples of height functions on closed manifolds and their 1st derivatives","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-05T00:54:16.202466Z"},"links":{"cited_paper":"/paper/1902.08841","citing_paper":"/paper/2608.00556"},"observation_digest":"sha256:4c630c2a961dbb4b43b235308439dbaec07b276f71da7278c504f26e7d3c09b5","observation_id":"25dea9b2-7d08-407b-baa3-58ab36094df2","resolution":{"observed_at":"2026-08-05T00:54:16.202466Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/1902.08841/citation-record","integrity":"/paper/1902.08841/integrity","json":"/paper/1902.08841/citation-record.json","paper":"/paper/1902.08841"},"outbound":[],"paper":{"arxiv_id":"1902.08841","last_updated":"2021-07-27T09:55:56Z","latest_version":5,"primary_category":"math.GT","snapshot_observed_at":"2026-08-14T17:12:17.730537Z","submitted_at":"2019-02-23T19:55:38Z","title":"On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"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":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 12 inbound Pith citation observations for arXiv:1902.08841."}