{"as_of":"2026-08-18T17:58:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:1f2d05cda014a071939dc56d45396f16b4a1d4aa9eee799ee853b849028c487a","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":"2026-08-12T13:48:56.209968Z","state":"measured"},{"denominator":25,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":25,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T15:08:07.706376Z","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":"2026-05-10T23:40:51.431077Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_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},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.15943","snapshot_observed_at":"2026-08-11T15:08:07.706376Z","title":"Kitazawa, On a classification of Morse functions on 3-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one , arXiv:2411.15943, 2024","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.11397","last_updated":"2024-12-22T05:55:37Z","snapshot_observed_at":"2026-08-13T23:06:10.514916Z","submitted_at":"2024-12-16T02:52:53Z","title":"Characterizing $3$-dimensional manifolds represented as connected sums of Lens spaces, $S^2 \\times S^1$, and torus bundles over the circle by certain Morse-Bott functions","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T15:08:07.706376Z"},"links":{"cited_paper":"/paper/2411.15943","citing_paper":"/paper/2412.11397"},"observation_digest":"sha256:dd84392b8b1e50ad7233f181c784760cf04adb256732cf9bbf95d83d33160979","observation_id":"eff49d91-fcfa-46f0-88d2-cdbe620dc521","resolution":{"observed_at":"2026-08-11T15:08:07.706376Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_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},"cited_work":{"arxiv_id":"2411.15943","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2411.15943","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Kitazawa, On a classification of Morse functions on 3-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one","venue":null,"work_id":"acb23e81-154a-4c69-baf2-976791f3c615","year":2026},"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":20,"source":"pdf_text","source_observed_at":"2026-05-10T18:57:35.894279Z"},"links":{"cited_paper":"/paper/2411.15943","citing_paper":"/paper/2604.04910"},"observation_digest":"sha256:09024ea353e75b093e6de49486ed06e9568809ab7a985b4b56f2f6bb6b1e14cd","observation_id":"ae1f53ca-bbac-4f7c-a287-76ece6376b58","resolution":{"observed_at":"2026-05-10T23:40:51.434207Z","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"}}],"links":{"evidence":"/evidence","html":"/paper/2411.15943/citation-record","integrity":"/paper/2411.15943/integrity","json":"/paper/2411.15943/citation-record.json","paper":"/paper/2411.15943"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T13:48:56.145960Z","title":"Gelbukh, A finite graph is homeomorphic to the Reeb graph of a Morse-Bot t function , Mathematica Slovaca, 71 (3), 757–772, 2021; doi: 10.1515/m s-2021-0018","venue":null,"work_id":null,"year":2021},"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":1,"source":"pdf_text","source_observed_at":"2026-08-12T13:48:56.145960Z"},"links":{"citing_paper":"/paper/2411.15943"},"observation_digest":"sha256:b0558565b1b001c6c329733c4927886b02130fbb33362178d53bd59721f33edf","observation_id":"6376113a-4036-46fa-89b4-ddbd48ef23c7","resolution":{"observed_at":"2026-08-12T13:48:56.145960Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-08-12T13:48:56.149335Z","title":"Gelbukh, Morse-Bott functions with two critical values on a surface , Czechoslovak Mathe- matical Journal, 71 (3), 865–880, 2021; doi: 10.21136/CMJ","venue":null,"work_id":null,"year":2021},"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":2,"source":"pdf_text","source_observed_at":"2026-08-12T13:48:56.149335Z"},"links":{"citing_paper":"/paper/2411.15943"},"observation_digest":"sha256:ac9d348e9ec9cfdb293748f3086155594552508e50b2e702350031d1bfc4ef1c","observation_id":"2009ad6c-c6a1-4daf-9221-eda61059cffd","resolution":{"observed_at":"2026-08-12T13:48:56.149335Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-08-12T13:48:56.152156Z","title":"Gelbukh, Criterion for a graph to admit a good orientation in terms of l eaf blocks, Monatsh","venue":null,"work_id":null,"year":2022},"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":3,"source":"pdf_text","source_observed_at":"2026-08-12T13:48:56.152156Z"},"links":{"citing_paper":"/paper/2411.15943"},"observation_digest":"sha256:c99a64e6bdb46f41e6519bf1f9b901dd74a71cfaaa4ffdbbdb0881ffb3390202","observation_id":"31b45d8b-7f0f-4d05-9fc7-fcef9b52f571","resolution":{"observed_at":"2026-08-12T13:48:56.152156Z","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":"2026-08-12T13:48:56.155267Z","title":"Gelbukh, Realization of a digraph as the Reeb graph of a Morse-Bott fun ction on a given surface, Topology and its Applications, 2024","venue":null,"work_id":null,"year":2024},"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":4,"source":"pdf_text","source_observed_at":"2026-08-12T13:48:56.155267Z"},"links":{"citing_paper":"/paper/2411.15943"},"observation_digest":"sha256:3814776a474c9159b1b70412ea0cc29dea74c9a433bac372b745c50325b6bfb1","observation_id":"71ca672b-bb8e-4d57-b8fa-28ae051c8045","resolution":{"observed_at":"2026-08-12T13:48:56.155267Z","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":"2026-08-12T13:48:56.158196Z","title":"Gelbukh, Reeb Graphs of Morse-Bott Functions on a Given Surface , Bulletin of the Iranian Mathematical Society, Volume 50 Article number 84, 2024","venue":null,"work_id":null,"year":2024},"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":5,"source":"pdf_text","source_observed_at":"2026-08-12T13:48:56.158196Z"},"links":{"citing_paper":"/paper/2411.15943"},"observation_digest":"sha256:1f65e7acac1c5a26f913408150bf31c9174199064bb2e5dcd02911bb9b63abaf","observation_id":"2d935bf5-44ec-4223-890c-c366de111095","resolution":{"observed_at":"2026-08-12T13:48:56.158196Z","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":"2026-08-12T13:48:56.161168Z","title":"Hempel, 3- Manifolds , AMS Chelsea Publishing, 2004","venue":null,"work_id":null,"year":2004},"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":6,"source":"pdf_text","source_observed_at":"2026-08-12T13:48:56.161168Z"},"links":{"citing_paper":"/paper/2411.15943"},"observation_digest":"sha256:074ce024dc2ac01e323d7cd3c82845bcc3f44a7824f300c67583015ec6dfd9dd","observation_id":"81a133b1-545a-4120-b6ea-89e15a254495","resolution":{"observed_at":"2026-08-12T13:48:56.161168Z","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":"2026-08-12T13:48:56.164137Z","title":"Kitazawa, On manifolds admitting fold maps with singular value sets of concentric spheres, Doctoral Dissertation, Tokyo Institute of Technology (201 4)","venue":null,"work_id":null,"year":null},"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":7,"source":"pdf_text","source_observed_at":"2026-08-12T13:48:56.164137Z"},"links":{"citing_paper":"/paper/2411.15943"},"observation_digest":"sha256:2b4ef367b9c9e6e95fd1822f2d56fffaf26f9442463f1cdb1d1abb4c91316c51","observation_id":"bb3a3706-1c95-4fde-9fec-d32bd2531f50","resolution":{"observed_at":"2026-08-12T13:48:56.164137Z","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":"2026-08-12T13:48:56.166812Z","title":"Kitazawa, Fold maps with singular value sets of concentric spheres , Hokkaido Mathemat- ical Journal Vol.43, No.3 (2014), 327–359","venue":null,"work_id":null,"year":2014},"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":8,"source":"pdf_text","source_observed_at":"2026-08-12T13:48:56.166812Z"},"links":{"citing_paper":"/paper/2411.15943"},"observation_digest":"sha256:ce9692f023b79c47dc6eac1eb568cf9c8f7ed78aa04ed7bc262c70e2346fccac","observation_id":"969bfc0f-0c0a-4574-934e-ad9d1d773895","resolution":{"observed_at":"2026-08-12T13:48:56.166812Z","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":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T13:48:56.173342Z","title":"Kitazawa, On Reeb graphs induced from smooth functions on 3-dimensional closed mani- folds which may not be orientable , Methods of Functional Analysis and Topology Vol","venue":null,"work_id":null,"year":2023},"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":10,"source":"pdf_text","source_observed_at":"2026-08-12T13:48:56.173342Z"},"links":{"citing_paper":"/paper/2411.15943"},"observation_digest":"sha256:9367e17cc173fa69b076c2029507615a44f0ae332c5b2cacb71595d656239007","observation_id":"0c89a871-dd1d-4b00-8f78-b2101519dcff","resolution":{"observed_at":"2026-08-12T13:48:56.173342Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2108.06913","last_updated":"2023-06-15T13:04:46Z","snapshot_observed_at":"2026-08-17T04:48:03.133137Z","submitted_at":"2021-08-16T06:17:58Z","title":"Realization problems of graphs as Reeb graphs of Morse functions with prescribed preimages","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2108.06913","snapshot_observed_at":"2026-08-12T13:48:56.176209Z","title":null,"venue":null,"work_id":null,"year":null},"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":11,"source":"pdf_text","source_observed_at":"2026-08-12T13:48:56.176209Z"},"links":{"cited_paper":"/paper/2108.06913","citing_paper":"/paper/2411.15943"},"observation_digest":"sha256:4fb54a38bf069ad043c5098e1e8f1ae14d38483cb96cf4ae9d0836a12732dee7","observation_id":"8c44caa0-8d7b-440f-b626-036953d4cb56","resolution":{"observed_at":"2026-08-12T13:48:56.176209Z","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":"2026-08-12T13:48:56.179410Z","title":"Martinez-Alfaro, I","venue":null,"work_id":null,"year":2016},"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":12,"source":"pdf_text","source_observed_at":"2026-08-12T13:48:56.179410Z"},"links":{"citing_paper":"/paper/2411.15943"},"observation_digest":"sha256:7fc3ff79161e15d23ddc444daa4a43f56ea2a93f36a5fb184f4fd2554279c810","observation_id":"c48c4dc2-4b19-4235-8758-41b95cc9e236","resolution":{"observed_at":"2026-08-12T13:48:56.179410Z","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":"2026-08-12T13:48:56.182210Z","title":"Marzantowicz and L","venue":null,"work_id":null,"year":2024},"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":13,"source":"pdf_text","source_observed_at":"2026-08-12T13:48:56.182210Z"},"links":{"citing_paper":"/paper/2411.15943"},"observation_digest":"sha256:4c4737b075ca94c8036b16032538d0151408eab034c7bbbbb5c89fd8ce3a6169","observation_id":"110e5883-ee0a-4005-8cdf-7682bb1a75b4","resolution":{"observed_at":"2026-08-12T13:48:56.182210Z","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":"2026-08-12T13:48:56.185496Z","title":"Masumoto and O","venue":null,"work_id":null,"year":2011},"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":14,"source":"pdf_text","source_observed_at":"2026-08-12T13:48:56.185496Z"},"links":{"citing_paper":"/paper/2411.15943"},"observation_digest":"sha256:8a2216f2b337ee4cfb9b469a1d4790452ea82d6ee7c40fbf012e1aec7a74234e","observation_id":"3616ca64-40ee-4d95-8f1f-603e3e4c46cf","resolution":{"observed_at":"2026-08-12T13:48:56.185496Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1805.06727","last_updated":"2018-09-17T09:56:21Z","snapshot_observed_at":"2026-08-14T19:14:14.948980Z","submitted_at":"2018-05-17T12:36:45Z","title":"Realization of a graph as the Reeb graph of a Morse function on a manifold","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1805.06727","snapshot_observed_at":"2026-08-12T13:48:56.188351Z","title":null,"venue":null,"work_id":null,"year":2018},"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":15,"source":"pdf_text","source_observed_at":"2026-08-12T13:48:56.188351Z"},"links":{"cited_paper":"/paper/1805.06727","citing_paper":"/paper/2411.15943"},"observation_digest":"sha256:f0f726aae092be1979f251c931f7d65158c731e97a7edd03a43b2e48ad9d1e27","observation_id":"1d3a0235-45fd-4970-a811-52780194fd5b","resolution":{"observed_at":"2026-08-12T13:48:56.188351Z","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":"2026-08-12T13:48:56.191313Z","title":null,"venue":null,"work_id":null,"year":2021},"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":16,"source":"pdf_text","source_observed_at":"2026-08-12T13:48:56.191313Z"},"links":{"citing_paper":"/paper/2411.15943"},"observation_digest":"sha256:1fcb0355e30d58a691ab9c28773f37aafccfbe4586a85880625bb913d45edad4","observation_id":"d345ff03-7ad2-4a38-8368-aced57e4f589","resolution":{"observed_at":"2026-08-12T13:48:56.191313Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2403.02291","last_updated":"2024-03-04T18:20:32Z","snapshot_observed_at":"2026-08-16T14:12:57.495615Z","submitted_at":"2024-03-04T18:20:32Z","title":"Reeb graph invariants of Morse functions and $3$-manifold groups","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.02291","snapshot_observed_at":"2026-08-12T13:48:56.194016Z","title":null,"venue":null,"work_id":null,"year":null},"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":17,"source":"pdf_text","source_observed_at":"2026-08-12T13:48:56.194016Z"},"links":{"cited_paper":"/paper/2403.02291","citing_paper":"/paper/2411.15943"},"observation_digest":"sha256:64f24186669edbcbedddc889f6caffe48b4f7d423a28d817182118e31866de9d","observation_id":"2f3228dd-ae81-4251-a478-230dc4247b39","resolution":{"observed_at":"2026-08-12T13:48:56.194016Z","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":"2026-08-12T13:48:56.196915Z","title":"Milnor, Lectures on the h-cobordism theorem , Math","venue":null,"work_id":null,"year":1965},"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":18,"source":"pdf_text","source_observed_at":"2026-08-12T13:48:56.196915Z"},"links":{"citing_paper":"/paper/2411.15943"},"observation_digest":"sha256:0ed458e11a1fcec4cb2c0fd050f0c7c708c246b9b92ce4e0066bb9c1658613b2","observation_id":"fa8b0805-4085-46fc-9f4b-f576076693be","resolution":{"observed_at":"2026-08-12T13:48:56.196915Z","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":"2026-08-12T13:48:56.199807Z","title":null,"venue":null,"work_id":null,"year":1946},"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":19,"source":"pdf_text","source_observed_at":"2026-08-12T13:48:56.199807Z"},"links":{"citing_paper":"/paper/2411.15943"},"observation_digest":"sha256:6280f11dd38e536679f8460f7137edb368f48a6285f2d4c773f914dffa10efdc","observation_id":"97a9e3f9-6912-4118-a780-d49edcc61e84","resolution":{"observed_at":"2026-08-12T13:48:56.199807Z","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":"2026-08-12T13:48:56.202560Z","title":"Saeki, Morse functions with sphere fibers , Hiroshima Math","venue":null,"work_id":null,"year":2006},"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":20,"source":"pdf_text","source_observed_at":"2026-08-12T13:48:56.202560Z"},"links":{"citing_paper":"/paper/2411.15943"},"observation_digest":"sha256:ef8cfdc6feb84738587a816d0c8b6f1dec92639b2e43a14e56399a6622b4e23c","observation_id":"a1d504ec-345a-4e70-99d6-8dd8b1bc1a45","resolution":{"observed_at":"2026-08-12T13:48:56.202560Z","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":"2026-08-12T13:48:56.205117Z","title":null,"venue":null,"work_id":null,"year":2022},"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":21,"source":"pdf_text","source_observed_at":"2026-08-12T13:48:56.205117Z"},"links":{"citing_paper":"/paper/2411.15943"},"observation_digest":"sha256:4677e5f1fb7bb0b1ff506279b06c159c59bd0c158c531dabc2827d88ede4d7a6","observation_id":"85843031-949b-424e-b2e3-952437873d83","resolution":{"observed_at":"2026-08-12T13:48:56.205117Z","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":"2026-08-12T13:48:56.207601Z","title":"Saeki and K","venue":null,"work_id":null,"year":2005},"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":22,"source":"pdf_text","source_observed_at":"2026-08-12T13:48:56.207601Z"},"links":{"citing_paper":"/paper/2411.15943"},"observation_digest":"sha256:a73ee73e7fc2eb3e0b2c6ca47a5460fc76fdf2e18b88b265df00caa5569a5cf3","observation_id":"80cfdf34-68fb-4211-84f1-ce1cd07bc7c8","resolution":{"observed_at":"2026-08-12T13:48:56.207601Z","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":"2026-08-12T13:48:56.421578Z","title":"Sharko, About Kronrod-Reeb graph of a function on a manifold , Methods of Functional Analysis and Topology 12 (2006), 389–396","venue":null,"work_id":"ce9fdbc5-b0c7-422e-8199-7248cd53de04","year":2006},"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":23,"source":"pdf_text","source_observed_at":"2026-08-12T13:48:56.209968Z"},"links":{"citing_paper":"/paper/2411.15943"},"observation_digest":"sha256:546913f0c23b4a2d3034c4dc0063c6dc0ef87a44d8ba8e51f8ef06424ff1863d","observation_id":"ef1f47f7-080c-4598-a53c-dfdc8e0c1207","resolution":{"observed_at":"2026-08-12T13:48:56.427034Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}}],"paper":{"arxiv_id":"2411.15943","last_updated":"2024-11-27T01:04:12Z","latest_version":2,"primary_category":"math.GT","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"},"reference_resolution":{"displayed":23,"state_counts":{"malformed_identifier":2,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":20,"verified_exact":0,"verified_fuzzy":1},"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":"2026-08-18T06:34:40.430872+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 23 of 23 outbound references and 2 inbound Pith citation observations for arXiv:2411.15943."}