{"as_of":"2026-08-18T16:38:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:20c6acc70cb4ead7ecb8942df425cdb41448115d4a4bea5a2259dc2d4454e962","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":9,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":9,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+00:00","state":"measured"},{"denominator":9,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":9,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T19:11:30.216392Z","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":"2026-07-01T14:15:47.296036Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"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":{"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":"2026-08-11T15:08:07.702217Z","title":null,"venue":null,"work_id":null,"year":null},"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":10,"source":"pdf_text","source_observed_at":"2026-08-11T15:08:07.702217Z"},"links":{"cited_paper":"/paper/2108.06913","citing_paper":"/paper/2412.11397"},"observation_digest":"sha256:3b7284ddb016a576aaaf8dc52783fc1df593c6255cb365c1c39be30986b9636f","observation_id":"2186d5b8-8203-48de-b607-69d124b5377c","resolution":{"observed_at":"2026-08-11T15:08:07.702217Z","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":"2026-08-15T19:11:30.216392Z","title":"Kitazawa,Realization problems of graphs as Reeb graphs of Morse functions with pre- scribed preimages, submitted to a refereed journal, arXiv:2108.06913","venue":null,"work_id":null,"year":null},"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":11,"source":"pdf_text","source_observed_at":"2026-08-15T19:11:30.216392Z"},"links":{"cited_paper":"/paper/2108.06913","citing_paper":"/paper/2506.17791"},"observation_digest":"sha256:f39ae32c4722618934f65adbf20e52a061ea4506d4f73e8b723fe4f9db593719","observation_id":"b565334f-db2a-4315-b8a7-8f0f43c8b28a","resolution":{"observed_at":"2026-08-15T19:11:30.216392Z","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":"2108.06913","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2108.06913","snapshot_observed_at":"2026-07-01T14:15:47.296036Z","title":"Kitazawa,Constructing Morse functions with given Reeb graphs and level sets, accepted for publication in Topol","venue":null,"work_id":"be4a03dc-1d8d-4e7f-827b-7ee951710720","year":2025},"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":15,"source":"pdf_text","source_observed_at":"2026-05-10T18:57:35.894279Z"},"links":{"cited_paper":"/paper/2108.06913","citing_paper":"/paper/2604.04910"},"observation_digest":"sha256:15b21084c330194a2cda9b1cb17d9fd50f06ee6b1469a32a6a0d148962faa4ce","observation_id":"fc129e00-a312-4f25-9b5e-1ee84728fe1c","resolution":{"observed_at":"2026-05-10T23:40:51.401306Z","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":"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":"2108.06913","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2108.06913","snapshot_observed_at":"2026-07-01T14:15:47.296036Z","title":"Kitazawa,Constructing Morse functions with given Reeb graphs and level sets, accepted for publication in Topol","venue":null,"work_id":"be4a03dc-1d8d-4e7f-827b-7ee951710720","year":2025},"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":9,"source":"pdf_text","source_observed_at":"2026-05-13T04:42:51.554526Z"},"links":{"cited_paper":"/paper/2108.06913","citing_paper":"/paper/2605.12219"},"observation_digest":"sha256:1609fc889340847579f25c854c1d00c0303849dd5a6b6e5ace3e5a4b45b4c349","observation_id":"b77767b0-dd9c-48f7-b1f6-82a7eb8a93f5","resolution":{"observed_at":"2026-05-13T05:12:18.408466Z","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":"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":"2108.06913","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2108.06913","snapshot_observed_at":"2026-07-01T14:15:47.296036Z","title":"Kitazawa,Constructing Morse functions with given Reeb graphs and level sets, accepted for publication in Topol","venue":null,"work_id":"be4a03dc-1d8d-4e7f-827b-7ee951710720","year":2025},"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":9,"source":"pdf_text","source_observed_at":"2026-06-30T22:09:11.987811Z"},"links":{"cited_paper":"/paper/2108.06913","citing_paper":"/paper/2605.12219"},"observation_digest":"sha256:ec17fa313b8ad4221d07af856e5767b3b05bca3e5691cd8580c0672445c01716","observation_id":"665e19f4-a311-46b6-8261-91e12cf76e95","resolution":{"observed_at":"2026-07-01T14:15:47.297500Z","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":"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":"2026-07-11T17:12:07.354182Z","title":"Kitazawa,Constructing Morse functions with given Reeb graphs and level sets, accepted for publication in Topol","venue":null,"work_id":null,"year":2025},"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":11,"source":"pdf_text","source_observed_at":"2026-07-11T17:12:07.354182Z"},"links":{"cited_paper":"/paper/2108.06913","citing_paper":"/paper/2607.04565"},"observation_digest":"sha256:edc7ad8b60db1ee2df61e6db2fa301c703ddf70bf13522652ca8afdb7f2bd0da","observation_id":"ceba27a0-8b90-41eb-8a41-911c8e1d3fdf","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":"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":"2026-08-01T18:58:35.191467Z","title":"Kitazawa, Constructing Morse functions with given Reeb graphs and lev el sets , accepted for publication in Topol","venue":null,"work_id":null,"year":2025},"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":14,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:35.191467Z"},"links":{"cited_paper":"/paper/2108.06913","citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:8bc2c40e39c6163e7a3f13e885fbd0832e6110cb1d2d04443ed104b88aa7175f","observation_id":"99e94745-ffe6-43c7-acd4-7efcce6bd589","resolution":{"observed_at":"2026-08-01T18:58:35.191467Z","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":"2026-08-05T00:54:16.725125Z","title":"Kitazawa, Constructing Morse functions with given Reeb graphs and lev el sets , accepted for publication in Topol","venue":null,"work_id":null,"year":2025},"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":20,"source":"pdf_text","source_observed_at":"2026-08-05T00:54:16.725125Z"},"links":{"cited_paper":"/paper/2108.06913","citing_paper":"/paper/2608.00556"},"observation_digest":"sha256:1bf66ca92eda1802f282b1c894964320104be524fcf3e9ca83d98e7752c9d9d1","observation_id":"e167c158-d63a-4da3-8877-28e5efa14e5a","resolution":{"observed_at":"2026-08-05T00:54:16.725125Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2108.06913/citation-record","integrity":"/paper/2108.06913/integrity","json":"/paper/2108.06913/citation-record.json","paper":"/paper/2108.06913"},"outbound":[],"paper":{"arxiv_id":"2108.06913","last_updated":"2023-06-15T13:04:46Z","latest_version":4,"primary_category":"math.GN","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"},"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 9 inbound Pith citation observations for arXiv:2108.06913."}