{"as_of":"2026-08-13T14:30:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ffff5c9a7d7ba5fcb60c38ca59c18b77a072363da70e21dea284ea16dd1a13de","coverage":[{"denominator":30,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":30,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T18:58:37.350850Z","state":"measured"},{"denominator":31,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":31,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-13T06:32:02.005865+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T00:54:16.975440Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-05T00:54:17.255244Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_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},"cited_work":{"arxiv_id":"2607.17180","doi":null,"metadata_source":"pith","pith_arxiv_id":"2607.17180","snapshot_observed_at":"2026-08-05T00:54:17.255244Z","title":"Regions represented as foliated forms and natural smooth maps onto them","venue":"math.AG","work_id":"d7b64f80-3cd5-4bcf-b1d6-d6db296f4a60","year":2026},"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":25,"source":"pdf_text","source_observed_at":"2026-08-05T00:54:16.975440Z"},"links":{"cited_paper":"/paper/2607.17180","citing_paper":"/paper/2608.00556"},"observation_digest":"sha256:85054b533f2240f06e5a716cc0642e787fefba97d9a6c14b2b23d9a84124aaec","observation_id":"c3ca4fb5-96b6-464e-9652-3f411e29625f","resolution":{"observed_at":"2026-08-05T00:54:17.259564Z","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"}}],"links":{"evidence":"/evidence","html":"/paper/2607.17180/citation-record","integrity":"/paper/2607.17180/integrity","json":"/paper/2607.17180/citation-record.json","paper":"/paper/2607.17180"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T18:58:33.387291Z","title":null,"venue":null,"work_id":null,"year":null},"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":1,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:33.387291Z"},"links":{"citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:cf9aefe8878e9876391d61665744f6c3f4f9daad03d425bb6d3b8ab98af00036","observation_id":"155e32c1-b454-42a2-a417-321657c18eb7","resolution":{"observed_at":"2026-08-01T18:58:33.387291Z","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":"2026-08-01T18:58:33.501248Z","title":"Burlet and G","venue":null,"work_id":null,"year":1974},"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":2,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:33.501248Z"},"links":{"citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:109e5140117245ad0a20cb8d1b14b73070db8828d897a41ad34baa25b4c0bdc2","observation_id":"b95c29ad-065e-4ca6-ba71-966c0dfd15f3","resolution":{"observed_at":"2026-08-01T18:58:33.501248Z","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":"2026-08-01T18:58:33.597036Z","title":"Eliashberg, On singularities of folding type , Math","venue":null,"work_id":null,"year":1970},"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":3,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:33.597036Z"},"links":{"citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:c2083a5bf9a48968b51f6ae8906c7cc0d42d44ac81dbfca4b261b25dffc6d32f","observation_id":"248f1b41-e981-4292-909d-8cf0dd1edc30","resolution":{"observed_at":"2026-08-01T18:58:33.597036Z","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":"2026-08-01T18:58:33.805424Z","title":"Eliashberg, Surgery of singularities of smooth mappings , Math","venue":null,"work_id":null,"year":1972},"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":4,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:33.805424Z"},"links":{"citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:741f702d532d250d86edbd9c48780737fa9004cada6517bf4abdf6b466e352dc","observation_id":"16fdd3da-cb2a-4dd1-ace6-7c86243b8329","resolution":{"observed_at":"2026-08-01T18:58:33.805424Z","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":"2026-08-01T18:58:33.964199Z","title":null,"venue":null,"work_id":null,"year":1990},"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":5,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:33.964199Z"},"links":{"citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:8584a288f4c04a6912ee2519d55f0e0bc4fe672452940cc6fe70884177bbb76f","observation_id":"0efe6c52-3906-4802-b5ee-80cd5e8be3d4","resolution":{"observed_at":"2026-08-01T18:58:33.964199Z","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":"10.1515/m","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T19:03:29.449329Z","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":"80bbd208-97ee-4ee3-aa4d-24b7732bbcba","year":2021},"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":6,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:34.096646Z"},"links":{"citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:523771d1438562ba0005d4ba71ab93aa0ccbf1d9615c3897d4ffc2421211664a","observation_id":"16db8194-fb2b-4cd9-a823-95884c75ebe6","resolution":{"observed_at":"2026-08-01T19:03:29.506227Z","resolver_source":"doi_truncated","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":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T18:58:34.198358Z","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":"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":7,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:34.198358Z"},"links":{"citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:aa5e8bb4b4e9e84847c12bb443f9ed0e47f3025a91b52d83c7c7378f1982e3fd","observation_id":"483254df-f65e-4edd-84e0-0ce07adecf7d","resolution":{"observed_at":"2026-08-01T18:58:34.198358Z","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":"2026-08-01T18:58:34.353802Z","title":"Gelbukh, On the topology of the Reeb graph , Publicationes Mathematicae Debrecen 104(3–","venue":null,"work_id":null,"year":null},"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":8,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:34.353802Z"},"links":{"citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:020a92546d8e559e9dfe1eaf029524c4e486901f9ba1834c423ea814a4b9d578","observation_id":"a46f6577-34b9-4c5a-a0e4-ca39fcdc89ff","resolution":{"observed_at":"2026-08-01T18:58:34.353802Z","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":"2026-08-01T18:58:34.541864Z","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":"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":9,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:34.541864Z"},"links":{"citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:de3399670b50a3e9f87e1a1c61270b05fa2d2593f3c0c9a1523690ec37b3d4ea","observation_id":"c32eae17-b4a9-435d-9d73-08befe156795","resolution":{"observed_at":"2026-08-01T18:58:34.541864Z","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":"2026-08-01T18:58:34.662042Z","title":"Gelbukh, Reeb Graphs of Morse-Bott Functions on a Given Surface , Bulletin of the Iranian Mathematical Society, Volume 50 Article number 84, 2024, 1– 17","venue":null,"work_id":null,"year":2024},"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":10,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:34.662042Z"},"links":{"citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:0974cb5fed89184661f46e39333fb0d93881c0f0059fdf187b2b344b6c49b2c7","observation_id":"a8e7c155-257e-499b-9e68-f2e46ad96eb2","resolution":{"observed_at":"2026-08-01T18:58:34.662042Z","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":"2026-08-13T02:51:22.471449Z","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":"sha256:83cd3858393b95be4b6b4fe72e26d8652661f23db75fafc0e08ae0442dfd65ef","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":"1908.04340","last_updated":"2022-03-25T10:19:39Z","snapshot_observed_at":"2026-08-13T13:30:04.387820Z","submitted_at":"2019-08-12T19:11:23Z","title":"On Reeb graphs induced from smooth functions on closed or open manifolds","version":8},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1908.04340","snapshot_observed_at":"2026-08-01T18:58:34.939137Z","title":"Kitazawa, On Reeb graphs induced from smooth functions on closed or ope n sur- faces, Methods of Functional Analysis and Topology Vol","venue":null,"work_id":null,"year":1908},"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":12,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:34.939137Z"},"links":{"cited_paper":"/paper/1908.04340","citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:8c2d82c6a462c0dc82bebe7f60e749315669ec6075e139cf4ea5bd5a5fc6dc84","observation_id":"946b64b2-bdde-40cf-a1c7-71c084a563f1","resolution":{"observed_at":"2026-08-01T18:58:34.939137Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2302.02339","last_updated":"2023-02-19T13:58:00Z","snapshot_observed_at":"2026-08-13T12:50:45.488191Z","submitted_at":"2023-02-05T09:01:31Z","title":"Real algebraic functions on closed manifolds whose Reeb spaces are given graphs","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2302.02339","snapshot_observed_at":"2026-08-01T18:58:35.070793Z","title":"Kitazawa, Real algebraic functions on closed manifolds whose Reeb gra phs are given graphs, Methods of Functional Analysis and Topology Vol","venue":null,"work_id":null,"year":2023},"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":13,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:35.070793Z"},"links":{"cited_paper":"/paper/2302.02339","citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:9f30d12e2c7408ee380ace944c9527dac253817a12b7d42a5d5acd652951ca22","observation_id":"d7695997-8aed-40e1-9ad2-1203a0f00f01","resolution":{"observed_at":"2026-08-01T18:58:35.070793Z","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":"2026-07-06T11:38:32.437113Z","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":"sha256:4938624b57aec386d2d3b4774a5f22de80c7bababcd64a15a65ad996867578d2","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":"2303.10723","last_updated":"2024-09-15T06:55:00Z","snapshot_observed_at":"2026-08-13T12:21:51.108545Z","submitted_at":"2023-03-19T17:40:33Z","title":"Reconstructing real algebraic maps locally like moment-maps with prescribed images and compositions with the canonical projections to the $1$-dimensional real affine space","version":8},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2303.10723","snapshot_observed_at":"2026-08-01T18:58:35.299919Z","title":null,"venue":null,"work_id":null,"year":null},"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":15,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:35.299919Z"},"links":{"cited_paper":"/paper/2303.10723","citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:37e2ffd8d8cdf467e4293d96f034df31c8635051ce393978a3b3b45b7909071f","observation_id":"85896afb-be26-4d25-9c26-ec98efc35389","resolution":{"observed_at":"2026-08-01T18:58:35.299919Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2312.10646","last_updated":"2025-03-27T06:41:16Z","snapshot_observed_at":"2026-08-13T05:00:09.431995Z","submitted_at":"2023-12-17T08:12:55Z","title":"Some remark on real algebraic maps which are topologically special generic maps and generalize the canonical projections of the unit spheres","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.10646","snapshot_observed_at":"2026-08-01T18:58:35.462916Z","title":"Kitazawa, Some remark on real algebraic maps which are topologically s pecial generic maps and generalize the canonical projections of the unit sp heres, arXiv:2312.10646, 2024","venue":null,"work_id":null,"year":2024},"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":16,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:35.462916Z"},"links":{"cited_paper":"/paper/2312.10646","citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:cd386c2ac1aff553dafc42d2a53c13e18560a005074ed3b9ac5d3dbe8224cbf2","observation_id":"a5bdd1cb-771c-4d7a-9ec0-6ada92e9c3af","resolution":{"observed_at":"2026-08-01T18:58:35.462916Z","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":"2026-08-01T18:58:35.579331Z","title":null,"venue":null,"work_id":null,"year":2026},"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":17,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:35.579331Z"},"links":{"citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:cc471c72823856ae645a6afb2b7e0843c8744e40cf3fb15177647346d452ed51","observation_id":"d64b800b-c07c-4b79-bb10-e69d73f5dd3f","resolution":{"observed_at":"2026-08-01T18:58:35.579331Z","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":"2026-08-01T18:58:35.682987Z","title":"Kitazawa, Fundamental examples of Reeb spaces of smooth functions deﬁ ned from two graphs of smooth functions with same asymptotic behaviors , arXiv:2602.17014, 2026/2","venue":null,"work_id":null,"year":2026},"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":18,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:35.682987Z"},"links":{"citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:afb4b71b8682fae4b86dd319a635d4f2e614c4c177d70c561cd2235ed7b37e8a","observation_id":"ce7bdaea-19db-43cd-ad0d-d43481f0ea22","resolution":{"observed_at":"2026-08-01T18:58:35.682987Z","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":"2026-08-01T18:58:35.849513Z","title":"Kitazawa, Reeb spaces of functions being analytic on dense subsets and their graph struc- tures, arXiv:2602.23380","venue":null,"work_id":null,"year":null},"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":19,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:35.849513Z"},"links":{"citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:e46e80062559bf481f39a61cc8d50a88ce70734175e234cc85a242e497971a10","observation_id":"5232ece3-bd6e-4e2f-aec7-3e54654cb873","resolution":{"observed_at":"2026-08-01T18:58:35.849513Z","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":"2026-08-01T18:58:35.929109Z","title":"Kitazawa, Reeb spaces of smooth functions associated to globally simi lar graphs of smooth functions, arXiv:2603.02791","venue":null,"work_id":null,"year":null},"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":20,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:35.929109Z"},"links":{"citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:41284465f6ab75aa140b75d52573ea92ca8389bfc1078fd1581dd596b7805204","observation_id":"a31663fd-a153-4b24-8272-800461c6302e","resolution":{"observed_at":"2026-08-01T18:58:35.929109Z","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":"2026-08-01T18:58:36.047389Z","title":"Masumoto and O","venue":null,"work_id":null,"year":2011},"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":21,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:36.047389Z"},"links":{"citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:a853d2c0d6e40dbbe1ddfebcdc5e1983fdc9de142ec655a53458e7a335cde6b5","observation_id":"6a3218b7-46bd-4037-aa13-2d1a6826bfe9","resolution":{"observed_at":"2026-08-01T18:58:36.047389Z","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":"2026-08-02T14:25:22.727238Z","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":"2026-08-01T18:58:36.217443Z","title":null,"venue":null,"work_id":null,"year":2018},"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":22,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:36.217443Z"},"links":{"cited_paper":"/paper/1805.06727","citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:ca7a849c1531c42de03e9c274e1d54c73706ae902bdc69b785c43b2125bc3a66","observation_id":"967873e8-70a7-4cbc-b3f4-7d1050100e11","resolution":{"observed_at":"2026-08-01T18:58:36.217443Z","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":"2026-08-01T18:58:36.315899Z","title":"Milnor, Morse Theory , Annals of Mathematic Studies AM-51, Princeton University Press; 1st Edition (1963.5.1)","venue":null,"work_id":null,"year":1963},"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":23,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:36.315899Z"},"links":{"citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:24658a2a50395563977dd3c27e34f69522a873ca6cbe26e08d89705e678ecca9","observation_id":"fc1ba694-f1d6-4582-aa4c-2a498f1c7397","resolution":{"observed_at":"2026-08-01T18:58:36.315899Z","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":"2026-08-01T18:58:36.466931Z","title":"Milnor, Lectures on the h-cobordism theorem , Math","venue":null,"work_id":null,"year":1965},"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":24,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:36.466931Z"},"links":{"citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:34f37dbea09a9dfd59c208af444e88f174bb2ec4cca06a9670fa6b26a8643439","observation_id":"25b6ac64-9158-47d7-a1e5-d8933f7d4b5f","resolution":{"observed_at":"2026-08-01T18:58:36.466931Z","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":"2026-08-01T18:58:36.603457Z","title":null,"venue":null,"work_id":null,"year":1946},"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":25,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:36.603457Z"},"links":{"citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:6707173f18f9aa2e8e30ebb3239d426b3277a656d5471788be9194265cea24b6","observation_id":"f33a3a8f-8088-4d18-985e-8d4bf9c70245","resolution":{"observed_at":"2026-08-01T18:58:36.603457Z","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":"2026-08-01T18:58:36.796481Z","title":"Saeki, Notes on the topology of folds , J","venue":null,"work_id":null,"year":1992},"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":26,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:36.796481Z"},"links":{"citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:d7720aef58f16521670269609fb16ed16bd9ae3e8dec2212d4458d23b0ac930f","observation_id":"029071f8-5f80-4632-a900-ea6a6788faed","resolution":{"observed_at":"2026-08-01T18:58:36.796481Z","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":"2026-08-01T18:58:36.929792Z","title":"Saeki, Topology of special generic maps of manifolds into Euclidea n spaces, Topology Appl","venue":null,"work_id":null,"year":1993},"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":27,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:36.929792Z"},"links":{"citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:1671f83dd9dcf597c079e92a5eae51e109123510e6b17b11464b73dfd68cdbb8","observation_id":"112ff211-6ecc-4da6-b9c4-aecca3c7c0d1","resolution":{"observed_at":"2026-08-01T18:58:36.929792Z","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":"2026-08-01T18:58:37.048310Z","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":null,"year":2006},"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":28,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:37.048310Z"},"links":{"citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:ee571383ea312b8ae7eee33cf38f20248219bd4a60574d64340ed8e5976e4fd1","observation_id":"ea6f76a2-1908-43a8-85f2-c81ea384ea22","resolution":{"observed_at":"2026-08-01T18:58:37.048310Z","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":"2026-08-01T18:58:37.183397Z","title":"Thom, Les singularites des applications diﬀerentiables , Ann","venue":null,"work_id":null,"year":1955},"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":29,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:37.183397Z"},"links":{"citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:da7c3b9a45347fd55c72cfb2f5212e3cbcf74830cda17f22a4f513f54689a9a2","observation_id":"1ed4a136-71d0-41a4-9efb-2b8ae2436a06","resolution":{"observed_at":"2026-08-01T18:58:37.183397Z","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":"2026-08-01T18:58:37.350850Z","title":"Whitney, On singularities of mappings of Euclidean spaces: I, mappin gs of the plane into the plane , Ann","venue":null,"work_id":null,"year":1955},"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":30,"source":"pdf_text","source_observed_at":"2026-08-01T18:58:37.350850Z"},"links":{"citing_paper":"/paper/2607.17180"},"observation_digest":"sha256:33f0d20a0890a419f0d1126b30edde73fa06bcb293bd8e227aaced5af8692f30","observation_id":"f0eca82a-49b5-46c7-8bea-a30a27b00840","resolution":{"observed_at":"2026-08-01T18:58:37.350850Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.17180","last_updated":"2026-07-27T08:31:17Z","latest_version":2,"primary_category":"math.AG","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"},"reference_resolution":{"displayed":30,"state_counts":{"malformed_identifier":2,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":28,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":30},"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 30 of 30 outbound references and 1 inbound Pith citation observation for arXiv:2607.17180."}