Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-05T00:54:17.047306Z
Paper Citation Record · LEDGER
As of 13 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 0 inbound Pith citation observations for arXiv:2608.00556.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-05T00:54:17.047306Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
49 of 49 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation e8584070-7ed4-4784-9972-5c83fedde0f0 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Banyaga and D
Reference 1
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5d3a06ec-39cf-4590-8f7a-c81786a61041 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Banchoff and F
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 0147e878-477c-4ca4-83a2-760e1a53c07f · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Burlet and V
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation b79e3abb-cee9-4bb6-82c2-a7293056e89f · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Bott, Nondegenerate critical manifolds , Ann
Reference 4
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ca835993-5969-4a38-bcd9-993e9490208e · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 5e19cef3-8121-484c-b883-06f674dc27e7 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Burlet and G
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 89778b40-be1f-4efd-b6c9-a32ce320eaa7 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 43fbbb40-07ea-42d4-8b33-2ff92042d557 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives 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
Reference 8
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a4ed3d6c-44ce-487f-87f4-ac9242d20a1a · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Gelbukh, Morse-Bott functions with two critical values on a surface , Czechoslovak Mathe- matical Journal, 71 (3), 865–880, 2021; doi: 10.21136/CMJ
Reference 9
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 963b031d-7408-44aa-8790-ad88b791b275 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Gelbukh, Realization of a graph as the Reeb graph of a height function o n an embedded surface, Topol
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 69a85b87-1620-4d8b-95af-2a6d4a6d1e7d · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Gelbukh, On the topology of the Reeb graph , Publicationes Mathematicae Debrecen 104(3–
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation e2251e1b-0f81-4bbb-a04a-e2db61f16658 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Gelbukh, Realization of a digraph as the Reeb graph of a Morse-Bott fun ction on a given surface, Topology and its Applications, 2024
Reference 12
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 563387ff-6070-4d5f-bbd6-479d755ea6ea · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives 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
Reference 13
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 8d55b1e2-28f1-4454-b316-612ab3fcf19f · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 82605845-16aa-4db4-89b9-d5527f3f0c37 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Golubitsky and V
Reference 15
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a5c30dc0-a66d-4ab1-af7f-2777d73f0177 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work
Reference 16
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 25dea9b2-7d08-407b-baa3-58ab36094df2 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values
Reference 17
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d4a3b6e0-0d81-40bf-ae2f-ad35a2329ec2 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives On Reeb graphs induced from smooth functions on closed or open manifolds
Reference 18
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0f8ead0f-b7bb-4df8-a540-ae1b4d4afbb4 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Real algebraic functions on closed manifolds whose Reeb spaces are given graphs
Reference 19
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e167c158-d63a-4da3-8877-28e5efa14e5a · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Realization problems of graphs as Reeb graphs of Morse functions with prescribed preimages
Reference 20
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6ec27fd1-de96-4a0b-9da2-606714af954b · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Reconstructing real algebraic maps locally like moment-maps with prescribed images and compositions with the canonical projections to the $1$-dimensional real affine space
Reference 21
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 40703d07-9ce5-4642-bacf-c546e69c5d52 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Some remark on real algebraic maps which are topologically special generic maps and generalize the canonical projections of the unit spheres
Reference 22
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 64fb4e93-a10e-4c0f-bd7e-bcd2450267a4 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work
Reference 23
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3fb814f6-cb3f-411c-9291-d460e7c39494 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives 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
Reference 24
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c3ca4fb5-96b6-464e-9652-3f411e29625f · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Regions represented as foliated forms and natural smooth maps onto them
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation c14033b5-e6dd-4074-8dae-9c2f6d178c22 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work
Reference 26
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 202d5e83-e071-4a28-a670-28eab3a446c7 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Martinez-Alfaro, I
Reference 27
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 37ef1885-c803-462a-b8d5-fc5faf56922e · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Masumoto and O
Reference 28
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c4253306-5c6d-43ad-810d-8e85c3b41d59 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives N Mather, Stability of C∞ mappings
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 9b511d86-c346-4bfd-98de-684683188e4c · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation b9c72295-e211-4335-bc9d-b57615126db9 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 1a3a6a9d-2ef2-435a-891d-50826283d9ab · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 24a45bc1-332f-49cb-9df1-bf4c023b5965 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 1c2b0c48-01f8-4a69-a000-a0cf0b780c29 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 29433566-c28b-4599-ae78-c712cbb5070a · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation f6080977-5c33-4fe4-b0a8-b3495cc054c6 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Mather, Notes on topological stability , Bull
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 719236fb-8068-4ec7-86be-65597ec51c18 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Realization of a graph as the Reeb graph of a Morse function on a manifold
Reference 37
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation da1fbe2a-7b74-420f-a84d-400b9e309c74 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Milnor, Morse Theory , Annals of Mathematic Studies AM-51, Princeton University Press; 1st Edition (1963.5.1)
Reference 38
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Unavailable: canonical work link unavailable.
Observation 8f2c1365-65b5-4431-b5fc-74e069db44c5 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Milnor, Lectures on the h-cobordism theorem , Math
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation c8932ef7-b193-4fee-8297-12fefe3896aa · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Morishita and O
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 5fc54445-424e-491d-b92e-fe8431715269 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work
Reference 41
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4e420f73-c8ba-47b4-8b0a-e2c9aa22c61b · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Saeki, Notes on the topology of folds , J
Reference 42
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 52c98521-acc9-4762-ad0f-c948e8543e3b · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Saeki, Topology of special generic maps of manifolds into Euclidea n spaces, Topology Appl
Reference 43
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c9482f1b-ed65-4c49-848b-5146fcad1bb3 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Saeki, Topology of singular fibers of differentiable maps , Lecture Notes in Math., Vol
Reference 44
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b8a750d7-7be9-41b8-b7fc-4df79261a713 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Unresolved cited work
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation a7c7dd44-499a-441e-9014-8c9191a96e44 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Saeki, Reeb spaces of smooth functions on manifolds II , Res
Reference 46
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9fbb6d04-a343-413d-b967-69b9c20dd7eb · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Sharko, About Kronrod-Reeb graph of a function on a manifold , Methods of Functional Analysis and Topology 12 (2006), 389–396
Reference 47
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 27f67d91-8329-41aa-b1e3-13ad555b6f8e · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Thom, Les singularites des applications differentiables , Ann
Reference 48
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1ad9c0c5-39f0-49a3-8baf-5546be47fc18 · outbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives Whitney, On singularities of mappings of Euclidean spaces: I, mappin gs of the plane into the plane , Ann
Reference 49
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
No inbound Pith citation observations are available.