Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T13:57:08.860174Z
Paper Citation Record · LEDGER
On Reeb graphs induced from smooth functions on closed or open manifolds
As of 18 August 2026, this Paper Citation Record lists 14 of 14 outbound references and 5 inbound Pith citation observations for arXiv:1908.04340.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-05T00:54:16.362099Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-07-01T14:15:47.323082Z
Reference resolution
14 of 14 outbound references displayed
- verified exact2
- verified fuzzy3
- unresolved9
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 1730da2e-2cc9-4447-bbaa-51418db82d71 · outbound
This paper cites an unresolved cited work.
On Reeb graphs induced from smooth functions on closed or open manifolds Unresolved cited work
Reference 1
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T13:57:09.086076Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 1236c2b5-d276-4e8f-950d-b0ba0005a218 · outbound
This paper cites Bott, Nondegenerate critical manifolds , Ann.
On Reeb graphs induced from smooth functions on closed or open manifolds Bott, Nondegenerate critical manifolds , Ann
Reference 2
- Resolution
- unresolved
- no resolver link, observed 2026-08-14T13:57:08.802852Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 94e8ac51-fc80-4dcd-bc8a-7d9532bacf30 · outbound
This paper cites Golubitsky and V.
On Reeb graphs induced from smooth functions on closed or open manifolds Golubitsky and V
Reference 3
- Resolution
- unresolved
- no resolver link, observed 2026-08-14T13:57:08.806869Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a0bd4bbe-4d9d-4383-8a2a-2ef378bcbd7c · outbound
This paper cites Structures of cobordism-like modules induced from generic maps of codimension -2.
On Reeb graphs induced from smooth functions on closed or open manifolds Structures of cobordism-like modules induced from generic maps of codimension -2
Reference 4
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T13:57:08.973682Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 30d79fc1-6401-4975-8d40-d8972e409e84 · outbound
This paper cites On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values.
On Reeb graphs induced from smooth functions on closed or open manifolds On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values
Reference 5
- Resolution
- unresolved
- no resolver link, observed 2026-08-14T13:57:08.816445Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 25725a8b-b13e-49dc-9679-11027f2ad1b6 · outbound
This paper cites Martinez-Alfaro, I.
On Reeb graphs induced from smooth functions on closed or open manifolds Martinez-Alfaro, I
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:57:09.050229Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 19444d6a-ec37-4054-9957-5bebba317eee · outbound
This paper cites Masumoto and O.
On Reeb graphs induced from smooth functions on closed or open manifolds Masumoto and O
Reference 7
- Resolution
- unresolved
- no resolver link, observed 2026-08-14T13:57:08.827012Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 662effb3-0d24-4f5d-a6b1-59bd6523a662 · outbound
This paper cites Realization of a graph as the Reeb graph of a Morse function on a manifold.
On Reeb graphs induced from smooth functions on closed or open manifolds Realization of a graph as the Reeb graph of a Morse function on a manifold
Reference 8
- Resolution
- unresolved
- no resolver link, observed 2026-08-14T13:57:08.831521Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a9983687-fad2-4fe3-aa56-e53f7dc0067f · outbound
This paper cites Combinatorial modifications of Reeb graphs and the realization problem.
On Reeb graphs induced from smooth functions on closed or open manifolds Combinatorial modifications of Reeb graphs and the realization problem
Reference 9
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T13:57:08.919870Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 79263499-c3fb-4f5c-ab96-1b7301d2c972 · outbound
This paper cites Milnor, Lectures on the h-cobordism theorem , Math.
On Reeb graphs induced from smooth functions on closed or open manifolds Milnor, Lectures on the h-cobordism theorem , Math
Reference 10
- Resolution
- unresolved
- no resolver link, observed 2026-08-14T13:57:08.841478Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c5ffaa47-1775-43b6-9e74-32639a12df21 · outbound
This paper cites an unresolved cited work.
On Reeb graphs induced from smooth functions on closed or open manifolds Unresolved cited work
Reference 11
- Resolution
- unresolved
- no resolver link, observed 2026-08-14T13:57:08.845976Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4e5bb373-43a3-4e7c-b2db-7e97d1a58fd4 · outbound
This paper cites Saeki, Topology of special generic maps of manifolds into Euclidea n spaces , Topology Appl.
On Reeb graphs induced from smooth functions on closed or open manifolds Saeki, Topology of special generic maps of manifolds into Euclidea n spaces , Topology Appl
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:57:09.005321Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 38771057-fbaa-45ef-ac5c-e7b53c6d6e81 · outbound
This paper cites Reeb spaces of smooth functions on manifolds.
On Reeb graphs induced from smooth functions on closed or open manifolds Reeb spaces of smooth functions on manifolds
Reference 13
- Resolution
- unresolved
- no resolver link, observed 2026-08-14T13:57:08.855557Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d2c0c6c4-4f2f-4130-9d20-e8e9d383ec2a · outbound
This paper cites Sharko, About Kronrod-Reeb graph of a function on a manifold , Methods of Functional Analysis and Topology 12 (2006), 389–396.
On Reeb graphs induced from smooth functions on closed or open manifolds Sharko, About Kronrod-Reeb graph of a function on a manifold , Methods of Functional Analysis and Topology 12 (2006), 389–396
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T13:57:08.989880Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Pith citing papers
Observation f83a5702-ddb1-485a-aebf-e6970078b7a7 · inbound
Representations of Reeb spaces via simplified graphs and examples cites this paper.
Representations of Reeb spaces via simplified graphs and examples On Reeb graphs induced from smooth functions on closed or open manifolds
Reference 7
- Resolution
- verified exact
- arxiv_id, observed 2026-05-13T05:12:18.405768Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 52c6cf7a-c1f9-400c-b88d-9c5839894632 · inbound
Representations of Reeb spaces via simplified graphs and examples cites this paper.
Representations of Reeb spaces via simplified graphs and examples On Reeb graphs induced from smooth functions on closed or open manifolds
Reference 7
- Resolution
- verified exact
- arxiv_id, observed 2026-07-01T14:15:47.324583Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.
Observation 8f7d357a-77a0-4415-833e-1a6e71360056 · inbound
Compactifying real analytic functions and resulting Reeb spaces cites this paper.
Compactifying real analytic functions and resulting Reeb spaces On Reeb graphs induced from smooth functions on closed or open manifolds
Reference 9
- Resolution
- unresolved
- no resolver link, observed 2026-07-11T17:12:07.354182Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 946b64b2-bdde-40cf-a1c7-71c084a563f1 · inbound
Regions represented as foliated forms and natural smooth maps onto them cites this paper.
Regions represented as foliated forms and natural smooth maps onto them On Reeb graphs induced from smooth functions on closed or open manifolds
Reference 12
- Resolution
- unresolved
- no resolver link, observed 2026-08-01T18:58:34.939137Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d4a3b6e0-0d81-40bf-ae2f-ad35a2329ec2 · inbound
Fundamental examples of height functions on closed manifolds and their 1st derivatives cites this paper.
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
- Resolution
- unresolved
- no resolver link, observed 2026-08-05T00:54:16.362099Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.