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Paper Citation Record · LEDGER

Realization problems of graphs as Reeb graphs of Morse functions with prescribed preimages

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.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2108.06913 v4

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 9 of 9 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 9 of 9 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T19:11:30.216392Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-07-01T14:15:47.296036Z

Reference resolution

0 of 0 outbound references displayed

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External citation measurements

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Outbound references

No outbound reference observations are available for this paper version.

Pith citing papers

Observation 8c44caa0-8d7b-440f-b626-036953d4cb56 · inbound

On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one cites this paper.

On a classification of Morse functions on $3$-dimensional manifolds represented as connected sums of manifolds of Heegaard genus one Realization problems of graphs as Reeb graphs of Morse functions with prescribed preimages

Reference 11

Resolution
unresolved
no resolver link, observed 2026-08-12T13:48:56.176209Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-12T13:48:56.176209Z digest=sha256:4fb54a38bf069ad043c5098e1e8f1ae14d38483cb96cf4ae9d0836a12732dee7

Observation 2186d5b8-8203-48de-b607-69d124b5377c · inbound

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 cites this paper.

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 Realization problems of graphs as Reeb graphs of Morse functions with prescribed preimages

Reference 10

Resolution
unresolved
no resolver link, observed 2026-08-11T15:08:07.702217Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T15:08:07.702217Z digest=sha256:3b7284ddb016a576aaaf8dc52783fc1df593c6255cb365c1c39be30986b9636f

Observation b565334f-db2a-4315-b8a7-8f0f43c8b28a · inbound

Moment-like maps and real algebraic functions with prescribed preimages cites this paper.

Moment-like maps and real algebraic functions with prescribed preimages Realization problems of graphs as Reeb graphs of Morse functions with prescribed preimages

Reference 11

Resolution
unresolved
no resolver link, observed 2026-08-15T19:11:30.216392Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T19:11:30.216392Z digest=sha256:f39ae32c4722618934f65adbf20e52a061ea4506d4f73e8b723fe4f9db593719

Observation fc129e00-a312-4f25-9b5e-1ee84728fe1c · inbound

Morse functions with regular level sets consisting of $2$-dimensional spheres, $2$-dimensional tori, or Klein Bottles cites this paper.

Morse functions with regular level sets consisting of $2$-dimensional spheres, $2$-dimensional tori, or Klein Bottles Realization problems of graphs as Reeb graphs of Morse functions with prescribed preimages

Reference 15

Resolution
verified exact
arxiv_id, observed 2026-05-10T23:40:51.401306Z

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.

source=pdf_text observed=2026-05-10T18:57:35.894279Z digest=sha256:15b21084c330194a2cda9b1cb17d9fd50f06ee6b1469a32a6a0d148962faa4ce

Observation b77767b0-dd9c-48f7-b1f6-82a7eb8a93f5 · inbound

Representations of Reeb spaces via simplified graphs and examples cites this paper.

Representations of Reeb spaces via simplified graphs and examples Realization problems of graphs as Reeb graphs of Morse functions with prescribed preimages

Reference 9

Resolution
verified exact
arxiv_id, observed 2026-05-13T05:12:18.408466Z

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.

source=pdf_text observed=2026-05-13T04:42:51.554526Z digest=sha256:1609fc889340847579f25c854c1d00c0303849dd5a6b6e5ace3e5a4b45b4c349

Observation 665e19f4-a311-46b6-8261-91e12cf76e95 · inbound

Representations of Reeb spaces via simplified graphs and examples cites this paper.

Representations of Reeb spaces via simplified graphs and examples Realization problems of graphs as Reeb graphs of Morse functions with prescribed preimages

Reference 9

Resolution
verified exact
arxiv_id, observed 2026-07-01T14:15:47.297500Z

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.

source=pdf_text observed=2026-06-30T22:09:11.987811Z digest=sha256:ec17fa313b8ad4221d07af856e5767b3b05bca3e5691cd8580c0672445c01716

Observation ceba27a0-8b90-41eb-8a41-911c8e1d3fdf · inbound

Compactifying real analytic functions and resulting Reeb spaces cites this paper.

Compactifying real analytic functions and resulting Reeb spaces Realization problems of graphs as Reeb graphs of Morse functions with prescribed preimages

Reference 11

Resolution
unresolved
no resolver link, observed 2026-07-11T17:12:07.354182Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-07-11T17:12:07.354182Z digest=sha256:edc7ad8b60db1ee2df61e6db2fa301c703ddf70bf13522652ca8afdb7f2bd0da

Observation 99e94745-ffe6-43c7-acd4-7efcce6bd589 · 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 Realization problems of graphs as Reeb graphs of Morse functions with prescribed preimages

Reference 14

Resolution
unresolved
no resolver link, observed 2026-08-01T18:58:35.191467Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T18:58:35.191467Z digest=sha256:8bc2c40e39c6163e7a3f13e885fbd0832e6110cb1d2d04443ed104b88aa7175f

Observation e167c158-d63a-4da3-8877-28e5efa14e5a · 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 Realization problems of graphs as Reeb graphs of Morse functions with prescribed preimages

Reference 20

Resolution
unresolved
no resolver link, observed 2026-08-05T00:54:16.725125Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-05T00:54:16.725125Z digest=sha256:1bf66ca92eda1802f282b1c894964320104be524fcf3e9ca83d98e7752c9d9d1