Paper Citation Record · LEDGER

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

As of 13 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 1 inbound Pith citation observation for arXiv:2412.11397.

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

pith.paper-citation-record.v1
2412.11397 v2

Coverage vector

measured 20 of 20 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T15:08:07.741148Z

measured 21 of 21 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-10T18:57:35.894279Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-10T23:40:51.417671Z

Reference resolution

20 of 20 outbound references displayed

verified exact1
verified fuzzy5
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External citation measurements

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Outbound references

Observation f821bf07-ec5c-40f6-ae50-4e28b3eb71ee · outbound

This paper cites 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.

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 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 1

Resolution: malformed identifier; no resolver link, observed 2026-08-11T15:08:07.662206Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e70e7a27-98ce-4712-96b3-7deb1d307532 · outbound

This paper cites Gelbukh, Morse-Bott functions with two critical values on a surface , Czechoslovak Mathe- matical Journal, 71 (3), 865–880, 2021; doi: 10.21136/CMJ.

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 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 2

Resolution: malformed identifier; no resolver link, observed 2026-08-11T15:08:07.667459Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5fee5e35-e794-405f-98d4-28e81c75fcc2 · outbound

This paper cites Gelbukh, Criterion for a graph to admit a good orientation in terms of l eaf blocks, Monatsh.

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 Gelbukh, Criterion for a graph to admit a good orientation in terms of l eaf blocks, Monatsh

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:08:08.127969Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 3ab30821-68c0-4e2b-845d-0cb218e420d3 · outbound

This paper cites Gelbukh, Realization of a digraph as the Reeb graph of a Morse-Bott fun ction on a given surface, Topology and its Applications, 2024.

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 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 4

Resolution: unresolved; no resolver link, observed 2026-08-11T15:08:07.675941Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 183e9603-1514-40cd-98ee-b718b9d26184 · outbound

This paper cites Gelbukh, Reeb Graphs of Morse-Bott Functions on a Given Surface , Bulletin of the Iranian Mathematical Society, Volume 50 Article number 84, 2024.

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 Gelbukh, Reeb Graphs of Morse-Bott Functions on a Given Surface , Bulletin of the Iranian Mathematical Society, Volume 50 Article number 84, 2024

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:08:08.107658Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 0aed5bea-07c3-4d60-95d2-2b555eeb43e1 · outbound

This paper cites Golubitsky and V.

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 Golubitsky and V

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-11T15:08:07.686414Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 381f0645-dc1a-4fc0-bbdc-dc28d05279a1 · outbound

This paper cites Hempel, 3- Manifolds , AMS Chelsea Publishing, 2004.

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 Hempel, 3- Manifolds , AMS Chelsea Publishing, 2004

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-11T15:08:07.690136Z

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Unavailable: canonical work link unavailable.

Observation 2e86fb1b-3e3c-425c-b337-2ca3253b852d · outbound

This paper cites Kitazawa, On Reeb graphs induced from smooth functions on 3-dimensional closed ori- entable manifolds with ﬁnitely many singular values , Topol.

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 Kitazawa, On Reeb graphs induced from smooth functions on 3-dimensional closed ori- entable manifolds with ﬁnitely many singular values , Topol

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:08:08.081730Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation be72341f-c77b-463a-ae79-eb9015fcf0ed · outbound

This paper cites Kitazawa, On Reeb graphs induced from smooth functions on 3-dimensional closed mani- folds which may not be orientable , Methods of Functional Analysis and Topology Vol.

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 Kitazawa, On Reeb graphs induced from smooth functions on 3-dimensional closed mani- folds which may not be orientable , Methods of Functional Analysis and Topology Vol

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-11T15:08:07.698147Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

This paper cites Realization problems of graphs as Reeb graphs of Morse functions with prescribed preimages.

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.

Observation eff49d91-fcfa-46f0-88d2-cdbe620dc521 · outbound

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

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

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-11T15:08:07.706376Z

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Observation f9255baa-31a8-4d11-ba63-d517567d7dee · outbound

This paper cites Marzantowicz and L.

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 Marzantowicz and L

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:08:08.062226Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d74b859a-112e-4e29-ac0e-b2faf74070da · outbound

This paper cites Realization of a graph as the Reeb graph of a Morse function on a manifold.

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 of a graph as the Reeb graph of a Morse function on a manifold

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-11T15:08:07.714448Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e0f48967-2702-46ca-8ea4-05eee4177e7d · outbound

This paper cites an unresolved cited work.

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 Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-11T15:08:07.718407Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b202aeb7-423c-4893-afa9-e2c66396e96f · outbound

This paper cites Reeb graph invariants of Morse functions and $3$-manifold groups.

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 Reeb graph invariants of Morse functions and $3$-manifold groups

Reference 15

Resolution: verified exact; local_arxiv, observed 2026-08-11T15:08:07.896740Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 649fc0f1-57d9-4515-81e4-57e0be40e2f0 · outbound

This paper cites Milnor, Lectures on the h-cobordism theorem , Math.

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 Milnor, Lectures on the h-cobordism theorem , Math

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-11T15:08:07.726129Z

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Observation ed8f55c7-3c31-4c77-8f96-3b1e397ed1ba · outbound

This paper cites an unresolved cited work.

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 Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-11T15:08:07.729834Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2368786c-97f2-436b-ac6c-bb54dbd8542b · outbound

This paper cites Saeki, Morse functions with sphere ﬁbers , Hiroshima Math.

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 Saeki, Morse functions with sphere ﬁbers , Hiroshima Math

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T15:08:08.029957Z

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No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation f8efd111-5fc3-4693-807c-cb9fdd6956c5 · outbound

This paper cites an unresolved cited work.

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 Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-11T15:08:07.737410Z

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Unavailable: canonical work link unavailable.

Observation 7b33a242-96d5-4faa-bcb1-a5c65974bb32 · outbound

This paper cites Saeki, Reeb spaces of smooth functions on manifolds II , Res.

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 Saeki, Reeb spaces of smooth functions on manifolds II , Res

Reference 20

Resolution: malformed identifier; raw_fallback, observed 2026-08-11T15:08:08.016509Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Pith citing papers

Observation 5437be9e-8ef6-4560-bbfb-b67d87dc9b9b · 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 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

Reference 21

Resolution: verified exact; arxiv_id, observed 2026-05-10T23:40:51.420919Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.