Paper Citation Record · LEDGER

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs

As of 13 August 2026, this Paper Citation Record lists 36 of 36 outbound references and 1 inbound Pith citation observation for arXiv:2507.09467.

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

pith.paper-citation-record.v1
2507.09467 v2

Coverage vector

measured 36 of 36 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T18:03:34.927618Z

measured 37 of 37 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T06:13:19.840655Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-06T06:13:21.933272Z

Reference resolution

36 of 36 outbound references displayed

verified exact4
verified fuzzy16
unresolved15
parse uncertain0
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External citation measurements

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Outbound references

Observation 2e07a6b6-03de-401c-a471-f5f3a5cca903 · outbound

This paper cites Bochnak, M.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Bochnak, M

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:03:40.441085Z

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 3093c57a-7ec9-4a38-8389-ba689dece929 · outbound

This paper cites Poincar\'e-Reeb graphs of real algebraic domains.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Poincar\'e-Reeb graphs of real algebraic domains

Reference 2

Resolution: malformed identifier; no resolver link, observed 2026-08-06T18:03:31.308443Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b2c1d864-4181-44e9-94ce-d5f0d921789f · outbound

This paper cites Bott, Nondegenerate critical manifolds , Ann.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Bott, Nondegenerate critical manifolds , Ann

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-06T18:03:31.397931Z

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Unavailable: canonical work link unavailable.

Observation d9441290-12d8-4624-9e40-6964d36cee69 · outbound

This paper cites Curley, Non-singular extensions of Morse functions , Topology (1) 16 (1977), 89–97.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Curley, Non-singular extensions of Morse functions , Topology (1) 16 (1977), 89–97

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:03:40.283983Z

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Observation 196d9c77-865d-436b-ac82-4152405ccc1c · outbound

This paper cites Normal forms of functions with degenerate singularities on surfaces equipped with semi-free circle actions.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Normal forms of functions with degenerate singularities on surfaces equipped with semi-free circle actions

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-08-06T18:03:36.373306Z

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Observation e0919b5e-3373-4761-b653-78968436ab08 · outbound

This paper cites The book of abstracts.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs The book of abstracts

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:03:40.041881Z

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 995f2500-7913-4799-a617-9fa0e6ac6bee · outbound

This paper cites Gelbukh, A finite graph is homeomorphic to the Reeb graph of a Morse-Bott function , Mathematica Slovaca, 71 (3), 757–772, 2021; doi: 10.1515/ms-2021-0018.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Gelbukh, A finite graph is homeomorphic to the Reeb graph of a Morse-Bott function , Mathematica Slovaca, 71 (3), 757–772, 2021; doi: 10.1515/ms-2021-0018

Reference 7

Resolution: verified exact; doi, observed 2026-08-06T18:03:35.157031Z

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Observation ed458355-4887-4dc5-8587-bf8cf08baeaf · 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.2021.0125-20.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Gelbukh, Morse-Bott functions with two critical values on a surface , Czechoslovak Mathe- matical Journal, 71 (3), 865–880, 2021; doi: 10.21136/CMJ.2021.0125-20

Reference 8

Resolution: verified exact; raw_fallback, observed 2026-08-06T18:03:36.092864Z

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Observation 5b4e2b65-aeb1-4b10-8f1f-60b0a0eb42ee · outbound

This paper cites Gelbukh, A finite graph is the Reeb graph of a Morse circle-valued function , Filomat 37 (11), 3575–3590, 2023.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Gelbukh, A finite graph is the Reeb graph of a Morse circle-valued function , Filomat 37 (11), 3575–3590, 2023

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:03:39.849350Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d424b09e-216f-479f-a51c-815f7080e44a · outbound

This paper cites Gelbukh, Reeb graphs of circle-valued functions: A survey and basic facts , Topological Methods in Nonlinear Analysis 61 (1): 59–81, 2023.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Gelbukh, Reeb graphs of circle-valued functions: A survey and basic facts , Topological Methods in Nonlinear Analysis 61 (1): 59–81, 2023

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:03:39.665033Z

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Observation 9e40ad46-d892-4eca-afc6-fd0530698a35 · outbound

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

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Gelbukh, Realization of a digraph as the Reeb graph of a Morse-Bott function on a given surface, Topology and its Applications, 2024

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:03:39.505751Z

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Observation 4fd33264-e21c-4003-a997-ea6856446fe1 · 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.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Gelbukh, Reeb Graphs of Morse-Bott Functions on a Given Surface, Bulletin of the Iranian Mathematical Society, Volume 50 Article number 84, 2024

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:03:39.378075Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d016f390-441b-4e9a-ba60-14b366eecc96 · outbound

This paper cites Golubitsky and V.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Golubitsky and V

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-06T18:03:32.279825Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3f555993-3094-4a2e-a688-26cb546e223a · outbound

This paper cites Hirsch, Smooth regular neighborhoods , Ann.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Hirsch, Smooth regular neighborhoods , Ann

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:03:39.246519Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation dddb0c28-93ee-47f8-9d0c-3e1672ffc42b · outbound

This paper cites Non-singular extensions of circle-valued Morse functions.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Non-singular extensions of circle-valued Morse functions

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-06T18:03:32.480959Z

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Unavailable: canonical work link unavailable.

Observation 6a0d15d7-77b9-4f8c-a1ad-c28e75683a6f · outbound

This paper cites On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-06T18:03:32.594906Z

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Observation bf42007d-cf61-4b94-a486-ed81891f7186 · outbound

This paper cites Real algebraic functions on closed manifolds whose Reeb spaces are given graphs.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Real algebraic functions on closed manifolds whose Reeb spaces are given graphs

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-06T18:03:32.754378Z

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Observation cfe665ef-fa2b-46b2-947e-57c046a12e2f · outbound

This paper cites The book of abstracts.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs The book of abstracts

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:03:39.131992Z

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Observation 0a226cdc-9fa9-4fee-bb40-845ff6691e3d · outbound

This paper cites Construction of real algebraic functions with prescribed preimages.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Construction of real algebraic functions with prescribed preimages

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-08-06T18:03:35.600999Z

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Observation 242b942a-4381-414d-9634-81b90328f525 · outbound

This paper cites Reconstructing real algebraic maps locally like moment-maps with prescribed images and compositions with the canonical projections to the $1$-dimensional real affine space.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs 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 20

Resolution: unresolved; no resolver link, observed 2026-08-06T18:03:33.130528Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 864d2c0c-2f6e-49a1-baea-e8eede7c51c4 · outbound

This paper cites Some remark on real algebraic maps which are topologically special generic maps and generalize the canonical projections of the unit spheres.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Some remark on real algebraic maps which are topologically special generic maps and generalize the canonical projections of the unit spheres

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-06T18:03:33.234509Z

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Unavailable: canonical work link unavailable.

Observation 2875da2e-4010-4da9-bdef-a9ef6a1bb8a1 · outbound

This paper cites an unresolved cited work.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:03:38.882902Z

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Observation c9257ab2-e15a-4560-b5ad-941b79619c7a · outbound

This paper cites Koll´ ar,Nash’s work in algebraic geometry , Bulletin (New Series) of the American Matem- atical Society (2) 54, 2017, 307–324.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Koll´ ar,Nash’s work in algebraic geometry , Bulletin (New Series) of the American Matem- atical Society (2) 54, 2017, 307–324

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-06T18:03:33.454951Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d2788270-b051-4fec-b5ec-7c0cd1e45d6e · outbound

This paper cites The masterpieces of John Forbes Nash Jr.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs The masterpieces of John Forbes Nash Jr

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-06T18:03:33.553779Z

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Observation 805c681d-c81f-4d6c-8abe-febfcfc2b34c · outbound

This paper cites Masumoto and O.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Masumoto and O

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:03:38.603390Z

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 da30aafa-e4af-45a1-b705-49b35bf548f1 · outbound

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

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Realization of a graph as the Reeb graph of a Morse function on a manifold

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-06T18:03:33.851174Z

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Unavailable: canonical work link unavailable.

Observation e865546a-d32a-49f9-9823-b7954ba7d185 · outbound

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

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Milnor, Lectures on the h-cobordism theorem, Math

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:03:38.343637Z

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Observation 9dae053a-5c64-4bdf-a723-b26b929c6394 · outbound

This paper cites Milnor and J.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Milnor and J

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:03:38.116413Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 05707d11-d84d-4f3d-a491-51ea69f42300 · outbound

This paper cites Nash, Real algbraic manifolds , Ann.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Nash, Real algbraic manifolds , Ann

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-06T18:03:34.241093Z

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Observation 7d9910ff-4de1-4b8a-bb26-0c7cd625eb22 · outbound

This paper cites an unresolved cited work.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-06T18:03:37.796974Z

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Observation 623e36a2-ff28-420c-b3e9-0d4222f87dc2 · outbound

This paper cites Saeki, Topology of special generic maps of manifolds into Euclidean spaces , Topology Appl.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Saeki, Topology of special generic maps of manifolds into Euclidean spaces , Topology Appl

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:03:37.467071Z

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Observation 716d6dee-6fae-491d-99b8-87649a83560f · outbound

This paper cites Reeb spaces of smooth functions on manifolds.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Reeb spaces of smooth functions on manifolds

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-06T18:03:34.526572Z

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Observation e162fdd4-ce07-47ba-856e-9be821ab952d · 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.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Sharko, About Kronrod-Reeb graph of a function on a manifold , Methods of Functional Analysis and Topology 12 (2006), 389–396

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-06T18:03:34.608787Z

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Unavailable: canonical work link unavailable.

Observation a7d2db34-716c-4514-b484-be02737ddc7b · outbound

This paper cites Shiota, Thom’s conjecture on triangulations of maps , Topology 39 (2000), 383–399.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Shiota, Thom’s conjecture on triangulations of maps , Topology 39 (2000), 383–399

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:03:37.181894Z

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Observation c8e4c27d-d237-4126-8001-60d0c061e663 · outbound

This paper cites Steenrod, The topology of fibre bundles , Princeton University Press (1951).

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Steenrod, The topology of fibre bundles , Princeton University Press (1951)

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:03:36.948273Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 910ef2d7-7d0e-459c-8c6d-544a336ce71c · outbound

This paper cites Tognoli, Su una congettura di Nash, Ann.

Reconstruction of real algebraic functions into curves with prescribed Reeb graphs Tognoli, Su una congettura di Nash, Ann

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T18:03:36.655784Z

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Pith citing papers

Observation 4ad0c078-1629-4825-9798-16b20a34822f · inbound

Graphs with tree decompositions of small graphs and realizing them as the Reeb graphs of real algebraic functions cites this paper.

Graphs with tree decompositions of small graphs and realizing them as the Reeb graphs of real algebraic functions Reconstruction of real algebraic functions into curves with prescribed Reeb graphs

Reference 10

Resolution: verified exact; local_arxiv, observed 2026-08-06T06:13:21.984415Z

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.