Paper Citation Record · LEDGER

Arrangements of small circles for Morse-Bott functions

As of 13 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2412.03846.

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

pith.paper-citation-record.v1
2412.03846 v3

Coverage vector

measured 25 of 25 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T22:14:58.664744Z

measured 25 of 25 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 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

25 of 25 outbound references displayed

verified exact0
verified fuzzy1
unresolved22
parse uncertain0
malformed identifier2
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 871635f0-70c9-478b-baa6-4243035b4f71 · outbound

This paper cites Bochnak, M.

Arrangements of small circles for Morse-Bott functions Bochnak, M

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-11T22:14:57.856122Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 473e575f-8e9e-4ac2-99b0-faca1a75ed9c · outbound

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

Arrangements of small circles for Morse-Bott functions Poincar\'e-Reeb graphs of real algebraic domains

Reference 2

Resolution: malformed identifier; no resolver link, observed 2026-08-11T22:14:57.866639Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 28b5058c-7f71-4fc3-8883-c60b2eb08efa · outbound

This paper cites Arrangements of orthogonal circles with many intersections.

Arrangements of small circles for Morse-Bott functions Arrangements of orthogonal circles with many intersections

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-11T22:14:57.879749Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cfb38ed3-c028-4dd4-a177-8caf0950fa47 · outbound

This paper cites Golubitsky and V.

Arrangements of small circles for Morse-Bott functions Golubitsky and V

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-11T22:14:57.904745Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a0c15746-580b-4d55-96d3-76f14e548181 · outbound

This paper cites Kitazawa, On round fold maps (in Japanese), RIMS Kokyuroku Bessatsu B38 (2013), 45–59.

Arrangements of small circles for Morse-Bott functions Kitazawa, On round fold maps (in Japanese), RIMS Kokyuroku Bessatsu B38 (2013), 45–59

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-11T22:14:57.924732Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cab783f1-7046-4adc-b6f3-f3b57adb7741 · outbound

This paper cites Kitazawa, On manifolds admitting fold maps with singular value sets of concentric spheres, Doctoral Dissertation, Tokyo Institute of Technology (201 4).

Arrangements of small circles for Morse-Bott functions Kitazawa, On manifolds admitting fold maps with singular value sets of concentric spheres, Doctoral Dissertation, Tokyo Institute of Technology (201 4)

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-11T22:14:57.944738Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 74319b95-11c1-4db3-a4dd-32feac1ab526 · outbound

This paper cites Kitazawa, Fold maps with singular value sets of concentric spheres , Hokkaido Mathemat- ical Journal Vol.43, No.3 (2014), 327–359.

Arrangements of small circles for Morse-Bott functions Kitazawa, Fold maps with singular value sets of concentric spheres , Hokkaido Mathemat- ical Journal Vol.43, No.3 (2014), 327–359

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-11T22:14:57.975270Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e62d9810-9768-49b0-8b5e-e41dcb2d6eee · outbound

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

Arrangements of small circles for Morse-Bott functions On Reeb graphs induced from smooth functions on 3-dimensional closed orientable manifolds with finitely many singular values

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-11T22:14:58.014737Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4d197d29-e32b-4caf-b358-d37ee5a5de06 · outbound

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

Arrangements of small circles for Morse-Bott functions Real algebraic functions on closed manifolds whose Reeb spaces are given graphs

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-11T22:14:58.047291Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 150ccc75-ff96-4e77-b797-5c8f0bfcb6c8 · outbound

This paper cites The book of abstracts.

Arrangements of small circles for Morse-Bott functions The book of abstracts

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:14:59.574752Z

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 6adca0c0-b0a1-48cc-8a03-8763d0937f21 · outbound

This paper cites an unresolved cited work.

Arrangements of small circles for Morse-Bott functions Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-11T22:14:58.125021Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 714330cf-7d40-45b2-89fc-2857be86fac9 · outbound

This paper cites Adjoints and Canonical Forms of Polypols.

Arrangements of small circles for Morse-Bott functions Adjoints and Canonical Forms of Polypols

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-11T22:14:58.137615Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9be4bed0-a430-4f85-be1a-a95d826e8929 · outbound

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

Arrangements of small circles for Morse-Bott functions Koll´ ar, Nash’s work in algebraic geometry , Bulletin (New Series) of the American Mathe- matical Society (2) 54, 2017, 307–324

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-11T22:14:58.175300Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fa6f5fe8-73e4-41d4-9462-410fd63515b6 · outbound

This paper cites Masumoto and O.

Arrangements of small circles for Morse-Bott functions Masumoto and O

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-11T22:14:58.196722Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 51d85cfa-06cb-4ac1-88cc-fe416ff2af6c · outbound

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

Arrangements of small circles for Morse-Bott functions Realization of a graph as the Reeb graph of a Morse function on a manifold

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-11T22:14:58.216624Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ddc8d26e-b0a7-4758-aece-fba12b7ade52 · outbound

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

Arrangements of small circles for Morse-Bott functions Milnor, Lectures on the h-cobordism theorem , Math

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-11T22:14:58.235873Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 49205957-4dab-49dd-b1ec-86b4aa37cb63 · outbound

This paper cites an unresolved cited work.

Arrangements of small circles for Morse-Bott functions Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-11T22:14:58.257228Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 32d74f57-0f8c-49e8-b431-048269511b75 · outbound

This paper cites an unresolved cited work.

Arrangements of small circles for Morse-Bott functions Unresolved cited work

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-11T22:14:58.284854Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 23fa042b-ce8c-4f9e-9c3f-ac674801f304 · outbound

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

Arrangements of small circles for Morse-Bott functions Saeki, Reeb spaces of smooth functions on manifolds II , Res

Reference 19

Resolution: malformed identifier; no resolver link, observed 2026-08-11T22:14:58.345272Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0e614641-0223-4050-b423-6b8fc9f7c964 · 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.

Arrangements of small circles for Morse-Bott functions Sharko, About Kronrod-Reeb graph of a function on a manifold , Methods of Functional Analysis and Topology 12 (2006), 389–396

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-11T22:14:58.404736Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0276f6f0-224b-4c95-957d-54e80c64f366 · outbound

This paper cites an unresolved cited work.

Arrangements of small circles for Morse-Bott functions Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:14:59.234742Z

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 21dcac85-b40a-4e72-806f-fed711605050 · outbound

This paper cites an unresolved cited work.

Arrangements of small circles for Morse-Bott functions Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-11T22:14:58.504739Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation aab5dd9d-2870-400a-ac30-7c4f26d50aa1 · outbound

This paper cites Tamaki, Algebraic Topology A Guide to literature, http://pantodon.jp/index.rb?body=about, 2023.

Arrangements of small circles for Morse-Bott functions Tamaki, Algebraic Topology A Guide to literature, http://pantodon.jp/index.rb?body=about, 2023

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-11T22:14:58.554751Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2a594f29-27a2-4326-bd67-79b366f1fdb9 · outbound

This paper cites Tamaki, Algebraic Topology A Guide to literature (Su bmanifold arrangement), http://pantodon.jp/index.rb?body=submanifold arrangement, 2023.

Arrangements of small circles for Morse-Bott functions Tamaki, Algebraic Topology A Guide to literature (Su bmanifold arrangement), http://pantodon.jp/index.rb?body=submanifold arrangement, 2023

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-11T22:14:58.614740Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 137fcf9c-78ea-4896-bcc6-c6fffdf7b3e5 · outbound

This paper cites Tamaki, Algebraic Topology A Guide to literature (Ar rangement variations), http://pantodon.jp/index.rb?body=arrangement variations, 2023.

Arrangements of small circles for Morse-Bott functions Tamaki, Algebraic Topology A Guide to literature (Ar rangement variations), http://pantodon.jp/index.rb?body=arrangement variations, 2023

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-11T22:14:58.664744Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.