Paper Citation Record · LEDGER

Notes on the Invariance of Tautness Under Lie Sphere Transformations

As of 8 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2506.08834.

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

pith.paper-citation-record.v1
2506.08834 v1

Coverage vector

measured 32 of 32 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:12:27.316743Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+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

32 of 32 outbound references displayed

verified exact0
verified fuzzy32
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c9f9c3aa-fd17-4f24-a915-5d2cb1ad5fc5 · outbound

This paper cites ´Alvarez Paiva,Contact topology, taut immersions, and Hilbert’s fourth problem, Differential and symplectic topology of knots and curves, 1–21, Amer.

Notes on the Invariance of Tautness Under Lie Sphere Transformations ´Alvarez Paiva,Contact topology, taut immersions, and Hilbert’s fourth problem, Differential and symplectic topology of knots and curves, 1–21, Amer

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.641180Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 7e5ebc06-b438-4a81-80c0-e429666cd7a9 · outbound

This paper cites ´Alvarez Paiva,Tautness is invariant under Lie sphere transforma- tions, preprint, 2001; http://www.math.poly.edu/∼alvarez/pdfs/invariance.pdf.

Notes on the Invariance of Tautness Under Lie Sphere Transformations ´Alvarez Paiva,Tautness is invariant under Lie sphere transforma- tions, preprint, 2001; http://www.math.poly.edu/∼alvarez/pdfs/invariance.pdf

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.631312Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e634959d-5d11-4441-a7fc-ec7a46a5ff15 · outbound

This paper cites Banchoff,The spherical two-piece property and tight surfaces in spheres, J.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Banchoff,The spherical two-piece property and tight surfaces in spheres, J

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.621725Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c08fa77f-ee46-4a92-aa61-61807fc80a32 · outbound

This paper cites Blaschke,Vorlesungen ¨ uber Differentialgeometrie und geometrische Grundlagen von Einsteins Relativit¨ atstheorie, Vol.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Blaschke,Vorlesungen ¨ uber Differentialgeometrie und geometrische Grundlagen von Einsteins Relativit¨ atstheorie, Vol

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.611775Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation dad9838f-d01f-4bde-915f-79a9f5bac286 · outbound

This paper cites Carter and A.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Carter and A

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.601564Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 4d4fa580-420a-4ce8-b783-c86719e8ef79 · outbound

This paper cites Cecil,Lie sphere geometry, with applications to submanifolds, Second Edition, Universitext, Springer, New York, 2008.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Cecil,Lie sphere geometry, with applications to submanifolds, Second Edition, Universitext, Springer, New York, 2008

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.592782Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 7b4719b8-4299-4f38-bc2d-7a2d0ee08c6f · outbound

This paper cites Cecil and S.-S.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Cecil and S.-S

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.583663Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 5e9d0dcf-ec55-4c6e-a612-7206203ee71d · outbound

This paper cites Cecil and S.-S.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Cecil and S.-S

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.574330Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation ac36624a-af05-4e13-96ad-04d2144dd3aa · outbound

This paper cites Cecil and S.-S.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Cecil and S.-S

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.565232Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 84017e20-3d58-404b-97fe-6af84567e429 · outbound

This paper cites Cecil, Q.-S.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Cecil, Q.-S

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.555707Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation a829e9d3-8922-4061-9024-542eb7a2447e · outbound

This paper cites Cecil and G.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Cecil and G

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.546414Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c5407c42-b7a7-4a6c-b2f0-9aa9c3d8f36d · outbound

This paper cites Cecil and G.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Cecil and G

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.536517Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 48e635f3-ce0e-49e7-b112-181e998f6ad1 · outbound

This paper cites Cecil and P.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Cecil and P

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.527419Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 5b1aa5c5-fce2-4848-90fa-4bdd723b60a3 · outbound

This paper cites Cecil and P.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Cecil and P

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.518960Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation da8fe049-2516-4961-aded-511a294336c3 · outbound

This paper cites Chern, An introduction to Dupin submanifolds,Differential geom- etry: A symposium in honour of Manfredo do Carmo, (Rio de Janeiro, 1988), Editors H.B.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Chern, An introduction to Dupin submanifolds,Differential geom- etry: A symposium in honour of Manfredo do Carmo, (Rio de Janeiro, 1988), Editors H.B

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.510552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation a017a415-7dc2-459e-b26e-9ed652134e99 · outbound

This paper cites Eilenberg and N.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Eilenberg and N

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.501622Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 8aeeecbd-5e0c-4b4b-8eed-77949e3b8801 · outbound

This paper cites Jensen, E.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Jensen, E

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.492772Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 37beeac3-1d22-49eb-86e0-e3ad8206b314 · outbound

This paper cites Kuiper,On convex maps, Nieuw Archief voor Wisk.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Kuiper,On convex maps, Nieuw Archief voor Wisk

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.484191Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 087a6ab3-d437-4140-bc7f-276da44b8b2b · outbound

This paper cites Kuiper,Minimal total absolute curvature for immersions, Invent.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Kuiper,Minimal total absolute curvature for immersions, Invent

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.475340Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 5a9c421a-7cbb-4abb-8000-4df62de5ee95 · outbound

This paper cites Kuiper,Tight embeddings and maps.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Kuiper,Tight embeddings and maps

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.466092Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 1a9c3364-def0-4dff-a775-864afabd1558 · outbound

This paper cites Kuiper,Taut sets in three space are very special, Topology 23 (1984), 323–336.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Kuiper,Taut sets in three space are very special, Topology 23 (1984), 323–336

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.456494Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 71c1e1ca-a00a-499f-b927-99549b64113b · outbound

This paper cites Lie, ¨Uber Komplexe, inbesondere Linien- und Kugelkomplexe, mit Anwendung auf der Theorie der partieller Differentialgleichungen, Math.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Lie, ¨Uber Komplexe, inbesondere Linien- und Kugelkomplexe, mit Anwendung auf der Theorie der partieller Differentialgleichungen, Math

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.446664Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation dda85e99-073e-44a5-8e27-2d41ade693e7 · outbound

This paper cites Milnor,Morse Theory, Ann.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Milnor,Morse Theory, Ann

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.437105Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 5ba1f13d-820d-4089-8eb2-2d59b4a51ad0 · outbound

This paper cites Miyaoka,Compact Dupin hypersurfaces with three principal curva- tures, Math.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Miyaoka,Compact Dupin hypersurfaces with three principal curva- tures, Math

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.426872Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation a16364fb-121b-4b82-8593-6deb7d1b6b69 · outbound

This paper cites Miyaoka,Taut embeddings and Dupin hypersurfaces, Differential Ge- ometry of Submanifolds, Proc.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Miyaoka,Taut embeddings and Dupin hypersurfaces, Differential Ge- ometry of Submanifolds, Proc

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.417746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 667073f0-45d1-4801-81da-d7f14b15c490 · outbound

This paper cites Miyaoka,Dupin hypersurfaces and a Lie invariant, Kodai Math.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Miyaoka,Dupin hypersurfaces and a Lie invariant, Kodai Math

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.407907Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 61a23367-9fc8-4c85-b9bd-8a0ae584608f · outbound

This paper cites Miyaoka,Dupin hypersurfaces with six principal curvatures, Kodai Math.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Miyaoka,Dupin hypersurfaces with six principal curvatures, Kodai Math

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.397795Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6aafa901-223f-4d05-a8f1-f1a171f71071 · outbound

This paper cites Morse and S.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Morse and S

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.387051Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation fff8b23e-1ee4-43c2-a17d-57d6a97abd8b · outbound

This paper cites Pinkall,Dupin ’sche Hyperfl¨ achen inE 4, Manuscr.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Pinkall,Dupin ’sche Hyperfl¨ achen inE 4, Manuscr

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.377292Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation bda9c2eb-4629-44ae-b760-311b7af89e29 · outbound

This paper cites Pinkall,Dupin hypersurfaces, Math.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Pinkall,Dupin hypersurfaces, Math

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.367439Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation bee083ca-1d92-4059-9728-17b4d00bbaca · outbound

This paper cites Pinkall,Curvature properties of taut submanifolds, Geom.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Pinkall,Curvature properties of taut submanifolds, Geom

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.357825Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation ce53324a-f4e0-49f7-9911-c74545062a2e · outbound

This paper cites Terng and G.

Notes on the Invariance of Tautness Under Lie Sphere Transformations Terng and G

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:12:27.346506Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Pith citing papers

No inbound Pith citation observations are available.