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Paper Citation Record · LEDGER

Rigidity for perimeter inequality under spherical symmetrisation

As of 16 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:1908.04865.

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

pith.paper-citation-record.v1
1908.04865 v2

Coverage vector

measured 32 of 32 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T13:36:02.032514Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+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 fuzzy23
  • unresolved9
  • parse uncertain0
  • malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7f884161-aa45-4d1b-ac3f-8f417ef729ae · outbound

This paper cites Ambrosio, V.

Rigidity for perimeter inequality under spherical symmetrisation Ambrosio, V

Reference 1

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 013ac339-a001-4599-9856-12ef5e1e172e · outbound

This paper cites Ambrosio, N.

Rigidity for perimeter inequality under spherical symmetrisation Ambrosio, N

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:36:02.484479Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:36:01.873874Z digest=sha256:482ed2be94573f276c1ffbd53738993be22e6f1f4c1cf091390797fdaf6427f2

Observation 1ba17ab2-27fd-449d-9972-a2b1185ef20e · outbound

This paper cites Barchiesi, F.

Rigidity for perimeter inequality under spherical symmetrisation Barchiesi, F

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:36:02.470368Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 6ecfa3ef-3f5d-493f-ad0e-1006e919ba0f · outbound

This paper cites Bartsch, T.

Rigidity for perimeter inequality under spherical symmetrisation Bartsch, T

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:36:02.457239Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:36:01.883461Z digest=sha256:0065ca615b3d54bcef191fefda65db160a9f98f278c5e20e2d59b9cd112edb0b

Observation cd34e906-bd66-461a-981d-a4414471422f · outbound

This paper cites Baernstein, A unified approach to symmetrization , Symposia Matematica, 35 (1995), pp.

Rigidity for perimeter inequality under spherical symmetrisation Baernstein, A unified approach to symmetrization , Symposia Matematica, 35 (1995), pp

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:36:02.443148Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:36:01.889694Z digest=sha256:1f9ea6efef8449711192ba47e45615379c5a6e617a66acfa0634edc82c935db5

Observation e6936fda-f860-4f29-8fa3-d7442d8acc42 · outbound

This paper cites an unresolved cited work.

Rigidity for perimeter inequality under spherical symmetrisation Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:36:02.429679Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation 36c27424-d17a-413f-ac95-502b4276e5dc · outbound

This paper cites B ¨ogelein, F.

Rigidity for perimeter inequality under spherical symmetrisation B ¨ogelein, F

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:36:02.415189Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation f058af19-fec0-43e3-93c2-da89ac556971 · outbound

This paper cites an unresolved cited work.

Rigidity for perimeter inequality under spherical symmetrisation Unresolved cited work

Reference 8

Resolution
unresolved
no resolver link, observed 2026-08-14T13:36:01.907165Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T13:36:01.907165Z digest=sha256:a67a1cb9d0dad1083d58b1a1bdafb85fd1659042c8bea50d2c813e4bc77b4278

Observation ba8dcf6b-a9c9-4243-88cf-9eac16e68475 · outbound

This paper cites Cagnetti, M.

Rigidity for perimeter inequality under spherical symmetrisation Cagnetti, M

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:36:02.394045Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:36:01.911457Z digest=sha256:b50fd932ccd65c9302053f94908c426e08ee1315e343a2e029ac44fea959a05c

Observation c89d3d3c-ab86-4704-9c93-704f09308615 · outbound

This paper cites an unresolved cited work.

Rigidity for perimeter inequality under spherical symmetrisation Unresolved cited work

Reference 10

Resolution
unresolved
no resolver link, observed 2026-08-14T13:36:01.915594Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T13:36:01.915594Z digest=sha256:bee3acafe17e9a45b04db3217ba54e34e606561a6ec682957ff14be7c94ec3c4

Observation 9ee32239-5e4a-4ef3-90ff-642f2d60a718 · outbound

This paper cites an unresolved cited work.

Rigidity for perimeter inequality under spherical symmetrisation Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:36:02.371660Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:36:01.919559Z digest=sha256:f602a3f5ccb090750830797e9cec0ad988cf8884285c3420ff85cb595b4ab8ab

Observation 96142a1d-615c-4d4c-9cc0-ba72a86ad0c7 · outbound

This paper cites Chleb´ık, A.

Rigidity for perimeter inequality under spherical symmetrisation Chleb´ık, A

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:36:02.354382Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:36:01.923886Z digest=sha256:51bc15457ca8155ac84b93fd1c47dd0132430cb54f3b9ba6ca0e4fc389481586

Observation 25d20160-1a5f-4df2-b9b7-4f1027a83531 · outbound

This paper cites Cianchi and N.

Rigidity for perimeter inequality under spherical symmetrisation Cianchi and N

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:36:02.342126Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:36:01.928950Z digest=sha256:ce399d7a5d23e75d811670c7968e1047102416f0ef7768a3788e144071da4e87

Observation 3527a0bf-43cd-4bbc-b20d-9ce7c56f1e0b · outbound

This paper cites Math., 203 (2006), pp.

Rigidity for perimeter inequality under spherical symmetrisation Math., 203 (2006), pp

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:36:02.328574Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:36:01.933175Z digest=sha256:afb6591e7d151ba2b6d240c1f3c016a192ab0c07a6c3bb78fe2b63210234c860

Observation 1048640b-5575-43ab-bcec-ec77d4031a48 · outbound

This paper cites Cianchi, N.

Rigidity for perimeter inequality under spherical symmetrisation Cianchi, N

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:36:02.312703Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:36:01.937655Z digest=sha256:8e8a2312333ba0e684af04c4c8bced325702e42f781c57c84de67390883296e9

Observation 086f2e34-b59b-4d64-84c4-1afedaf67a8c · outbound

This paper cites De Giorgi, Sulla propriet` a isoperimetrica dell’ipersfera, nella classe degli insiemi aventi frontiera orientata di misura finita , Atti Accad.

Rigidity for perimeter inequality under spherical symmetrisation De Giorgi, Sulla propriet` a isoperimetrica dell’ipersfera, nella classe degli insiemi aventi frontiera orientata di misura finita , Atti Accad

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:36:02.299438Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:36:01.942037Z digest=sha256:4443cccce3c07bbb44cdcedde2fd495e9ad50e79d1dcd4d52956d47f57a6711f

Observation 28ce454d-82b7-4887-8bed-1fd50f3f8c38 · outbound

This paper cites [Author name on title page: Ennio Giorgi], Edited by Luigi Ambrosio, Gianni Dal Maso, Marco Forti, Mario Miranda and Sergio Spagnolo, Reprint of the 2006 edition.

Rigidity for perimeter inequality under spherical symmetrisation [Author name on title page: Ennio Giorgi], Edited by Luigi Ambrosio, Gianni Dal Maso, Marco Forti, Mario Miranda and Sergio Spagnolo, Reprint of the 2006 edition

Reference 17

Resolution
unresolved
no resolver link, observed 2026-08-14T13:36:01.946069Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T13:36:01.946069Z digest=sha256:cd3fcc1c0fb0633676957d098b31d63c9454a0820e74dfe4588a87131e23af1e

Observation d6d36c25-8bc5-4064-9693-816ca9a8a6b3 · outbound

This paper cites Giaquinta, G.

Rigidity for perimeter inequality under spherical symmetrisation Giaquinta, G

Reference 18

Resolution
unresolved
no resolver link, observed 2026-08-14T13:36:01.950406Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-14T13:36:01.950406Z digest=sha256:6eb767d6ce134634c7e188f880bf6b7c93ad6e9aaf998c02ec896785b5aebeb9

Observation 0010859b-6243-41fb-86d6-881bf3a3581c · outbound

This paper cites Gidas, W.M.

Rigidity for perimeter inequality under spherical symmetrisation Gidas, W.M

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:36:02.270853Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:36:01.957919Z digest=sha256:9833daaf7464eb4176e80a193bcbd696d942a8cf7195f307f69e8ff657d66a9d

Observation 3519c7c1-bf53-4190-9cc0-c353ee19e20e · outbound

This paper cites Kawohl, Rearrangements and convexity of level sets in PDE , vol.

Rigidity for perimeter inequality under spherical symmetrisation Kawohl, Rearrangements and convexity of level sets in PDE , vol

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:36:02.258811Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:36:01.962752Z digest=sha256:5927175d2c90f94b947301d2d31ba299218f05a7e61c16b39779bea6f894b31f

Observation f2f7b6cc-8bc6-4a85-9c1c-a016b068c7b7 · outbound

This paper cites Rational Mech.

Rigidity for perimeter inequality under spherical symmetrisation Rational Mech

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:36:02.246377Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:36:01.967295Z digest=sha256:4ad8f4dd21a58aa31304d3ac0ff7cae2dd9403cbb019f820677578f1d2ca73bc

Observation a7187339-1d98-4342-aa68-2a93f770256f · outbound

This paper cites Maggi, Sets of finite perimeter and geometric variational problems, vol.

Rigidity for perimeter inequality under spherical symmetrisation Maggi, Sets of finite perimeter and geometric variational problems, vol

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:36:02.233474Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:36:01.973199Z digest=sha256:c22855fcd14178768f92ca8744cd36f92a832fc8c3e879f6c83eba9c5959a07d

Observation 3a3c98a0-46e0-4674-b1fc-8ae76046c763 · outbound

This paper cites McGillivray, An isoperimetric inequality in the plane with a log-convex density , Ric.

Rigidity for perimeter inequality under spherical symmetrisation McGillivray, An isoperimetric inequality in the plane with a log-convex density , Ric

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:36:02.217614Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:36:01.977305Z digest=sha256:4108121d42e5a304adca543008a2ea2b07187ec3228b874776979f77563b37ac

Observation 776b03e7-72a5-418d-b9f4-b7235839de48 · outbound

This paper cites Morgan, S.

Rigidity for perimeter inequality under spherical symmetrisation Morgan, S

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:36:02.200988Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:36:01.982787Z digest=sha256:d0312a9dbe38084367bb751bf97bc639fd44577aaf689827495ad6b156e1a793

Observation 0c6b25ec-3c80-4608-a135-06601d5436e8 · outbound

This paper cites Morgan, A.

Rigidity for perimeter inequality under spherical symmetrisation Morgan, A

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:36:02.187174Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:36:01.988986Z digest=sha256:79cc941f232fa0892c5a3749bdbbd307db213502319b8cb1a84833571f36cb6a

Observation 4ad175ae-0d5c-4e85-8065-bc4670427589 · outbound

This paper cites Perugini, Rigidity of Steiner’s inequality for the anisotropic perimeter (preprint).

Rigidity for perimeter inequality under spherical symmetrisation Perugini, Rigidity of Steiner’s inequality for the anisotropic perimeter (preprint)

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:36:02.173832Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:36:01.998404Z digest=sha256:0656cb76f4e3674c64ea09689f043ab7c6242737fe795b9e0e6173c57b1c6060

Observation afefdefc-6d00-4e0c-adc5-bd75e70d48cd · outbound

This paper cites P´olya, Sur la sym´ etrisation circulaire.

Rigidity for perimeter inequality under spherical symmetrisation P´olya, Sur la sym´ etrisation circulaire

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:36:02.160661Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:36:02.004949Z digest=sha256:3a27613e539f3de7dcfb85966feded36552f7ba46eef61787e4950276f0d6caa

Observation 462ed7b5-08e1-4132-8c11-4ce1df284d7e · outbound

This paper cites an unresolved cited work.

Rigidity for perimeter inequality under spherical symmetrisation Unresolved cited work

Reference 28

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:36:02.145528Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:36:02.012571Z digest=sha256:f819efed322750d56d28f0aaf15b9e3d4e3055bd6f0c94f66765ff7a2a5d8c6c

Observation 6af1c1ae-092a-4e84-be46-4eb1898e2ed9 · outbound

This paper cites Serrin, A symmetry property in potential theory , Arch.

Rigidity for perimeter inequality under spherical symmetrisation Serrin, A symmetry property in potential theory , Arch

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:36:02.130496Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:36:02.017817Z digest=sha256:995bf76d99331788564642000dcfe9cac789cb9af15eb42acc719662cc640836

Observation d15e95fa-8a9e-4911-8ea2-114c8f1f83ad · outbound

This paper cites an unresolved cited work.

Rigidity for perimeter inequality under spherical symmetrisation Unresolved cited work

Reference 30

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:36:02.110440Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:36:02.022260Z digest=sha256:4805e6e98d3b856f4c05500e9bd3117db7fa6f879870e68db55037f4ca58b69d

Observation b299b4ba-028f-42ef-b71f-cf72f1e03d1a · outbound

This paper cites Smets, M.

Rigidity for perimeter inequality under spherical symmetrisation Smets, M

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:36:02.093281Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:36:02.027454Z digest=sha256:0e694cf0d1a1e3d24eff2838cd1ab00ee9f7016224c5aa51b72ed3f9e140ba98

Observation 435105d0-4005-4a3e-9943-5b94880d7253 · outbound

This paper cites an unresolved cited work.

Rigidity for perimeter inequality under spherical symmetrisation Unresolved cited work

Reference 32

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:36:02.075819Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T13:36:02.032514Z digest=sha256:4641d5bcc3715481144f5bad6d3bab4e4e75996e49380757e16d920b670311e9

Pith citing papers

No inbound Pith citation observations are available.