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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
raw_fallback, observed 2026-08-14T13:36:02.498985Z

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=2026-08-14T13:36:01.868748Z digest=sha256:162b11047cb81161402c280b62e76eb7d1ce9ba9280d27a1e7c1485b09c0c345

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:c4a192ea13e37f5aa8594d7a9df6104a65d037ad82b238c2badc693837b4aa9c

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:b5350d3d91b00fa6a718c0c38b5b980891ab164d4126ffc38dbc21f3a3cb613e

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=sha256:6d14f86edfe416f83d86408cce2d446ac6e11dd7839106187e6d7e4822f583fa

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.

source=pdf_text observed=2026-08-14T13:36:01.901678Z digest=sha256:acba236ccadf53222c933ccf61cb12f53d5dc135732c19c5f8e757af9bf7297f

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=sha256:4a625014314a30cfed55b5273fd1b4d16ce36d9cd8f4349e40388a386ac7b2ed

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=sha256:74472df82e80b6af1ecdcbfe333c1830c4fa8c5541fbad7f5851d21220ef1f1f

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:d84466ef7215faa4539b1d74dd07675c076aac6852661f32d8f40de92875c0df

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=sha256:24cfc132a4b27f972cd82d5d6347e4f494bfca4f8ff45a127c363225581ea2dc

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=sha256:1b827df2e4d69b44db313bd3a79377781f453a94826a67e79dba0c99d3cbc782

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=sha256:9f3a6a05273001dd3a8f57eefcb81adb870da4d4d5359ea09da5517ece853357

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=sha256:34d0d8a3bc6b637d0e1267beb9896f9675a2de3b4be71d0bf483cb7b1ec4681a

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:c02ef83484fd180f57905bebac2e6bec84d0d1c773b80744871f023a57e75c1b

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=sha256:638f4767730958eb4f7c28ea8efa14a8d437864d5297d9abe42add83da97c334

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
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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=sha256:00e6409e505d1844f3a5b6c2f78ecb4984b6fbb15556086ad4cf160887dddace

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=sha256:76bc46667b6e6a5a3f3a42739718af9e2416d616a69b88941cf4c5867e472dbb

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=sha256:3741c21b3468e35c41c64559d17e025f453913b0597e067625c07c0df1221b02

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=sha256:563a9b4fda4abaf090fa7b35e5d99f114f2004d6572512bc24a6144f0978c4b6

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=sha256:7b9b66a0a998adcf84779382297c3fd9b405058c1704a7dabec67e13afc2389d

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=sha256:3cc3428554d4b09202bd33827a75e56c8ed6db4008e46c414ae02afd0f9f61f7

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=sha256:211643e43a3c5c2dbe5e16e9dac40c28a2c37d3a85b2a99fa62a5051daf616a5

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=sha256:5bd06a41f64da2a1edab7cc0caa57b8e1b02d4c13549554d606f33b247e9f77f

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=sha256:7e514c2231866f578772dad845ed7dfcba71e362c7c8b3e6d97572c5b5b17823

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=sha256:488a6d2a03a2b407f828f87293ab9f50d68996452d201eaa72e539a8e7e306a6

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=sha256:63d911c38b72cfc365f18c77b8f12a87294ea60616b0239424ad8654affbd4e8

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=sha256:0ab7f763e9927b6717e7d93e4fa9b211486837306fe763c57a64c629b3aef1fd

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:bbd19504a21bef939215596f059ecefd4fc383e60381483cefd7147d7e3c6092

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:a293db8ae1d1bc841e8f64abf69e5782cf8bfbc2f03e10e6e9eaf87146d488b6

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=sha256:7178aed9aff73c7d09f1c2bd84bd1fb88a7650b82f12e2e0594727bc291db5bb

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=sha256:8834001a8f82abeee5f67d39b2bb51afd630c6082be7d32d9c17a25e44835742

Pith citing papers

No inbound Pith citation observations are available.