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Paper Citation Record · LEDGER

The p-widths of $RP^2$

As of 14 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 0 inbound Pith citation observations for arXiv:2501.13311.

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

pith.paper-citation-record.v1
2501.13311 v3

Coverage vector

measured 33 of 33 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T16:33:29.331293Z

measured 33 of 33 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

33 of 33 outbound references displayed

  • verified exact5
  • verified fuzzy22
  • unresolved6
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation df012ded-823a-44ac-8a01-83bad67cf280 · outbound

This paper cites 4, 257--299.

The p-widths of $RP^2$ 4, 257--299

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T16:33:30.251081Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.050751Z digest=sha256:4f2a8cbbc72b74f1528ac437c7af7c20805531a14647d9c3089922c6983aa275

Observation e1402e80-ca8c-4c10-89ba-c141ff501e66 · outbound

This paper cites an unresolved cited work.

The p-widths of $RP^2$ Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-10T16:33:30.235898Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.056423Z digest=sha256:04648674dd7e1da8be09c8f9be2e0c71d320700250950a4a842cd8bb88a947f4

Observation 3c6b2305-eb5a-4a61-9c31-bb22553b1212 · outbound

This paper cites Riemannian metrics on the sphere with Zoll families of minimal hypersurfaces.

The p-widths of $RP^2$ Riemannian metrics on the sphere with Zoll families of minimal hypersurfaces

Reference 3

Resolution
verified exact
local_arxiv, observed 2026-08-10T16:33:29.712896Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.061191Z digest=sha256:638dac065ee087824ad02a8ba0b59e1fcd893d2fad080c091972edb7fd9a57e3

Observation bf2eb323-3b50-481c-9f94-e617de8b31ea · outbound

This paper cites Rigidity theorems for the area widths of Riemannian manifolds.

The p-widths of $RP^2$ Rigidity theorems for the area widths of Riemannian manifolds

Reference 4

Resolution
unresolved
no resolver link, observed 2026-08-10T16:33:29.066500Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-10T16:33:29.066500Z digest=sha256:f39c63181e93faac185ea7c9d1b22a1422d525a325b38d7baf1d737224af1d54

Observation abb4ddb4-8fc3-4d97-a693-430c4743c8e3 · outbound

This paper cites 93, Springer Science & Business Media, 2012.

The p-widths of $RP^2$ 93, Springer Science & Business Media, 2012

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T16:33:30.220992Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.071995Z digest=sha256:6605baa14c15338aff20180edf511edc2b16281fa38e7f7565aec03729c7d01b

Observation 493ad1c9-43e3-4852-abec-83bd3e1d96dc · outbound

This paper cites 1, 213--328.

The p-widths of $RP^2$ 1, 213--328

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T16:33:30.207194Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.077092Z digest=sha256:b8dc7d25e54d3d05fca880ad52c08550de8ef1d9b0a7e603493d64ddd6ac4cd9

Observation cb14e943-c12a-41a4-abd1-5738cf93d1fa · outbound

This paper cites 1, 245--342.

The p-widths of $RP^2$ 1, 245--342

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T16:33:30.193266Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.082504Z digest=sha256:8259fe59f095cad2633d52eefc584c5ac3226c2550a68ade79e9b321aef7757b

Observation ee73516c-532f-4f90-a2ee-751bb0895512 · outbound

This paper cites an unresolved cited work.

The p-widths of $RP^2$ Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-10T16:33:30.178518Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.087487Z digest=sha256:53f9410abdf11d95b4619351966b271cd804f2b6e7d4fcab412a24d602a740ca

Observation ceb9ef81-fcf6-425b-ad3b-241267c3352b · outbound

This paper cites U ber fl \.

The p-widths of $RP^2$ U ber fl \

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T16:33:30.163098Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.092557Z digest=sha256:ac8667ebc011e9f25ba2cf2dcf26adbf4242b280bf9ff77eeb6e42eb2ebd3462

Observation 72ccdf7b-b5df-45f9-8b00-11e84aeae544 · outbound

This paper cites 1, 175--177.

The p-widths of $RP^2$ 1, 175--177

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T16:33:30.148392Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.097653Z digest=sha256:66e12814d02b30720dc2fb3e0a835940e22b97e0c07ac25734cee5e2ffea4dbb

Observation 16c97470-1789-427a-aac4-138190687753 · outbound

This paper cites report, SIS-2003-246, 2002.

The p-widths of $RP^2$ report, SIS-2003-246, 2002

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T16:33:30.133257Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.102600Z digest=sha256:84fb83991639877e86d402c37c7fb1767d959af9001f658adf275b1fa733982e

Observation 271ad82a-3efb-428b-a42f-50cb4d284ba6 · outbound

This paper cites 132--184.

The p-widths of $RP^2$ 132--184

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T16:33:30.117978Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.112910Z digest=sha256:cbb07ebca5b3b639e4f0c6468594fc6fdcb91e3e19e44ed3ed0129301eb60fde

Observation c1888605-6096-4b55-9ecb-6a94c7917602 · outbound

This paper cites part 2: From combinatorics to topology via algebraic isoperimetry, Geometric and Functional Analysis 20 (2010), no.

The p-widths of $RP^2$ part 2: From combinatorics to topology via algebraic isoperimetry, Geometric and Functional Analysis 20 (2010), no

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T16:33:30.102734Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.135079Z digest=sha256:b549652596c7560a02c41dae347db4f10e6b8ae64f0b6b35d8b6a7e4055c73fd

Observation 3078fa14-0ecb-4ff4-9377-d73c83696210 · outbound

This paper cites 1, 85--119.

The p-widths of $RP^2$ 1, 85--119

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T16:33:30.086324Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.174350Z digest=sha256:a2ba0afa74e630118163f3d30a6a0e43e50986462b4415fd48799fe8e6b4a796

Observation 6f0b9f32-d04c-4a57-b0a1-9dc11c7c27be · outbound

This paper cites an unresolved cited work.

The p-widths of $RP^2$ Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-10T16:33:30.070291Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.184870Z digest=sha256:2a6ab273a76341164017f323cc32b541fa97c43fbe162407aa153ec86208a3d2

Observation 2fdb05b8-c4fa-45a3-9531-eb246dfe4220 · outbound

This paper cites 3, 963--972.

The p-widths of $RP^2$ 3, 963--972

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T16:33:30.054907Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.189731Z digest=sha256:2abb6e6fb522abc7ddb715dd4ba33312f124dad9ac0686ca2ea4913d0e7d5094

Observation cd4e6377-4216-49fb-9a52-64570f19c67c · outbound

This paper cites 3, 933--961.

The p-widths of $RP^2$ 3, 933--961

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T16:33:30.040320Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.194432Z digest=sha256:908c98ea109a17e5ba60a925ca8f96f4a0e4218295bd54dfa591d287cbf164d6

Observation 64b02f94-472e-4a81-b386-46ee02a11563 · outbound

This paper cites The Isospectral Problem for p-widths: An Application of Zoll Metrics.

The p-widths of $RP^2$ The Isospectral Problem for p-widths: An Application of Zoll Metrics

Reference 18

Resolution
verified exact
local_arxiv, observed 2026-08-10T16:33:29.578992Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.199406Z digest=sha256:bdf2e6b28d777dee7bfaec887b262ec1c9f9293fd3395de9fe624c71eb1689f7

Observation 28267e96-8e1c-41a8-92cc-531a7e5c5b91 · outbound

This paper cites Index, Intersections, and Multiplicity of Min-Max Geodesics.

The p-widths of $RP^2$ Index, Intersections, and Multiplicity of Min-Max Geodesics

Reference 19

Resolution
verified exact
local_arxiv, observed 2026-08-10T16:33:29.556645Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.204698Z digest=sha256:95c69462213d24497599a4a02bb24ab21ac4d39d97bf56d8b43226a4cc256822

Observation 8e8a9e99-e51e-40f3-a7d6-a438e32aa79d · outbound

This paper cites 1, 81--111.

The p-widths of $RP^2$ 1, 81--111

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T16:33:30.025609Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.210076Z digest=sha256:2b4147b29ba45ba246fb37ed4b32a0ad095508fcaf48493f177c230676e6a170

Observation 9fa659e3-d1d5-4efb-a2e1-568602b6ad9e · outbound

This paper cites an unresolved cited work.

The p-widths of $RP^2$ Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-10T16:33:30.009601Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.214919Z digest=sha256:ec3363501d1c33745610305dc2ecd33b9ec404ce60323cb91679f1150f3a378d

Observation 2a54715a-9738-4d83-8941-910616ded933 · outbound

This paper cites Morse index and multiplicity of min-max minimal hypersurfaces.

The p-widths of $RP^2$ Morse index and multiplicity of min-max minimal hypersurfaces

Reference 22

Resolution
verified exact
local_arxiv, observed 2026-08-10T16:33:29.535521Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.219351Z digest=sha256:3d78979e93827430d5dcedda5c5748aae97c997c66ae17d95a9fdd37c634adda

Observation 580b9c8f-24e1-41d7-a2ff-75f4a3ac0050 · outbound

This paper cites 2, 577--616.

The p-widths of $RP^2$ 2, 577--616

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T16:33:29.994017Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.224431Z digest=sha256:28cc91fdc4a7d09fd21ce862c9440784252afd70fc4526c71f2439b48462a76d

Observation b5135ca2-3171-41b8-92fc-31ab2af951e1 · outbound

This paper cites 41--77, Springer International Publishing, Cham, 2020.

The p-widths of $RP^2$ 41--77, Springer International Publishing, Cham, 2020

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T16:33:29.979560Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.229133Z digest=sha256:408ced251259677b9ca148b88eef5d5d9430371cf0755d5ad0d915e920a911fb

Observation f6a6d3c0-f256-48f7-9589-65a9129d7952 · outbound

This paper cites an unresolved cited work.

The p-widths of $RP^2$ Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-08-10T16:33:29.964779Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.236723Z digest=sha256:a8ec42b28bf623a804c5e0aa4e7c115669561d6b5a7a5cfd83d697f275e96380

Observation 233ca429-e877-4ebe-ace6-9cb7af3ba435 · outbound

This paper cites 2, 421--443.

The p-widths of $RP^2$ 2, 421--443

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T16:33:29.949219Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.240985Z digest=sha256:3102cddd9eec4e602f7d8c87426b222d11c4be6d7ab8288f0fbaecd30a7c86fc

Observation e832c536-b062-49f5-bf38-1a0a3388e1fd · outbound

This paper cites 18, American Mathematical Soc., 1934.

The p-widths of $RP^2$ 18, American Mathematical Soc., 1934

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T16:33:29.933019Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.250053Z digest=sha256:29ecaeb7ffda679b1a469ef7b24e2527ed950912f6d4ce28488b9d7bb7f9e23a

Observation a9251740-136d-4b67-a057-2de88797d93e · outbound

This paper cites Pitts, Regularity and singularity of one dimensional stationary integral varifolds on manifolds arising from variational methods in the large, Symposia M athematica, V ol.

The p-widths of $RP^2$ Pitts, Regularity and singularity of one dimensional stationary integral varifolds on manifolds arising from variational methods in the large, Symposia M athematica, V ol

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T16:33:29.915865Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.299561Z digest=sha256:bbbbe4b32e28169b9e53328894b1361fc23d39808fc9e798ce76a24545dc05c6

Observation aff192ce-6949-44ed-bd71-9d9c48f1a4e4 · outbound

This paper cites 27, Princeton University Press, 2014.

The p-widths of $RP^2$ 27, Princeton University Press, 2014

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T16:33:29.899339Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.306687Z digest=sha256:35c26c689cf4b5d911929924a7a76d2763fe63753526ced7217eb1c7fedbfc4e

Observation 67fbd689-2db1-44a3-9d6e-38f4f0b3a878 · outbound

This paper cites Existence of infinitely many minimal hypersurfaces in closed manifolds.

The p-widths of $RP^2$ Existence of infinitely many minimal hypersurfaces in closed manifolds

Reference 30

Resolution
verified exact
local_arxiv, observed 2026-08-10T16:33:29.431628Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.317006Z digest=sha256:4a2aabe6f56ce9f216872a121ee0606bbc47008b3660cb5e189a9df86b9bea72

Observation 57217a4d-686d-4606-b249-b2ab1abd4d79 · outbound

This paper cites 102, 1982, pp.

The p-widths of $RP^2$ 102, 1982, pp

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T16:33:29.881820Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.322277Z digest=sha256:a6d8a0559625fb91b36e0897a6c2afac93e47940c17ff9b520efcf3aefd82c89

Observation 10fa573f-b0d1-4eda-bacc-bf6389902ef7 · outbound

This paper cites 3, 767--820.

The p-widths of $RP^2$ 3, 767--820

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T16:33:29.835412Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.326948Z digest=sha256:c371d73c7e6c47d7b2158dfd5386781b290cbf21f7ebc699ad9e1df9e1e5b2e5

Observation 37b1ba62-674a-4e39-9cdc-3c579d3417e5 · outbound

This paper cites a chen mit scharen von geschlossenen geod \.

The p-widths of $RP^2$ a chen mit scharen von geschlossenen geod \

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T16:33:29.781729Z

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.

source=arxiv_source observed=2026-08-10T16:33:29.331293Z digest=sha256:2fa5e8ee05c15d0bb1c6ddee35de8894e05cdf9bdbd968b947879d572472490c

Pith citing papers

No inbound Pith citation observations are available.