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Paper Citation Record · LEDGER

The p-widths of $RP^2$

As of 15 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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.050751Z digest=sha256:644fcbb1b1a68d9201e00568ca0547a7120f48d8284574615593a7c7684c3614

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.056423Z digest=sha256:c862e9fe70cb75da4e37d868ac9e63ec1378f83e7c0c865ddabcad0e7af751ec

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.061191Z digest=sha256:106554fe85c3fa8877e22ebd40ae051f29d0832a62be8bdcbdeff5cc81d249e1

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.071995Z digest=sha256:900e28fc47fa65084aca7f803ce052e3e0ea8b532e8ecb72b2fa99ee0c93ab22

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.077092Z digest=sha256:5d490bf5b89aec7bf7f0ec9297f9f8df708c38a89f3b6371fb7a8f6ead0c9d23

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.082504Z digest=sha256:7bfe51d7de75436daba09c2233acdcdb722a9ba16b7082dd738912c8987b11f4

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.087487Z digest=sha256:12fff7a64476e347f0dad39565259a938f608918189932e47d769b4bf2b6d110

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.092557Z digest=sha256:ecf7eb6c9a300c6b0b6104bea54a9f10f226eee104102537cd1f1331f59bbbad

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.097653Z digest=sha256:fad18cd9b6190a720e4370f310d8e3fb29641881fee586cceadb222c9706b647

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.102600Z digest=sha256:944c84c20ccde407ec0fb0a95cddb3a1a49f32bad9e57c73320630c4e3caf822

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.112910Z digest=sha256:1acf2b297cbaf17d5aceda61bef473efc285c02d90bfa0c515467d3a0cb347ed

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.135079Z digest=sha256:9bc3c816bb06d8a3bf062956f85b5f1b5ed206995e910a7a58869534a416e5ae

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.174350Z digest=sha256:fd68ba4b447de2c0343eff92299dc5fda972fbfbcaefb247768faacd3275391b

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.184870Z digest=sha256:aea0984b0bbfe6e8ceaf48b01a07cf102257785d652f97db5c4b3b2e3c1e7944

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.189731Z digest=sha256:b7295f7b467753c17de0a1cc60688444dd513b42792636df13fa5f878231d72e

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.194432Z digest=sha256:efb318ba547015dfc9f11e1407bbbb13bf8cb1b5c0f1a342208b996234bf8442

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.199406Z digest=sha256:d21a2d0ba5f1aba5123c0c4db0c6b9458e66e65073ae6e0043dcb0d6242c8f5d

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.204698Z digest=sha256:215cf649df08f1a12b6391d066929bd82db5ed8d631e57ab83ae90be07c259e0

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.210076Z digest=sha256:826a1153d1460ca29fc41a41a87793549716ce11b7181e58044a1b27a48c8e07

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.214919Z digest=sha256:08bdf3f8135c5a8e616ebe7ee3fea40db89c8563907a3d0599d34b2935b5dcc5

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.219351Z digest=sha256:b91e6a4110e4891d9435dcfc94bc3b11a84dbba66b226ab942233c998a7ae42a

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.224431Z digest=sha256:024b8a310e3ccdc2717e74fad55b38e28117704b73042b701b3812445d837672

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.229133Z digest=sha256:2f7c6324baaad34df35f132376c33e4b54a059a7c9b679576ce0e1d3669b6c13

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.236723Z digest=sha256:a7642927940f1f0ab129306820473a2cf19f041dde47f3c748fbbae2a5c9ea9e

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.240985Z digest=sha256:046915b5f7e3f6f3563ca08780892dac7f11923ff718dbb365fb1be78bfef03d

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.250053Z digest=sha256:ec5b8494a68d4f5bdde55823384a21bc379b5c2b2f0f1034a25cb2d9e30949ed

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.299561Z digest=sha256:a1e1cf2b444f3d74203fc585c9edc9aeaa1aecea363db100ff6ac7a0458d68e8

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.306687Z digest=sha256:765d794e50d943f45ef73e68390fbe82e0cca89506ad2f22d6b7497361e0de4b

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.317006Z digest=sha256:79348a65932c6a55dd94dae37460dbc96d0247f71df55bec6c6dd83c1323c372

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.322277Z digest=sha256:b38cc948b4066175f1df68ca084be11096150506c165f05e4f31606f4325dc14

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.326948Z digest=sha256:bc16a8c49e9be47bad989a9d0cba9f605c1597e822b207aa0c73b3886dd42941

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 2026-08-15T06:32:42.880941+00:00.

source=arxiv_source observed=2026-08-10T16:33:29.331293Z digest=sha256:31e6c04660aa91900cdb2c93ee1eddf5b37d1356d27103f1a8f135a91942329a

Pith citing papers

No inbound Pith citation observations are available.