Paper Citation Record · LEDGER

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach

As of 14 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 1 inbound Pith citation observation for arXiv:2506.22273.

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

pith.paper-citation-record.v1
2506.22273 v1

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T22:16:35.936065Z

measured 39 of 39 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T16:47:12.723160Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-08-06T16:47:14.726594Z

Reference resolution

38 of 38 outbound references displayed

verified exact0
verified fuzzy23
unresolved15
parse uncertain0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d85f518f-bc08-4b9b-9b61-96e7200c7ea0 · outbound

This paper cites Ambrosio, N.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Ambrosio, N

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-06T22:16:31.546505Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 944ab6c1-a6f2-4e0e-b45a-5ff1c86fe7b1 · outbound

This paper cites Bonnivard, E.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Bonnivard, E

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:16:41.352361Z

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.

Observation 1613068c-812a-4500-bc14-7fe519f53966 · outbound

This paper cites A cahn--hilliard--willmore phase field model for non-oriented interfaces, 2024.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach A cahn--hilliard--willmore phase field model for non-oriented interfaces, 2024

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:16:41.243597Z

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.

Observation 651bbfc8-6f38-4827-a0df-520590b9679f · outbound

This paper cites A penalized allen-cahn equation for the mean curvature flow of thin structures, 2024.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach A penalized allen-cahn equation for the mean curvature flow of thin structures, 2024

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:16:41.145401Z

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.

Observation 1a23b576-53fa-4a14-a7e5-d1d26cd45ee3 · outbound

This paper cites On a phase field approximation of the planar steiner problem: existence, regularity, and asymptotic of minimizers.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach On a phase field approximation of the planar steiner problem: existence, regularity, and asymptotic of minimizers

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:16:41.062366Z

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.

Observation c257bfba-e64b-4933-9d82-26bf0e9a357f · outbound

This paper cites Bonnivard, A.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Bonnivard, A

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:16:40.984550Z

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.

Observation 09c98872-619c-4f5b-b767-5b47fd165396 · outbound

This paper cites A numerical method for computing minimal surfaces in arbitrary dimension.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach A numerical method for computing minimal surfaces in arbitrary dimension

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:16:40.832960Z

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.

Observation 3955384d-1e70-4b26-a2fe-e3281abd8824 · outbound

This paper cites an unresolved cited work.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:16:40.701917Z

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.

Observation 0fa0b74a-ea99-431a-901a-f578fb1a0a47 · outbound

This paper cites A phase-field approximation of the Steiner problem in dimension two.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach A phase-field approximation of the Steiner problem in dimension two

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:16:40.599696Z

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.

Observation c87ce41c-29c3-4cc0-a286-118a4c385b82 · outbound

This paper cites Coppin and D.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Coppin and D

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:16:40.343835Z

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.

Observation 46fc7130-9ed3-4862-85d3-ef00fb485b19 · outbound

This paper cites an unresolved cited work.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:16:40.082531Z

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.

Observation 2ca343ac-cdb9-4bc7-8b1b-b5730fbd655c · outbound

This paper cites an unresolved cited work.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:16:39.807271Z

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.

Observation c0d021f4-993f-4c5d-b0eb-9e2cf9a6d113 · outbound

This paper cites Su una teoria generale della misura \((r-1)\) -dimensionale in uno spazio ad \(r\) dimensioni.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Su una teoria generale della misura \((r-1)\) -dimensionale in uno spazio ad \(r\) dimensioni

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:16:39.599276Z

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.

Observation cf7311af-aad7-4085-a3b6-84eea77b5767 · outbound

This paper cites Frontiere orientate di misura minima.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Frontiere orientate di misura minima

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:16:39.336565Z

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.

Observation 1f151013-fe48-4009-b07a-b8c1b0049cdf · outbound

This paper cites Hutchinson.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Hutchinson

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:16:39.182421Z

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.

Observation 7ea1f518-f713-47bf-b493-81764113f212 · outbound

This paper cites Hutchinson.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Hutchinson

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:16:39.046644Z

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.

Observation 52ab4941-a5f5-42fe-a266-39b67d6f9b2a · outbound

This paper cites A direct approach to plateau's problem.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach A direct approach to plateau's problem

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-06T22:16:33.872535Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f8a827f6-9621-4f57-bfe7-ac51aec76454 · outbound

This paper cites A method of numerical solution of the problem of P lateau.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach A method of numerical solution of the problem of P lateau

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:16:38.888097Z

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.

Observation 78bde3c2-cd6a-42a4-8a75-d56dee36e5ff · outbound

This paper cites Dugundji.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Dugundji

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:16:38.700985Z

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.

Observation f2e02383-7193-42d2-b6ba-7c9da3b14bda · outbound

This paper cites an unresolved cited work.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:16:38.566861Z

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No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b287f9c7-e2da-494a-bbc5-54046da16939 · outbound

This paper cites an unresolved cited work.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:16:38.403898Z

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.

Observation e2ac7173-e93d-4ccf-b67e-e0202e6360f4 · outbound

This paper cites an unresolved cited work.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:16:38.268499Z

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.

Observation 2326e5ac-0720-4037-baef-f7803b0f1563 · outbound

This paper cites Minimal surfaces and functions of bounded variation , volume 80 of Monogr.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Minimal surfaces and functions of bounded variation , volume 80 of Monogr

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:16:38.139840Z

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.

Observation be900196-805d-4481-a735-bd79a6f49ff8 · outbound

This paper cites Soap film solutions to plateau’s problem.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Soap film solutions to plateau’s problem

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:16:38.010463Z

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.

Observation fadd3702-0cdf-4254-b169-4ac87594101b · outbound

This paper cites Existence and soap film regularity of solutions to plateau’s problem.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Existence and soap film regularity of solutions to plateau’s problem

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:16:37.870726Z

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.

Observation 5ffdd143-497a-48b4-98d1-1203006471d9 · outbound

This paper cites Blaine jun.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Blaine jun

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:16:37.746130Z

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.

Observation 4c36fb5d-3a81-4797-8ace-874ef45fb49a · outbound

This paper cites A Modica - Mortola approximation for the Steiner problem.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach A Modica - Mortola approximation for the Steiner problem

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:16:37.597080Z

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.

Observation 723b8335-d3e7-43c9-9692-aba885fcdf24 · outbound

This paper cites Machefert.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Machefert

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:16:37.425928Z

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.

Observation 8210f207-88ed-4c63-b46e-618e16b20f69 · outbound

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

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Sets of finite perimeter and geometric variational problems

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:16:37.292729Z

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.

Observation 70f46230-44c8-4182-a4b7-92ade9964ae2 · outbound

This paper cites A hierarchy of Plateau problems and the approximation of Plateau's laws via the Allen--Cahn equation.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach A hierarchy of Plateau problems and the approximation of Plateau's laws via the Allen--Cahn equation

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-06T22:16:35.237598Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 07bf4d96-39ac-41b7-88e8-160edd9251da · outbound

This paper cites Plateau borders in soap films and Gauss' capillarity theory.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Plateau borders in soap films and Gauss' capillarity theory

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-06T22:16:35.325060Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 26a0dbad-7382-4f8e-9445-c79b395adf4a · outbound

This paper cites On the problem of Plateau , volume 2 of Ergeb.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach On the problem of Plateau , volume 2 of Ergeb

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:16:37.129457Z

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.

Observation 1c6469e5-9544-4dd4-89ea-361f87dce2b9 · outbound

This paper cites an unresolved cited work.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:16:36.991098Z

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.

Observation 8f3b1108-15a1-433d-bc46-a701c7a921af · outbound

This paper cites an unresolved cited work.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:16:36.824469Z

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.

Observation fc1a06f2-a354-47fd-b021-eaab8bbff8d2 · outbound

This paper cites an unresolved cited work.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:16:36.657277Z

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.

Observation 99919f55-6b93-40ff-be60-e2208953a826 · outbound

This paper cites an unresolved cited work.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:16:36.536358Z

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.

Observation fa3fecf2-bfed-4fca-9557-3e4044a02c7e · outbound

This paper cites an unresolved cited work.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-08-06T22:16:36.316306Z

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.

Observation 3bd5beea-ba1f-4856-90a8-2002216a249e · outbound

This paper cites Computing minimal surfaces with differential forms.

Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach Computing minimal surfaces with differential forms

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T22:16:36.153603Z

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.

Pith citing papers

Observation 3729b622-e985-4a47-9949-b16064aad44f · inbound

Optimal regularity up to the boundary for Plateau-quasi-minimizers cites this paper.

Optimal regularity up to the boundary for Plateau-quasi-minimizers Phase field approximation for Plateau's problem: a curve geodesic distance penalty approach

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-08-06T16:47:14.746554Z

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.