Paper Citation Record · LEDGER

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems

As of 13 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 3 inbound Pith citation observations for arXiv:2412.00781.

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

pith.paper-citation-record.v1
2412.00781 v4

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T05:10:35.197041Z

measured 37 of 37 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 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-04T13:25:44.765036Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-04T20:50:11.338398Z

Reference resolution

34 of 34 outbound references displayed

verified exact13
verified fuzzy4
unresolved17
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 2b2de0e2-f68d-43a1-b90a-ff40eec67e37 · outbound

This paper cites Alper , On the singular set of free interface in an optimal partition problem, Commun.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Alper , On the singular set of free interface in an optimal partition problem, Commun

Reference 1

Resolution: verified exact; doi, observed 2026-08-12T05:10:35.415735Z

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 30c48d32-ac68-499f-96d2-dfc06cc5db9c · outbound

This paper cites an unresolved cited work.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Unresolved cited work

Reference 2

Resolution: verified exact; doi, observed 2026-08-12T05:10:35.405353Z

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 6c211cb0-00d4-42b0-ace6-019ab7405215 · outbound

This paper cites Bucur , G.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Bucur , G

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:10:35.744238Z

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 bb9620fe-60d8-40e9-a379-b74a6fa0990d · outbound

This paper cites an unresolved cited work.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-12T05:10:35.077330Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c1f11db8-0927-4573-bcd7-c00f72ac28fe · outbound

This paper cites an unresolved cited work.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Unresolved cited work

Reference 5

Resolution: verified exact; doi, observed 2026-08-12T05:10:35.385697Z

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 bc44d114-e866-4551-8504-a51d0a09fd70 · outbound

This paper cites an unresolved cited work.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-12T05:10:35.085958Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 87b5a57a-0f5d-4e12-b104-0185627e7723 · outbound

This paper cites Conti , S.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Conti , S

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-12T05:10:35.090235Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 53c32ee6-6f7b-4c41-8963-6a949cbb40d1 · outbound

This paper cites Conti , S.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Conti , S

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-12T05:10:35.093991Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a4581212-4cc9-4e70-b864-c16744fc841a · outbound

This paper cites Conti , S.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Conti , S

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-12T05:10:35.097924Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d9343ff5-585c-40a6-92aa-c7fa272b4762 · outbound

This paper cites De Lellis , J.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems De Lellis , J

Reference 10

Resolution: verified exact; raw_fallback, observed 2026-08-12T05:10:35.697829Z

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 5d38d834-c358-4795-87bf-106e5d0a1ad1 · outbound

This paper cites Fine structure of the singular set of area minimizing hypersurfaces modulo $p$.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Fine structure of the singular set of area minimizing hypersurfaces modulo $p$

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-12T05:10:35.105835Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6a20eae8-f9ca-49d2-af09-d68372a8a1f6 · outbound

This paper cites De Lellis , J.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems De Lellis , J

Reference 12

Resolution: verified exact; doi, observed 2026-08-12T05:10:35.345315Z

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 1811ded5-1770-41a4-a0cb-30c12a82acb5 · outbound

This paper cites an unresolved cited work.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Unresolved cited work

Reference 13

Resolution: verified exact; doi, observed 2026-08-12T05:10:35.332772Z

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 feb02256-bbe5-476e-8da2-951371c338ca · outbound

This paper cites Focardi and E.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Focardi and E

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:10:35.733072Z

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 66d474a7-cf3b-402c-8de5-5c79b5a8984d · outbound

This paper cites Friedland and W.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Friedland and W

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-12T05:10:35.122013Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6f426000-e870-4cb1-a9f9-a3e4472d4fe6 · outbound

This paper cites Garofalo , A.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Garofalo , A

Reference 16

Resolution: verified exact; doi, observed 2026-08-12T05:10:35.314002Z

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 32125aa2-8651-45fe-af5c-2f06c51ebfee · outbound

This paper cites Gromov and R.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Gromov and R

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:10:35.721635Z

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 33e9e994-5914-4de6-b6ed-fe84b038d794 · outbound

This paper cites Helffer , On spectral minimal partitions: a survey, Milan J.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Helffer , On spectral minimal partitions: a survey, Milan J

Reference 18

Resolution: verified exact; doi, observed 2026-08-12T05:10:35.302621Z

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 c42ce949-e332-4d4b-a79a-f367ffcf3e6b · outbound

This paper cites Helffer , T.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Helffer , T

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-12T05:10:35.135613Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5e6cab1b-9b2e-416f-a545-ec20939011ac · outbound

This paper cites Helffer and T.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Helffer and T

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T05:10:35.708147Z

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 82f699a6-7bdd-47ff-83f1-8f687a95642c · outbound

This paper cites Helffer , T.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Helffer , T

Reference 21

Resolution: verified exact; doi, observed 2026-08-12T05:10:35.281700Z

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 c4eb9f23-fcd0-4acf-a45e-d0e33ee9dc41 · outbound

This paper cites an unresolved cited work.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-12T05:10:35.147318Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1cb2ef58-4d9d-41ff-adca-5f20ffdfc9af · outbound

This paper cites Generic configurations in 2D strongly competing systems.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Generic configurations in 2D strongly competing systems

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-12T05:10:35.151050Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 48b86e6d-1f37-4445-a7dc-81254eaaaba9 · outbound

This paper cites Free boundary regularity for semilinear variational problems with a topological constraint.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Free boundary regularity for semilinear variational problems with a topological constraint

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-08-12T05:10:35.611844Z

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 46315688-f603-4ff5-82c6-d6d0daf0ca9a · outbound

This paper cites Boundary regularity of the free interface in spectral optimal partition problems.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Boundary regularity of the free interface in spectral optimal partition problems

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-12T05:10:35.159160Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5f6ea5b2-d168-4c62-9198-a4cf7c8d5895 · outbound

This paper cites Simon , Cylindrical tangent cones and the singular set of minimal submanifolds, J.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Simon , Cylindrical tangent cones and the singular set of minimal submanifolds, J

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-12T05:10:35.163285Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 289ffeca-3afe-40d2-9ee3-71d64276b0fa · outbound

This paper cites Soave and S.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Soave and S

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-12T05:10:35.167651Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 68989d73-b3b5-4653-88f9-51736c6475c2 · outbound

This paper cites On partially segregated harmonic maps: optimal regularity and structure of the free boundary.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems On partially segregated harmonic maps: optimal regularity and structure of the free boundary

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-12T05:10:35.171759Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a28eaa24-d760-4af1-af3e-995d7bd8ee6c · outbound

This paper cites On some singularly perturbed elliptic systems modeling partial segregation: uniform H\"older estimates and basic properties of the limits.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems On some singularly perturbed elliptic systems modeling partial segregation: uniform H\"older estimates and basic properties of the limits

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-12T05:10:35.176490Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation caf7f950-554f-43f5-849d-aba40d11cb9e · outbound

This paper cites Sun , Regularity of harmonic maps to trees, Am.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Sun , Regularity of harmonic maps to trees, Am

Reference 30

Resolution: verified exact; raw_fallback, observed 2026-08-12T05:10:35.496403Z

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 503e336a-3f8a-4b8b-b88e-6a7725f9acd3 · outbound

This paper cites Tavares and S.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Tavares and S

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-12T05:10:35.184551Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 55345a2a-0c25-4538-860a-a6948ba8ddb1 · outbound

This paper cites an unresolved cited work.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Unresolved cited work

Reference 32

Resolution: verified exact; doi, observed 2026-08-12T05:10:35.248834Z

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 ce51ffcb-ce68-4bb9-b6f2-8277ecf4d905 · outbound

This paper cites an unresolved cited work.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Unresolved cited work

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-12T05:10:35.193059Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2e1d9167-b5db-467d-b5e7-2e4ea5841b8e · outbound

This paper cites an unresolved cited work.

Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems Unresolved cited work

Reference 34

Resolution: verified exact; doi, observed 2026-08-12T05:10:35.229945Z

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 755df006-e317-49a6-8970-b79b177c81f5 · inbound

Spectral minimal partitions of unbounded domains cites this paper.

Spectral minimal partitions of unbounded domains Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-04T13:25:44.765036Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1a9db552-2f95-4a8d-b861-d0deac83287f · inbound

On a Multiphase Vectorial Bernoulli Free Boundary Problem cites this paper.

On a Multiphase Vectorial Bernoulli Free Boundary Problem Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems

Reference 56

Resolution: verified exact; arxiv_id, observed 2026-06-08T02:03:41.773737Z

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 f310c1e5-1279-41f3-843f-f2e7eea58a53 · inbound

Optimal partition and segregation problems driven by torsional rigidity cites this paper.

Optimal partition and segregation problems driven by torsional rigidity Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems

Reference 23

Resolution: verified exact; local_arxiv, observed 2026-07-04T20:50:11.340135Z

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.