Paper Citation Record · LEDGER

The lens cluster and triod cluster uniquely minimize the anisotropic perimeter in $\mathbb{R}^2$

As of 13 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 1 inbound Pith citation observation for arXiv:2604.03510.

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

pith.paper-citation-record.v1
2604.03510 v2

Coverage vector

measured 12 of 12 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-19T17:25:14.488096Z

measured 13 of 13 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 2026-07-14T10:18:32.879564Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

12 of 12 outbound references displayed

verified exact10
verified fuzzy1
unresolved0
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7bbcde31-b944-4d81-8308-87b3b00c05db · outbound

This paper cites The standard lens cluster inR2 uniquely minimizes relative perimeter.

The lens cluster and triod cluster uniquely minimize the anisotropic perimeter in $\mathbb{R}^2$ The standard lens cluster inR2 uniquely minimizes relative perimeter

Reference 1

Resolution: verified exact; doi, observed 2026-05-19T17:27:41.113107Z

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 43ce8bb7-7bd6-49f4-83fd-78b6d33c5535 · outbound

This paper cites Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints.

The lens cluster and triod cluster uniquely minimize the anisotropic perimeter in $\mathbb{R}^2$ Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-19T17:27:41.922859Z

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 903c3036-b1da-4aea-a10e-e28f03c96523 · outbound

This paper cites The standard double soap bubble inR2 uniquely minimizes perimeter.

The lens cluster and triod cluster uniquely minimize the anisotropic perimeter in $\mathbb{R}^2$ The standard double soap bubble inR2 uniquely minimizes perimeter

Reference 3

Resolution: verified exact; doi, observed 2026-05-19T17:27:41.115897Z

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 1b9a31a0-9835-4955-8d7d-00df861b900b · outbound

This paper cites On the Steiner property for planar minimizing clusters. The anisotropic case.

The lens cluster and triod cluster uniquely minimize the anisotropic perimeter in $\mathbb{R}^2$ On the Steiner property for planar minimizing clusters. The anisotropic case

Reference 4

Resolution: verified exact; doi, observed 2026-05-19T17:27:41.121091Z

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 e791a4f3-dd62-405b-8d6c-82e9a5b28c71 · outbound

This paper cites Proof of the Double Bubble Conjecture.

The lens cluster and triod cluster uniquely minimize the anisotropic perimeter in $\mathbb{R}^2$ Proof of the Double Bubble Conjecture

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-05-19T17:27:41.096798Z

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 de54b3de-8ce3-4ad1-8271-8689db67a08e · outbound

This paper cites Sobolev and mean-value inequalities on generalized submanifolds of Rn.

The lens cluster and triod cluster uniquely minimize the anisotropic perimeter in $\mathbb{R}^2$ Sobolev and mean-value inequalities on generalized submanifolds of Rn

Reference 6

Resolution: verified exact; doi, observed 2026-05-19T17:27:41.104972Z

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 84b030b7-7b2e-4d73-a0d9-9e86dc7cfc10 · outbound

This paper cites Plateau Bubbles and the Quintuple Bubble Theorem on $\mathbb{S}^n$.

The lens cluster and triod cluster uniquely minimize the anisotropic perimeter in $\mathbb{R}^2$ Plateau Bubbles and the Quintuple Bubble Theorem on $\mathbb{S}^n$

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-05-19T17:27:41.101652Z

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 984bd4a2-52f8-4ae3-89a8-a17b3d111d70 · outbound

This paper cites The structure of isoperimetric bubbles onRn andS n.

The lens cluster and triod cluster uniquely minimize the anisotropic perimeter in $\mathbb{R}^2$ The structure of isoperimetric bubbles onRn andS n

Reference 8

Resolution: verified exact; doi, observed 2026-05-19T17:27:41.126264Z

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 12ee6942-8f1f-4e17-abcc-378bae0c5de9 · outbound

This paper cites Soap bubbles inR2 and in surfaces.

The lens cluster and triod cluster uniquely minimize the anisotropic perimeter in $\mathbb{R}^2$ Soap bubbles inR2 and in surfaces

Reference 9

Resolution: verified exact; doi, observed 2026-05-19T17:27:41.123591Z

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 fe628c3c-adbc-494e-b423-c0c50e2fd882 · outbound

This paper cites Wulff clusters inR2.

The lens cluster and triod cluster uniquely minimize the anisotropic perimeter in $\mathbb{R}^2$ Wulff clusters inR2

Reference 10

Resolution: verified exact; doi, observed 2026-05-19T17:27:41.107598Z

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 50483c43-39f4-4264-982b-3b5b3549b25e · outbound

This paper cites Caputo, F.

The lens cluster and triod cluster uniquely minimize the anisotropic perimeter in $\mathbb{R}^2$ Caputo, F

Reference 11

Resolution: malformed identifier; doi_truncated, observed 2026-05-19T17:27:41.110072Z

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 73764e05-3325-4c9b-b8fe-b1c26c1245b8 · outbound

This paper cites The planar triple bubble.

The lens cluster and triod cluster uniquely minimize the anisotropic perimeter in $\mathbb{R}^2$ The planar triple bubble

Reference 12

Resolution: verified exact; doi, observed 2026-05-19T17:27:41.118515Z

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 5f8e5ce2-4b63-481c-9f53-4105cfb4d9e8 · inbound

Anisotropic isoperimetric double tilings of the plane cites this paper.

Anisotropic isoperimetric double tilings of the plane The lens cluster and triod cluster uniquely minimize the anisotropic perimeter in $\mathbb{R}^2$

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-14T10:18:32.879564Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.