Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-05-19T17:25:14.488096Z
Paper Citation Record · LEDGER
The lens cluster and triod cluster uniquely minimize the anisotropic perimeter in $\mathbb{R}^2$
As of 10 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.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-07-14T10:18:32.879564Z
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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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 2026-08-10T06:31:04.303077+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.