Paper Citation Record · LEDGER

Existence of minimizers for interaction energies with external potentials

As of 16 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2509.08761.

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

pith.paper-citation-record.v1
2509.08761 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T16:15:54.876082Z

measured 37 of 37 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+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

37 of 37 outbound references displayed

verified exact3
verified fuzzy2
unresolved32
parse uncertain0
malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 15fee559-8ff1-4846-9748-03e92a78f109 · outbound

This paper cites Balagu \'e , J.

Existence of minimizers for interaction energies with external potentials Balagu \'e , J

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-15T16:15:54.717860Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f1936c2e-107b-4ca9-8697-cd37ecd729bc · outbound

This paper cites Balagu \'e , J.

Existence of minimizers for interaction energies with external potentials Balagu \'e , J

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-15T16:15:54.722548Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1b6bebed-4fe7-443f-bf3a-9af2f3913a65 · outbound

This paper cites an unresolved cited work.

Existence of minimizers for interaction energies with external potentials Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:15:55.371996Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 17e01d46-24f4-4db3-be15-d6a091157758 · outbound

This paper cites an unresolved cited work.

Existence of minimizers for interaction energies with external potentials Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:15:55.358820Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 5205a485-66c5-44b3-a01c-6532db3e922c · outbound

This paper cites an unresolved cited work.

Existence of minimizers for interaction energies with external potentials Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-15T16:15:54.735667Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a674a217-f48a-4598-a311-15a69e97e448 · outbound

This paper cites an unresolved cited work.

Existence of minimizers for interaction energies with external potentials Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-15T16:15:54.740022Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 83b1a9ae-ca63-4b07-a4c4-800cdcf38449 · outbound

This paper cites Choksi, R.

Existence of minimizers for interaction energies with external potentials Choksi, R

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-15T16:15:54.745423Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 00cbac23-eaa2-459d-9fdb-dae96e05acc1 · outbound

This paper cites an unresolved cited work.

Existence of minimizers for interaction energies with external potentials Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-15T16:15:54.750216Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f7365d27-248f-40a7-964f-96ad70201b64 · outbound

This paper cites an unresolved cited work.

Existence of minimizers for interaction energies with external potentials Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-15T16:15:54.754551Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1415baac-7446-4bd5-a3c3-c5ae9fa07077 · outbound

This paper cites an unresolved cited work.

Existence of minimizers for interaction energies with external potentials Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-15T16:15:54.758609Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d9707abf-1ebd-44de-a989-66ef5069d2e1 · outbound

This paper cites Chafa\"i, R.

Existence of minimizers for interaction energies with external potentials Chafa\"i, R

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:15:55.294517Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 4dece38f-2312-4125-b5db-7eaad0241638 · outbound

This paper cites an unresolved cited work.

Existence of minimizers for interaction energies with external potentials Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-15T16:15:54.766679Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3305e3ad-1719-4038-82cb-05fdf2231f8e · outbound

This paper cites an unresolved cited work.

Existence of minimizers for interaction energies with external potentials Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-15T16:15:54.771448Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ee347df8-53f2-434b-8fc3-ccf30005a92d · outbound

This paper cites an unresolved cited work.

Existence of minimizers for interaction energies with external potentials Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-15T16:15:54.775334Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b6f09ae6-3a2c-4354-bdfc-a88d468f0c79 · outbound

This paper cites Davies, T.

Existence of minimizers for interaction energies with external potentials Davies, T

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-15T16:15:54.779904Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation da660177-0e82-45e4-a6e5-e34c7dc57287 · outbound

This paper cites Davies, T.

Existence of minimizers for interaction energies with external potentials Davies, T

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-15T16:15:54.784209Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c1eba451-ffb1-41cf-9834-bde150f8ae24 · outbound

This paper cites Riesz equilibrium on a ball in the external field of a point charge.

Existence of minimizers for interaction energies with external potentials Riesz equilibrium on a ball in the external field of a point charge

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-08-15T16:15:55.077173Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e9c37ef5-eb45-48e8-bab1-e80693baa272 · outbound

This paper cites an unresolved cited work.

Existence of minimizers for interaction energies with external potentials Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:15:55.236204Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 7f69faab-9cfe-4379-b4da-074e2c7dd279 · outbound

This paper cites Minimizers for an aggregation model with attractive-repulsive interaction.

Existence of minimizers for interaction energies with external potentials Minimizers for an aggregation model with attractive-repulsive interaction

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-15T16:15:54.795458Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c6363ba2-a9eb-43b9-8f3b-ce193f62d274 · outbound

This paper cites an unresolved cited work.

Existence of minimizers for interaction energies with external potentials Unresolved cited work

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-15T16:15:54.799771Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ec031714-f1c8-4a5d-b333-cf29d816b020 · outbound

This paper cites an unresolved cited work.

Existence of minimizers for interaction energies with external potentials Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-15T16:15:54.803607Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9d27181f-aed5-42f5-b296-fd6bd1bff07a · outbound

This paper cites an unresolved cited work.

Existence of minimizers for interaction energies with external potentials Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:15:55.214911Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 77144a8c-d4f8-4a46-bd46-8a75538bea34 · outbound

This paper cites an unresolved cited work.

Existence of minimizers for interaction energies with external potentials Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-15T16:15:54.810533Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a3d2b819-c106-4765-b354-3fb4d139adb1 · outbound

This paper cites Mateu, M.

Existence of minimizers for interaction energies with external potentials Mateu, M

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-15T16:15:54.814390Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cca0e4aa-27a4-40c6-8d12-16954925f296 · outbound

This paper cites Mateu, M.

Existence of minimizers for interaction energies with external potentials Mateu, M

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-15T16:15:54.818286Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e62e0add-eb8b-45c3-a1b7-7eb893892c96 · outbound

This paper cites an unresolved cited work.

Existence of minimizers for interaction energies with external potentials Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-15T16:15:54.823162Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c842fbce-3b0d-4e07-90c5-f470eea96e59 · outbound

This paper cites Extended convexity and uniqueness of minimizers for interaction energies.

Existence of minimizers for interaction energies with external potentials Extended convexity and uniqueness of minimizers for interaction energies

Reference 27

Resolution: verified exact; local_arxiv, observed 2026-08-15T16:15:54.962683Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 1257112d-1204-485f-93d9-0b9f43808f67 · outbound

This paper cites A family of explicit minimizers for interaction energies.

Existence of minimizers for interaction energies with external potentials A family of explicit minimizers for interaction energies

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-15T16:15:54.833443Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a06f8e17-2190-4cbc-91e3-db171aafda7b · outbound

This paper cites Simione, D.

Existence of minimizers for interaction energies with external potentials Simione, D

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-15T16:15:54.838521Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2042685b-c111-41df-914c-1129ceb2f9d0 · outbound

This paper cites an unresolved cited work.

Existence of minimizers for interaction energies with external potentials Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:15:55.156710Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation e4c174dd-443c-4319-99e4-662c04a4861b · outbound

This paper cites Shu and E.

Existence of minimizers for interaction energies with external potentials Shu and E

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:15:55.144567Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation d16e24e9-5c34-4ee4-8c1a-d501d123feb3 · outbound

This paper cites The Sharp Erd\H{o}s-Tur\'an Inequality.

Existence of minimizers for interaction energies with external potentials The Sharp Erd\H{o}s-Tur\'an Inequality

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-15T16:15:54.851975Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a292ec37-adb6-492e-8a3f-8ce33782b962 · outbound

This paper cites Inner Riesz balayage in minimum energy problems with external fields.

Existence of minimizers for interaction energies with external potentials Inner Riesz balayage in minimum energy problems with external fields

Reference 33

Resolution: verified exact; local_arxiv, observed 2026-08-15T16:15:54.918662Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation dbaa9ad7-412a-4462-8fc9-79692fa62536 · outbound

This paper cites an unresolved cited work.

Existence of minimizers for interaction energies with external potentials Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:15:55.131073Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 9d624137-37b9-4f85-bdf4-770fdf62aa35 · outbound

This paper cites an unresolved cited work.

Existence of minimizers for interaction energies with external potentials Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:15:55.117420Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 4c71492a-d362-4d2b-8210-567fc04e8bd9 · outbound

This paper cites an unresolved cited work.

Existence of minimizers for interaction energies with external potentials Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:15:55.103183Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 2668b9a1-eaa6-4e9d-8976-3d9122091ef8 · outbound

This paper cites an unresolved cited work.

Existence of minimizers for interaction energies with external potentials Unresolved cited work

Reference 37

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:15:55.090198Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Pith citing papers

No inbound Pith citation observations are available.