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Paper Citation Record · LEDGER

Proportional Clustering, the $\beta$-Plurality Problem, and Metric Distortion

As of 17 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2502.10068.

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

pith.paper-citation-record.v1
2502.10068 v1

Coverage vector

measured 25 of 25 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T19:40:37.152805Z

measured 25 of 25 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

25 of 25 outbound references displayed

  • verified exact1
  • verified fuzzy12
  • unresolved12
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c8fd1015-c72f-487e-bb3e-7a40e731e31e · outbound

This paper cites Anshelevich, O.

Proportional Clustering, the $\beta$-Plurality Problem, and Metric Distortion Anshelevich, O

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T19:40:37.700803Z

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.

source=arxiv_source observed=2026-08-07T19:40:36.873921Z digest=sha256:a433ac63465a033242303eecf8ee211098350994556adbbdaaf2c0f2c1e795aa

Observation fa65ca8c-7f31-49c2-9d20-09090b6e40f3 · outbound

This paper cites Aronov, M.

Proportional Clustering, the $\beta$-Plurality Problem, and Metric Distortion Aronov, M

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T19:40:37.682240Z

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.

source=arxiv_source observed=2026-08-07T19:40:36.905733Z digest=sha256:06d91f24220ff6b5f6bc4d4bb79329887696688d81fa27b25a74f0f88920970c

Observation cd69a3b1-d1e4-47f2-a009-af446c84b896 · outbound

This paper cites Aziz and B.

Proportional Clustering, the $\beta$-Plurality Problem, and Metric Distortion Aziz and B

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T19:40:37.664588Z

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.

source=arxiv_source observed=2026-08-07T19:40:36.985054Z digest=sha256:fc3edff361deff47a40bec5fe4cbf5aa6eb3ded571569f5761cff81a98c8d6ed

Observation 3bc4b12e-665d-4340-97ef-2c67c6c2565b · outbound

This paper cites an unresolved cited work.

Proportional Clustering, the $\beta$-Plurality Problem, and Metric Distortion Unresolved cited work

Reference 4

Resolution
unresolved
no resolver link, observed 2026-08-07T19:40:37.001044Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-07T19:40:37.001044Z digest=sha256:0239d5aab3794e225294ed0bed140d0e5c241afa872d8285147724a9f4ffb1ff

Observation 8f5b76cc-0b04-4cad-a76b-cefe40e60379 · outbound

This paper cites an unresolved cited work.

Proportional Clustering, the $\beta$-Plurality Problem, and Metric Distortion Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-07T19:40:37.634057Z

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.

source=arxiv_source observed=2026-08-07T19:40:37.007784Z digest=sha256:a7a7bf8e44d0535524770d64058fbe9273f6826deed8a559f10f6adc5700d385

Observation 6deaf86d-00fd-47fd-b399-3a30492635f9 · outbound

This paper cites an unresolved cited work.

Proportional Clustering, the $\beta$-Plurality Problem, and Metric Distortion Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-07T19:40:37.613097Z

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.

source=arxiv_source observed=2026-08-07T19:40:37.014349Z digest=sha256:2a81a86a0f0688c94dedaf98fb2841457bbcd592757d1dde2bddf880ba1aac6a

Observation 5f35f421-db5a-41dc-8a66-2bb3975d8906 · outbound

This paper cites Robust and Verifiable Proportionality Axioms for Multiwinner Voting.

Proportional Clustering, the $\beta$-Plurality Problem, and Metric Distortion Robust and Verifiable Proportionality Axioms for Multiwinner Voting

Reference 7

Resolution
unresolved
no resolver link, observed 2026-08-07T19:40:37.020498Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-07T19:40:37.020498Z digest=sha256:03e9647ff72fba39f5e28851ac2c8fd3042873c621e3b88d05566ba2505a15b5

Observation 23287c8e-d985-47f6-9631-e8cadcf3d10d · outbound

This paper cites Caragiannis, E.

Proportional Clustering, the $\beta$-Plurality Problem, and Metric Distortion Caragiannis, E

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T19:40:37.592531Z

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.

source=arxiv_source observed=2026-08-07T19:40:37.027124Z digest=sha256:8898ce6080e162d97043e0568184dc14a7540fba9b71a6947957f1ade1df221c

Observation 066e645d-44c3-4a50-be97-f0490babebb4 · outbound

This paper cites an unresolved cited work.

Proportional Clustering, the $\beta$-Plurality Problem, and Metric Distortion Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-07T19:40:37.569624Z

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.

source=arxiv_source observed=2026-08-07T19:40:37.033045Z digest=sha256:52412f5daa6ad8c579a3a30f91b6bf4b324dec11058d4ffc63f73483d64a7ebf

Observation 671c2b3d-a247-4f79-80d0-44fe16a3c886 · outbound

This paper cites an unresolved cited work.

Proportional Clustering, the $\beta$-Plurality Problem, and Metric Distortion Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-07T19:40:37.544143Z

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.

source=arxiv_source observed=2026-08-07T19:40:37.039192Z digest=sha256:aff4e16aad52dc0281660fc30e9e8351d14de6aac36c8af095ba9bea5cfc3557

Observation a4fa6ea9-b42d-4250-b245-ecd5ae5901d3 · outbound

This paper cites an unresolved cited work.

Proportional Clustering, the $\beta$-Plurality Problem, and Metric Distortion Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-07T19:40:37.516509Z

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.

source=arxiv_source observed=2026-08-07T19:40:37.044818Z digest=sha256:5db4b2dd016655df2e55737b7cc75e011663b5ac5e8d7df8eb93bf827ea6efcd

Observation 6abaef20-7549-439c-9da4-cb69b18a4705 · outbound

This paper cites Ebadian and E.

Proportional Clustering, the $\beta$-Plurality Problem, and Metric Distortion Ebadian and E

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T19:40:37.486612Z

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.

source=arxiv_source observed=2026-08-07T19:40:37.051663Z digest=sha256:2a2fe0e3a308e92a497e426d26c9c03b3441fc43997f2836f409b3a132ea4356

Observation d1265768-5f5c-4671-a124-e5d3b95dcc0e · outbound

This paper cites Enelow and M.

Proportional Clustering, the $\beta$-Plurality Problem, and Metric Distortion Enelow and M

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T19:40:37.463516Z

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.

source=arxiv_source observed=2026-08-07T19:40:37.058108Z digest=sha256:a590f912062009f1e0b81bdbc1f7a4fd61875d87bcbc4ee8f37e13fbbdee3913

Observation 5b9ffc2d-64cf-4653-a053-39de9764a7b4 · outbound

This paper cites Filtser and O.

Proportional Clustering, the $\beta$-Plurality Problem, and Metric Distortion Filtser and O

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T19:40:37.442348Z

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.

source=arxiv_source observed=2026-08-07T19:40:37.066508Z digest=sha256:cb5f1d8f08ff8f8736f1e3abb3b28ce02959ff2dd4f3db05f9314cb2c8d6fed6

Observation df90ae0f-dbf2-4951-bf13-346d9e03a1f5 · outbound

This paper cites Gkatzelis, D.

Proportional Clustering, the $\beta$-Plurality Problem, and Metric Distortion Gkatzelis, D

Reference 15

Resolution
unresolved
no resolver link, observed 2026-08-07T19:40:37.073146Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-07T19:40:37.073146Z digest=sha256:5ba6f2dc3d45715b6068551938d63ec0e3b0ffbfd8d9961d4bc7cbe5921d706a

Observation 45f93639-d2d6-469d-8c45-6ff8f3c48ead · outbound

This paper cites an unresolved cited work.

Proportional Clustering, the $\beta$-Plurality Problem, and Metric Distortion Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-07T19:40:37.410590Z

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.

source=arxiv_source observed=2026-08-07T19:40:37.085827Z digest=sha256:d42d4a518080627dcf162d90500bc40a1786ec5986572b1857487b9e0aa8643b

Observation 4417e989-5978-4c40-8765-8623faace190 · outbound

This paper cites Kellerhals and J.

Proportional Clustering, the $\beta$-Plurality Problem, and Metric Distortion Kellerhals and J

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T19:40:37.389430Z

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.

source=arxiv_source observed=2026-08-07T19:40:37.093257Z digest=sha256:47ab4e750fca53d32889c7104f037d1a3576499b8cb8715b2a542f2e03d084b6

Observation 09df87ee-c4a9-44f8-b059-7fe93c7308f1 · outbound

This paper cites an unresolved cited work.

Proportional Clustering, the $\beta$-Plurality Problem, and Metric Distortion Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-07T19:40:37.369452Z

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.

source=arxiv_source observed=2026-08-07T19:40:37.102416Z digest=sha256:200d99697f11b66bffe57759d90d2bad85edb1b1448f9282fd6a316a1e4b83c5

Observation 5a8a8fd7-557e-496a-8e93-4e35af5a461b · outbound

This paper cites an unresolved cited work.

Proportional Clustering, the $\beta$-Plurality Problem, and Metric Distortion Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-07T19:40:37.351068Z

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.

source=arxiv_source observed=2026-08-07T19:40:37.110548Z digest=sha256:e6196554036aa3c722d0423facf0bb0cbd2dd76d784bc5920257deadffc8ecb8

Observation a2ea4b18-8150-4340-b5aa-9efb00efb368 · outbound

This paper cites The Condorcet Dimension of Metric Spaces.

Proportional Clustering, the $\beta$-Plurality Problem, and Metric Distortion The Condorcet Dimension of Metric Spaces

Reference 20

Resolution
verified exact
local_arxiv, observed 2026-08-07T19:40:37.211059Z

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.

source=arxiv_source observed=2026-08-07T19:40:37.120340Z digest=sha256:0eda9745d87d4cb71e806a633b669a4dc08b10148967d3a161c4c3bf1410b602

Observation ff07b7df-a063-4043-a772-64f9aaa94446 · outbound

This paper cites Masa r \' k, G.

Proportional Clustering, the $\beta$-Plurality Problem, and Metric Distortion Masa r \' k, G

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T19:40:37.330500Z

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.

source=arxiv_source observed=2026-08-07T19:40:37.127305Z digest=sha256:1b5b1063554d7c6204e0f7424631a82fad3b1c057185c3c3793e472aa7ebf1af

Observation e63b368d-3fbc-4c06-9b42-36fb4505336b · outbound

This paper cites McCune and A.

Proportional Clustering, the $\beta$-Plurality Problem, and Metric Distortion McCune and A

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T19:40:37.312652Z

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.

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Observation 4d2f6b4e-841b-45d0-b86d-2ac6a7f1a59b · outbound

This paper cites Micha and N.

Proportional Clustering, the $\beta$-Plurality Problem, and Metric Distortion Micha and N

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T19:40:37.293659Z

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.

source=arxiv_source observed=2026-08-07T19:40:37.140731Z digest=sha256:d68967809b489cefcae1883c9f9184ce4362c8be928ef188ad74bfe091ddbcbe

Observation cf3f432d-f819-46b0-a885-6ac93e10ff68 · outbound

This paper cites Peters and P.

Proportional Clustering, the $\beta$-Plurality Problem, and Metric Distortion Peters and P

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T19:40:37.274030Z

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.

source=arxiv_source observed=2026-08-07T19:40:37.147109Z digest=sha256:294210755cb47b655276a4c97ce1b2f46ce17dc8f39fb74fb35a00ec1bcfef21

Observation cda961f2-233f-4d8d-84db-acfcdf8ea303 · outbound

This paper cites an unresolved cited work.

Proportional Clustering, the $\beta$-Plurality Problem, and Metric Distortion Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-08-07T19:40:37.254917Z

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.

source=arxiv_source observed=2026-08-07T19:40:37.152805Z digest=sha256:005ba9fad009ff4ea9ee343069efac94e21f5ab1554a03b2d02a907c0bcc4566

Pith citing papers

No inbound Pith citation observations are available.