{"as_of":"2026-08-19T20:14:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ccc4cc4ab68934539836b17b630c1fafcb0190de9ce1d8d2e4eac0b498e641d7","coverage":[{"denominator":54,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":54,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T11:54:16.450669Z","state":"measured"},{"denominator":55,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":55,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-19T06:32:44.657259+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T00:47:34.089974Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-07T00:47:34.128097Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"cited_work":{"arxiv_id":"2504.14683","doi":null,"metadata_source":"pith","pith_arxiv_id":"2504.14683","snapshot_observed_at":"2026-08-07T00:47:34.128097Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","venue":"cs.DS","work_id":"9799329e-4716-4710-bbf3-958a0ded7b31","year":2025},"citing_paper":{"arxiv_id":"2506.13191","last_updated":"2025-06-16T07:59:42Z","snapshot_observed_at":"2026-08-07T00:33:30.970585Z","submitted_at":"2025-06-16T07:59:42Z","title":"FPT Constant Approximation Algorithms for Colorful Sum of Radii","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T00:47:34.089974Z"},"links":{"cited_paper":"/paper/2504.14683","citing_paper":"/paper/2506.13191"},"observation_digest":"sha256:c880fdd3dcaa10172b092ebbb3f598d8eb6669fd94c700c0a8bedbd1e980007f","observation_id":"1f2dce8f-f409-41d8-b331-a07e39f5c1bf","resolution":{"observed_at":"2026-08-07T00:47:34.135877Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2504.14683/citation-record","integrity":"/paper/2504.14683/integrity","json":"/paper/2504.14683/citation-record.json","paper":"/paper/2504.14683"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:17.167126Z","title":"Chen, Allen Liu, Sandeep Silwal, Pattara Sukprasert, Ali Vakil- ian, and Fred Zhang","venue":null,"work_id":"ac9fc999-35d5-47b8-8ffc-3ed0f12db7e8","year":2023},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.223060Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:6f959c86a1f4aea8c893655915b5f13d8e4e37b0660543fac12edd386eb91dfc","observation_id":"e2a64135-7fdc-409f-a0d9-ab0b1d1ed81d","resolution":{"observed_at":"2026-08-16T11:54:17.171564Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:17.153802Z","title":"Fair clustering via equi- table group representations","venue":null,"work_id":"7d93a85e-6168-499c-b494-1b469ac79b8d","year":2021},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.228530Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:d1ec2ae8715be4cee7cf13da9005a4fad07b3fca2099934f4d5d195b5e68d387","observation_id":"05d82380-fba5-4979-9ba8-35adbf544460","resolution":{"observed_at":"2026-08-16T11:54:17.158286Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4230/lipics.icalp.2016.69","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:17.139820Z","title":"Approximation Algorithms for Clustering Problems with Lower Bounds and Outliers","venue":null,"work_id":"ff5c5c51-648f-4b46-84b4-b507c3abc31e","year":2016},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.233059Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:ff0137e5cf1985e965df012cb1813a7284a5aff4649aff4a8f168e059379c3bd","observation_id":"6a5daa9e-6449-4afd-85f4-2ac649a24aec","resolution":{"observed_at":"2026-08-16T11:54:17.144427Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:17.125049Z","title":"A technique for obtaining true approximations for k-center with covering constraints","venue":null,"work_id":"7a5abbd3-47bf-4758-8493-ee53743218b1","year":2020},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.237658Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:c4d7a5eee71aebfcb2c4cb95e146b4e2f97950de8e8b3f1eecb966627a23e115","observation_id":"3d0504d4-6439-49af-bc6f-2753f0fbda38","resolution":{"observed_at":"2026-08-16T11:54:17.129794Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:17.110683Z","title":"Local search heuristics for k-median and facility location problems","venue":null,"work_id":"ffa40c06-a592-41c8-9b5c-6cb0ba49a6ce","year":2004},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.241948Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:8cd3620298594c0381611c87d0b544abe69d760cf2b0daf2d6c9633b7741f73f","observation_id":"bd0629fe-7d5e-43e8-aee1-8563b2c187a2","resolution":{"observed_at":"2026-08-16T11:54:17.115062Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:17.095442Z","title":"Scalable fair clustering","venue":null,"work_id":"9d1264d5-8a50-4df2-aadf-5dbfd0cb6a67","year":null},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.246471Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:dedcc393865369084eebe8700eacac55f9302c6612bc0022c7654085dcad670a","observation_id":"31a5e8b1-6d03-4db3-b5d5-04a597d0dca9","resolution":{"observed_at":"2026-08-16T11:54:17.100137Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.10378","last_updated":"2025-02-27T16:29:30Z","snapshot_observed_at":"2026-08-18T18:28:17.325975Z","submitted_at":"2024-05-16T18:17:44Z","title":"A Polynomial-Time Approximation for Pairwise Fair $k$-Median Clustering","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.10378","snapshot_observed_at":"2026-08-16T11:54:16.250905Z","title":"A polynomial- time approximation for pairwise fair k-median clustering","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.250905Z"},"links":{"cited_paper":"/paper/2405.10378","citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:ef5914ce77c7696445d703a6ad1a2865a7f790703ccb0333658c4f582fbd5367","observation_id":"b1000775-fb0f-4bbe-b8da-e158c17aac86","resolution":{"observed_at":"2026-08-16T11:54:16.250905Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:17.082085Z","title":"A constant approximation for colorfulk-center","venue":null,"work_id":"11927ddf-e853-4a0b-b390-29aab6ab5ae7","year":2019},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.255623Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:f5a3a118358c40ab8f59215e0363a2f4e83dd4b8acd8be404ea6232106b9bbb6","observation_id":"56d615f0-5fc3-4dff-a647-4cba058f632e","resolution":{"observed_at":"2026-08-16T11:54:17.086289Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:17.068357Z","title":"FPT constant-approximations for capacitated clustering to minimize the sum of cluster radii","venue":null,"work_id":"91eeeaf4-ce90-40d2-a51f-3a6239ed7858","year":2023},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.260156Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:0f29a7123530d7f510f8dae81fcde346bda3d1c302c1460e78e7ebc27f8b5a5e","observation_id":"dc6a1fb9-e3b7-487f-8371-19546eb23a9f","resolution":{"observed_at":"2026-08-16T11:54:17.072619Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.264256Z","title":"Varadarajan","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.264256Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:9b0c5db5cc6f059c2037063b71dc674afacfcca04a99476729d9c0323adcd2b2","observation_id":"f5f60519-7bf6-4dac-b92e-4ba65dec8eda","resolution":{"observed_at":"2026-08-16T11:54:16.264256Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:17.055542Z","title":"Novel properties of hierar- chical probabilistic partitions and their algorithmic applications","venue":null,"work_id":"450064ae-ae97-41c6-8c79-5dc25d78f49f","year":2024},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.268487Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:79e66b31cffb428bbeddc1c62fd0c68d2647bcd4b7803131fd3b4316a116bb43","observation_id":"c25caa0f-7bde-49c1-8e01-e078610b6ae8","resolution":{"observed_at":"2026-08-16T11:54:17.059767Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:17.042640Z","title":"Improved fixed-parameter bounds for min-sum-radii and diameters k-clustering and their fair variants","venue":null,"work_id":"3b98c1f4-4380-45ae-92c5-53ab2ef84a42","year":2025},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.272549Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:626b23067019f61cadc40fc792ec92c825bf37a25ed6174e43c22997569dafc5","observation_id":"5db5c995-7396-4587-bbbc-a2dcf8e1937e","resolution":{"observed_at":"2026-08-16T11:54:17.046985Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.276680Z","title":"Salavatipour","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.276680Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:388242baf7f5ec18e164df30c4ac5565d32da035fc1fbfd77c4c77728c4f7323","observation_id":"9eec356c-249e-4df7-b11f-dd4f3ccb7c02","resolution":{"observed_at":"2026-08-16T11:54:16.276680Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:17.029881Z","title":"Fair algorithms for clustering","venue":null,"work_id":"3dee0e8f-2714-4b52-b7bd-8fab96dd0273","year":2019},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.280760Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:86e263cfcab3c55eb92cf887de94cf248036bd5c607f35c1156762dcca9380a9","observation_id":"f7988cd0-8805-471f-b1e0-f3edb055155c","resolution":{"observed_at":"2026-08-16T11:54:17.034024Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:17.016601Z","title":"On the cost of essentially fair clusterings","venue":null,"work_id":"7e7de9d8-ddd2-46a1-a8c7-e184a0676ad7","year":2019},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.284766Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:3f0fb4a00051ed8f631f2d0b53161d782ebb9f734d17e2742dc91f15931c7938","observation_id":"d673321f-2cd6-4c7d-9edd-1fc22278e151","resolution":{"observed_at":"2026-08-16T11:54:17.021052Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2002.07892","last_updated":"2021-03-05T23:52:05Z","snapshot_observed_at":"2026-08-19T05:44:58.568720Z","submitted_at":"2020-02-18T21:54:01Z","title":"Fair Clustering with Multiple Colors","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2002.07892","snapshot_observed_at":"2026-08-16T11:54:16.289090Z","title":"Fair clustering with multiple colors","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.289090Z"},"links":{"cited_paper":"/paper/2002.07892","citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:05780e80f0dbd3e1f32977bc94f47ce4eaa8afdbdffa33b3a20d2b0dc3d1d47e","observation_id":"e178091d-4071-4810-917c-b30936128ad7","resolution":{"observed_at":"2026-08-16T11:54:16.289090Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:17.003073Z","title":"Fairness, semi- supervised learning, and more: A general framework for clustering with stochastic pairwise constraints","venue":null,"work_id":"384f6a93-0649-4be1-b34b-35ef48b52726","year":2021},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.293688Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:b1f5e751614cfdf3fb5a65832d125f5df41e0285a290bbfae5132bb6db615a8c","observation_id":"f390b9f2-0f73-403e-8939-8982fcb55423","resolution":{"observed_at":"2026-08-16T11:54:17.007413Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.989410Z","title":"A (3 + ϵ)- approximation algorithm for the minimum sum of radii problem with outliers and extensions for generalized lower bounds","venue":null,"work_id":"d432e54b-d577-45b9-83a4-dd2d2e020b44","year":2024},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.297984Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:22e4e9f2bdbbb4aad580643b71dac2ed6d15d890714e6b5b5b17578d38ec7156","observation_id":"748fba34-623c-4bfa-be78-902208e1e5ab","resolution":{"observed_at":"2026-08-16T11:54:16.993954Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.301954Z","title":"FPT Ap- proximations for Fairk-Min-Sum-Radii","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.301954Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:1f5b486aa3bb8c31549a3493f4f25c2d4aee957252585c8dfd12eff16aa04294","observation_id":"ac9b44a2-5230-4e23-beb0-470ab4a27b26","resolution":{"observed_at":"2026-08-16T11:54:16.301954Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.306371Z","title":"Clustering to minimize the sum of cluster diameters","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.306371Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:db6b7b08706e6d64f21eca2e4b27a1aee54274c7fe2e10e7789c1df607c9911d","observation_id":"a751d630-3156-4d9f-971a-e1682106e83c","resolution":{"observed_at":"2026-08-16T11:54:16.306371Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.976488Z","title":"Matroid and knapsack center problems","venue":null,"work_id":"fb7e715a-ebb0-4c76-a203-389afe28cd5c","year":2016},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.310465Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:88a7daa5bf969059607a5c1d2e11f14c38bca1ecb24af392f79771812c9ac35c","observation_id":"02a9d881-271c-4fba-a7a1-4d01255be1b7","resolution":{"observed_at":"2026-08-16T11:54:16.980856Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.963187Z","title":"Parameterized approximation algorithms for sum of radii clustering and variants","venue":null,"work_id":"383e433e-cd67-4b07-a23a-215f24b0cd47","year":2024},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.314534Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:d674d3ae4ff54d338acaa502d8b167d6bc7b5d712d04eb7817ec9dc873282173","observation_id":"a5d13732-a258-43a1-bd5f-30d102320139","resolution":{"observed_at":"2026-08-16T11:54:16.967319Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.949522Z","title":"Proportionally fair clustering","venue":null,"work_id":"092232a4-28ef-4c7c-8049-2494f2378670","year":2019},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.318630Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:bc09847945bb48f7692c8ceb2f0c3a1c5851df70f52eeacc0b4527046828c8dd","observation_id":"f6a8fdb7-82bd-41fd-84f4-427776275f90","resolution":{"observed_at":"2026-08-16T11:54:16.954255Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.934554Z","title":"Fair clustering through fairlets","venue":null,"work_id":"b4d1fa7a-4a05-419a-8b77-5ad21a8bacb4","year":null},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.322694Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:09a3d55f32d2cc05b610866c33382930bb37bbdda223a65a98ecb7567adf1b0d","observation_id":"a5694255-b864-4792-a0dc-59ac59bd03c7","resolution":{"observed_at":"2026-08-16T11:54:16.939451Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.919206Z","title":"How to solve fair k-center in massive data models","venue":null,"work_id":"26e929c1-f3c4-452b-90b3-247a62a239ef","year":2020},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.327112Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:4dd1aa892047021d746ea69d289c15aad8b39b64e24c86e9693bec38a8163ce4","observation_id":"7d3d1f16-acfa-4ed2-9111-0792d0ee4f63","resolution":{"observed_at":"2026-08-16T11:54:16.924679Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.905888Z","title":"Approximating fair clustering with cascaded norm objectives","venue":null,"work_id":"5ef6384e-e364-4fb1-ba62-f2f151264366","year":2022},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.331237Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:844dfab440c8ab64d438b6f3fda9f6e038f10ab9106aafd9c44c25f47b53fd56","observation_id":"0a4262e2-f994-48c0-93d3-4f0c5af1b728","resolution":{"observed_at":"2026-08-16T11:54:16.910135Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.892145Z","title":"Fair representation clustering with several protected classes","venue":null,"work_id":"5f888128-5575-4274-95c2-29403e04cf09","year":2022},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.335196Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:9d084e46397a20e241c51861f78febefd3cc5df46f54c54d91c53ebedd6cf909","observation_id":"d994fca3-32ed-4699-aed3-8943acdcea0c","resolution":{"observed_at":"2026-08-16T11:54:16.896651Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.878522Z","title":"Marathe, S","venue":null,"work_id":"72100322-3b81-4d93-8a6e-a87dbcc84f2f","year":2000},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.339509Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:788839512efbbad510b9a70f78b5fffc131aec7d9b30f5f2a8e687ccf79ea97c","observation_id":"d87bde2f-7d50-4302-b929-30ca2fcb0243","resolution":{"observed_at":"2026-08-16T11:54:16.882738Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.864055Z","title":"Ap- proximating fair k-min-sum-radii in euclidean space","venue":null,"work_id":"573ff639-9b91-454d-bf1a-23809651f518","year":2023},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.343534Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:a2acfbd6ce8f8a6a5a1809f4b822fddd9825cfb730c47c0ba192638077ee9e52","observation_id":"ad8a0a95-fba0-4ba8-be2c-6ecc8359d0d1","resolution":{"observed_at":"2026-08-16T11:54:16.869008Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2409.04984","last_updated":"2025-09-06T12:50:56Z","snapshot_observed_at":"2026-08-16T13:20:27.977949Z","submitted_at":"2024-09-08T05:46:21Z","title":"FPT approximations for Capacitated Sum of Radii and Diameters","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.04984","snapshot_observed_at":"2026-08-16T11:54:16.347655Z","title":"Fpt approximations for capacitated sum of radii and diameters","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.347655Z"},"links":{"cited_paper":"/paper/2409.04984","citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:cc80f7a8484cb8e9ae849027245cf64c21c740759836042fa79e6d62e0101758","observation_id":"a6bf5bb5-9e25-4092-a989-6584af036d01","resolution":{"observed_at":"2026-08-16T11:54:16.347655Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.352103Z","title":"Improved Polynomial-Time Approximations for Clustering with Minimum Sum of Radii or Diameters","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.352103Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:14fc790daa2ed9a72f063e4fff9a7d3ab199ca235fc5a25b2232a94ff7035733","observation_id":"15c56f80-4373-4d4f-9c63-da10f6e00fb2","resolution":{"observed_at":"2026-08-16T11:54:16.352103Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.841316Z","title":"An efficient reduction technique for degree-constrained subgraph and bidi- rected network flow problems","venue":null,"work_id":"df124504-85a8-4362-a776-cb6ba108969d","year":1983},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.356425Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:821135c16608205737a7bbab0712b41b1f1d58b187a97b7b8ef71ae5df0666cd","observation_id":"2145d503-28b5-4953-babe-f2bad0ba95d9","resolution":{"observed_at":"2026-08-16T11:54:16.845727Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.828516Z","title":null,"venue":null,"work_id":"ce7d2a5e-4dad-40fe-bd59-01fe0a9dbc8d","year":2021},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.360622Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:aeefa40bf6975846f04dfb308bb3f5e3eed7f82122ad26c6bcdcde6947f67037","observation_id":"b5008a98-07f0-49d5-9df1-29dd2514e347","resolution":{"observed_at":"2026-08-16T11:54:16.832717Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2206.11210","last_updated":"2022-06-22T16:57:17Z","snapshot_observed_at":"2026-08-18T23:26:39.800735Z","submitted_at":"2022-06-22T16:57:17Z","title":"Constant-Factor Approximation Algorithms for Socially Fair $k$-Clustering","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2206.11210","snapshot_observed_at":"2026-08-16T11:54:16.364678Z","title":"Constant-factor approximation al- gorithms for socially fair k-clustering","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.364678Z"},"links":{"cited_paper":"/paper/2206.11210","citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:0273058db9933ce4fabfb0ef1d7940f47cdae823822bdf773972f81128f323ad","observation_id":"e69d1fb8-3c93-4eb0-b35e-417def3488f9","resolution":{"observed_at":"2026-08-16T11:54:16.364678Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00453-009-9282-7","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-18T11:03:46.223893Z","title":"Pirwani, and Kasturi R","venue":"Algorithmica","work_id":"d9ae595e-3b5a-43ab-a17b-52c82247f8d1","year":2010},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.369579Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:e3e39b764948c4bea09ba661cd636ed26f90671e19f203e59d640d4e0cefb8d6","observation_id":"2e5370d5-f78d-4d55-9729-157e09670780","resolution":{"observed_at":"2026-08-16T11:54:16.527239Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.374130Z","title":"Pirwani, and Kasturi R","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.374130Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:b7b0fe8c6c5279ece8b4adc9a028bdb536fb1702023dfa0c5f15f9f3bf034330","observation_id":"058e392d-6234-4729-a384-107a818cecfd","resolution":{"observed_at":"2026-08-16T11:54:16.374130Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.814821Z","title":"Clustering to minimize the maximum intercluster distance","venue":null,"work_id":"dfc5aa15-16aa-433c-93e4-29979f277e22","year":1985},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.378318Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:12eda66713696cc3e7121220d81cc9b037723f149e8b01f5c4fc5d8b387fca21","observation_id":"d839c04c-74e6-4434-a82f-4b45c3c39e19","resolution":{"observed_at":"2026-08-16T11:54:16.819120Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2211.14873","last_updated":"2024-06-20T04:02:53Z","snapshot_observed_at":"2026-08-16T16:13:01.232167Z","submitted_at":"2022-11-27T16:07:21Z","title":"Which $L_p$ norm is the fairest? Approximations for fair facility location across all \"$p$\"","version":4},"cited_work":{"arxiv_id":"2211.14873","doi":null,"metadata_source":"pith","pith_arxiv_id":"2211.14873","snapshot_observed_at":"2026-08-16T11:54:16.575187Z","title":"Which $L_p$ norm is the fairest? Approximations for fair facility location across all \"$p$\"","venue":"cs.DS","work_id":"e18c9d62-e136-42bf-86d0-011da5dec19c","year":2022},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.382315Z"},"links":{"cited_paper":"/paper/2211.14873","citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:0bda397b8e2c02647d9496149546d9c9c602244b7bd26855b240906288fc5286","observation_id":"73e7a437-cf5a-41d3-b172-4cdb556d2808","resolution":{"observed_at":"2026-08-16T11:54:16.580167Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.386641Z","title":"Optimal broadcast domination in polynomial time","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.386641Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:1e4f5bcf3f1fc701bf31c7123a100ff4b1151d11e3fb6ba8165301ab847070df","observation_id":"d851e88e-b014-4646-b3a6-ed3cf0b6c4d6","resolution":{"observed_at":"2026-08-16T11:54:16.386641Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00453-020-00721-7","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-18T11:03:46.223893Z","title":"Dynamic clustering to minimize the sum of radii","venue":"HAL (Le Centre pour la Communication Scientifique Directe)","work_id":"e8a6fc85-b263-4a9b-af67-8bd450acf51f","year":2020},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.390707Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:ebdc129681b3bc03fc4705e4f93abda39af1ef23e7305a0bc5e2309a423f1bf4","observation_id":"1d251c68-9db4-4325-9947-4a773225ab16","resolution":{"observed_at":"2026-08-16T11:54:16.497103Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.802012Z","title":"Approximation algorithms for fair range clustering","venue":null,"work_id":"cbb0fb21-e133-4542-b3ed-1ca8b167443d","year":2023},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.394844Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:165bd5efbe2887cb5658756675cc2a6a5d1e4811d304dd44e0e3ddd7bcabc70a","observation_id":"272ddf17-0707-455d-94e3-aa94bbb71abb","resolution":{"observed_at":"2026-08-16T11:54:16.806195Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.400614Z","title":"Varadarajan","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.400614Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:c9e0f693da26008b69b30390354845f268c8bf415c22d8726d2daab71f8e12ee","observation_id":"5b3717e5-5cd3-4048-9b08-e3bd631fc2a9","resolution":{"observed_at":"2026-08-16T11:54:16.400614Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.788857Z","title":"FPT approximation for capacitated sum of radii","venue":null,"work_id":"f4040b40-39fe-4365-8d2d-b3d97ca91a47","year":2024},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.405035Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:aed584c46efe78b076ddb7f4660634a2533415e1ccabca17532a232705905266","observation_id":"77c74bef-2887-418b-a34f-8bc11c73767f","resolution":{"observed_at":"2026-08-16T11:54:16.792924Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.775819Z","title":"Fair colorfulk-center clustering","venue":null,"work_id":"2d88edcd-4a14-4c55-a73e-17b525d1547a","year":null},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.409323Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:a576bb1cdfb6c1cf2840b205fbcbfb8b517a9a71525462ed0faf8f9af049b599","observation_id":"7fc260d1-2abc-48f3-9a95-de3a79d18968","resolution":{"observed_at":"2026-08-16T11:54:16.780037Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.762864Z","title":"A center in your neighborhood: Fairness in facility location","venue":null,"work_id":"d92bc565-34db-4409-b65a-4e3990d7e1fa","year":2020},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.413628Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:8323e8ab15ccbba4638a56c25b827b26f8aa4999b27b6bd89d64880c6ddb3c4b","observation_id":"cc5190bf-3bb2-4527-a301-ba6752cc504f","resolution":{"observed_at":"2026-08-16T11:54:16.767265Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.749922Z","title":"Mount, Nathan S","venue":null,"work_id":"353f4001-a34a-435a-8bf5-ea748bd2b050","year":2004},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.417643Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:95703078378ca9fb8d4a338447f20ced0e3c0ac20edc1758f53c1a72b8213f53","observation_id":"ced3313d-b31e-4618-a610-ea99c64ef2de","resolution":{"observed_at":"2026-08-16T11:54:16.754012Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.736733Z","title":"Fair k-center clustering for data summarization","venue":null,"work_id":"ca7fec77-b3c8-4e72-a01a-116289162803","year":2019},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.421625Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:5af56cf7f150367cd7378d53652430885f7920debb94d4422b1985e6c77b91df","observation_id":"f717f761-e5ce-41e2-979e-d29c368a0583","resolution":{"observed_at":"2026-08-16T11:54:16.740998Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.723325Z","title":"Constant approximation for k-median and k-means with outliers via iterative rounding","venue":null,"work_id":"d5c917b2-1dd1-4ba6-b977-7287392454a6","year":2018},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.425789Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:b8e1f9d408edee54bbfa2152e801fc305fc44810f44b39bd806bcafe711119cc","observation_id":"7687a5d8-4089-4e2d-8953-33e1e60e263a","resolution":{"observed_at":"2026-08-16T11:54:16.728194Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.709651Z","title":"Approximation algorithms for socially fair clustering","venue":null,"work_id":"00673a48-fec2-4d06-9ee9-cd72e210312c","year":2021},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.429863Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:062378062c152c44765895464f6624cb1fcf9749144fa7c26ab0cb1dd43522d4","observation_id":"1bf4c128-5bac-41b3-93c7-1c3983bc9227","resolution":{"observed_at":"2026-08-16T11:54:16.713933Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.695803Z","title":"Proportionally fair clustering revisited","venue":null,"work_id":"bc12a379-4059-4315-9749-c8710418f266","year":2020},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.433826Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:b49c0510723b8ccb2e90dab19732acca887bd0af33b6624203434f5c28319cf2","observation_id":"9621a5e4-a1cd-4da5-a5c3-95cc68d53246","resolution":{"observed_at":"2026-08-16T11:54:16.699930Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.682631Z","title":"Better algorithms for individually fair k- clustering","venue":null,"work_id":"d4f293d7-a637-4ff8-abad-58af516bd509","year":null},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.437851Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:83924b7cb1b8f3e4607073e2d5b36b8c3451abac0455d4606805d4e61150f10a","observation_id":"7c17ff45-9c98-447a-8b94-5bd0fb14b41c","resolution":{"observed_at":"2026-08-16T11:54:16.686820Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.669653Z","title":"Computing a many-to-many matching with de- mands and capacities between two sets using the hungarian algorithm.Journal of mathematics, 2023(1):7761902, 2023","venue":null,"work_id":"6dfd9fb9-75d1-487f-9521-60ec07e9185b","year":2023},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.442357Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:b01809060f7c3c6efdf6cc31b1303f6121c9a0e350f0a68ec09e0c844d1cbe10","observation_id":"3b3db008-0549-4507-9f34-91c5d931828e","resolution":{"observed_at":"2026-08-16T11:54:16.673893Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.655834Z","title":"Fair coresets and streaming algorithms for fair k-means","venue":null,"work_id":"c1470b31-94ad-4182-b0c9-93aafc4b06f2","year":2019},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.446535Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:c960d7d21d8307fe0be0422733116af07dea9f0b2b7e613517d9ce979750889d","observation_id":"f6f9d3d5-64e9-492e-8841-f44a30e3bdd8","resolution":{"observed_at":"2026-08-16T11:54:16.660839Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-16T11:54:16.641755Z","title":"Improved approximation algorithms for individually fair clustering","venue":null,"work_id":"793bb19a-fb96-483e-a6ae-9a3da89f5db7","year":2022},"citing_paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering","version":2},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-16T11:54:16.450669Z"},"links":{"citing_paper":"/paper/2504.14683"},"observation_digest":"sha256:14d505f3c0e9435791ba9a974d5185f0b2b36775602dcf3ef42f92373769f4b2","observation_id":"a872b4dc-6be0-43b4-9a5d-25a11c98e855","resolution":{"observed_at":"2026-08-16T11:54:16.646992Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2504.14683","last_updated":"2025-08-01T04:12:22Z","latest_version":2,"primary_category":"cs.DS","snapshot_observed_at":"2026-08-17T23:40:20.982621Z","submitted_at":"2025-04-20T17:19:03Z","title":"Polynomial-Time Constant-Approximation for Fair Sum-of-Radii Clustering"},"reference_resolution":{"displayed":54,"state_counts":{"malformed_identifier":2,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":11,"verified_exact":4,"verified_fuzzy":37},"total_outbound_references":54},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 19 August 2026, this Paper Citation Record lists 54 of 54 outbound references and 1 inbound Pith citation observation for arXiv:2504.14683."}