{"as_of":"2026-08-18T17:04:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:0c95f027ad4f164aa7ded3a51dc5cba889cf427d5af46276363d9dc3a6a043af","coverage":[{"denominator":23,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":23,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T00:47:34.089974Z","state":"measured"},{"denominator":25,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":25,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-16T07:24:07.482157Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-16T07:27:31.721407Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_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},"cited_work":{"arxiv_id":"2506.13191","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2506.13191","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"FPT constant approximation algorithms for colorful sum of radii.CoRR, abs/2506.13191","venue":null,"work_id":"0f15f94f-99cf-4c00-bd3f-6aa2ad7273b8","year":2025},"citing_paper":{"arxiv_id":"2602.05476","last_updated":"2026-04-24T11:47:11Z","snapshot_observed_at":"2026-07-06T22:44:37.993093Z","submitted_at":"2026-02-05T09:29:09Z","title":"FPT Approximations for Fair Sum of Radii with Outliers and General Norm Objectives","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-05-16T07:24:07.482157Z"},"links":{"cited_paper":"/paper/2506.13191","citing_paper":"/paper/2602.05476"},"observation_digest":"sha256:6cecb301d828e66b2c4a14d8fe866a4eb3b96ef953927a28613ddafaa3b9d9aa","observation_id":"5af41279-f684-49c8-8f8a-c661d0709f13","resolution":{"observed_at":"2026-05-16T07:27:31.723604Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_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},"cited_work":{"arxiv_id":"2506.13191","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2506.13191","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"FPT constant approximation algorithms for colorful sum of radii.CoRR, abs/2506.13191","venue":null,"work_id":"0f15f94f-99cf-4c00-bd3f-6aa2ad7273b8","year":2025},"citing_paper":{"arxiv_id":"2605.06398","last_updated":"2026-05-07T15:10:33Z","snapshot_observed_at":"2026-08-16T19:23:18.356276Z","submitted_at":"2026-05-07T15:10:33Z","title":"On the Parameterized Approximability of (Mergeable) Sum of Radii Clustering","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-05-08T05:47:36.257454Z"},"links":{"cited_paper":"/paper/2506.13191","citing_paper":"/paper/2605.06398"},"observation_digest":"sha256:0a598d254a89e77a79474625bb5f436e8d5fd5a524804b248979e5dd5336cc06","observation_id":"cc0009ac-7a02-461c-a46f-f0649a57e9c7","resolution":{"observed_at":"2026-05-11T21:21:13.190031Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2506.13191/citation-record","integrity":"/paper/2506.13191/integrity","json":"/paper/2506.13191/citation-record.json","paper":"/paper/2506.13191"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T00:47:34.478575Z","title":"Clustering what matters: Optimal approximation for clustering with outliers","venue":null,"work_id":"e5dc7f59-ef2c-42fe-bc49-0359f0c669f9","year":2023},"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":1,"source":"pdf_text","source_observed_at":"2026-08-07T00:47:33.992507Z"},"links":{"citing_paper":"/paper/2506.13191"},"observation_digest":"sha256:e293531faef537a0ca5fca1bc51fa64664d83f72551d7d6c7e7f0cc42b30c8ac","observation_id":"d761c2bc-554f-4a43-85be-96d7b796fa5c","resolution":{"observed_at":"2026-08-07T00:47:34.483224Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T00:47:34.463707Z","title":"A technique for obtaining true approximations for k-center with covering constraints","venue":null,"work_id":"670324dd-cd80-44d7-b6ed-ef0a5d0cb083","year":2022},"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":2,"source":"pdf_text","source_observed_at":"2026-08-07T00:47:33.997443Z"},"links":{"citing_paper":"/paper/2506.13191"},"observation_digest":"sha256:d405ac689203845eb483e854349e56a1b7d9afb70471d2306ab125583c71cde1","observation_id":"6c5760b1-2ba6-4a09-80ab-8d183a02e3f7","resolution":{"observed_at":"2026-08-07T00:47:34.468540Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T00:47:34.448577Z","title":"A constant approximation for colorful k-center","venue":null,"work_id":"6971594c-58e4-4146-97cf-916e3d924e26","year":2019},"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":3,"source":"pdf_text","source_observed_at":"2026-08-07T00:47:34.001948Z"},"links":{"citing_paper":"/paper/2506.13191"},"observation_digest":"sha256:dc160c63d1268257c52b76d19e2b89241782cc93ee55f78a42c0012b3c00c0b3","observation_id":"d1e6fe38-e27a-4c3d-a9c3-383a61754b15","resolution":{"observed_at":"2026-08-07T00:47:34.453386Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T00:47:34.433410Z","title":"Fair algorithms for clustering","venue":null,"work_id":"a9d97d76-faa2-43da-827f-0b91163df554","year":2019},"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":4,"source":"pdf_text","source_observed_at":"2026-08-07T00:47:34.006411Z"},"links":{"citing_paper":"/paper/2506.13191"},"observation_digest":"sha256:ad1f582ae774532bcf1a255528fbb3e59fab6f43c0cd26cf240b174bf6267696","observation_id":"72485aa9-b90f-4a27-8865-edea25fce836","resolution":{"observed_at":"2026-08-07T00:47:34.438245Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T00:47:34.418664Z","title":null,"venue":null,"work_id":"560e6a53-f8c3-403c-b13d-78113d34fd65","year":2024},"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":5,"source":"pdf_text","source_observed_at":"2026-08-07T00:47:34.011543Z"},"links":{"citing_paper":"/paper/2506.13191"},"observation_digest":"sha256:db5cf176cd7944635ec285f7d0338db875ce642080d3bf1329b25cb092ff46cc","observation_id":"16608608-f23a-4a63-ae7a-3cd02f5c56c1","resolution":{"observed_at":"2026-08-07T00:47:34.422823Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T00:47:34.404002Z","title":"Fpt approximations for fair k-min-sum-radii","venue":null,"work_id":"61bdc5c4-855b-47bc-a492-1ddbc11bde31","year":2024},"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":6,"source":"pdf_text","source_observed_at":"2026-08-07T00:47:34.015981Z"},"links":{"citing_paper":"/paper/2506.13191"},"observation_digest":"sha256:4a5d3a651c513793c1d6a7304162f2f445af70cba30505d9fcd38b49872784ed","observation_id":"25c8d010-0c99-4c29-9ef7-0a3854b1f675","resolution":{"observed_at":"2026-08-07T00:47:34.408693Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T00:47:34.389002Z","title":"Algorithms for facility location problems with outliers","venue":null,"work_id":"23070929-d947-439b-9891-d93143487b8e","year":2001},"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":7,"source":"pdf_text","source_observed_at":"2026-08-07T00:47:34.021327Z"},"links":{"citing_paper":"/paper/2506.13191"},"observation_digest":"sha256:f31920285e066bba42be9f03c8c4d0fc5f4485f665317d8e47c71fa1a56bd0e6","observation_id":"f968dbb4-37b0-40f2-9d15-b74587d98cd8","resolution":{"observed_at":"2026-08-07T00:47:34.393814Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T00:47:34.373839Z","title":"Clustering to minimize the sum of cluster diameters","venue":null,"work_id":"c0d2bb01-9b6a-4112-8ae1-fdaccd8cc123","year":2004},"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":8,"source":"pdf_text","source_observed_at":"2026-08-07T00:47:34.025689Z"},"links":{"citing_paper":"/paper/2506.13191"},"observation_digest":"sha256:323f6407ba939e07a269d5b92a1020dbb3b008910ce9ccadff20aedb8ee776a6","observation_id":"2492517b-e72a-4060-b027-847e4e70514c","resolution":{"observed_at":"2026-08-07T00:47:34.378490Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T00:47:34.359119Z","title":"Algorithms for covering multiple submodular constraints and applications","venue":null,"work_id":"cca3b51f-51bf-457c-b003-d73af99000b5","year":2022},"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":9,"source":"pdf_text","source_observed_at":"2026-08-07T00:47:34.029879Z"},"links":{"citing_paper":"/paper/2506.13191"},"observation_digest":"sha256:b2921f6c920acffc55974c58786e296dd3944b3b8723d5e8fe303ea3d9f86b1b","observation_id":"facbaac5-6eaa-44f4-a2b5-06c928a55855","resolution":{"observed_at":"2026-08-07T00:47:34.363809Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T00:47:34.344431Z","title":"Parameter- ized approximation algorithms for sum of radii clustering and variants","venue":null,"work_id":"14fa3a73-214e-43e2-adf7-75f8c88a46c2","year":2024},"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":10,"source":"pdf_text","source_observed_at":"2026-08-07T00:47:34.034075Z"},"links":{"citing_paper":"/paper/2506.13191"},"observation_digest":"sha256:5883281e61b410bd9d256257692502638f10d70a8ecfdf3b0eb3464238289077","observation_id":"a5b58420-5844-48f6-8200-6501861db83e","resolution":{"observed_at":"2026-08-07T00:47:34.348872Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T00:47:34.329764Z","title":"Pro- portionally fair clustering","venue":null,"work_id":"ff5c963a-0743-4c12-8cdb-86c319cceb1b","year":2019},"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":11,"source":"pdf_text","source_observed_at":"2026-08-07T00:47:34.038888Z"},"links":{"citing_paper":"/paper/2506.13191"},"observation_digest":"sha256:83d290bc6993f45bf821b13654ded646b40902bca40441bf8ebf641d608af9b3","observation_id":"caa5eef5-48a5-4079-8be7-c88d7a0e63e7","resolution":{"observed_at":"2026-08-07T00:47:34.333969Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T00:47:34.314330Z","title":"Fair clustering through fairlets","venue":null,"work_id":"ec160ab2-d729-4dc3-942a-82a4b472023e","year":2017},"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":12,"source":"pdf_text","source_observed_at":"2026-08-07T00:47:34.043146Z"},"links":{"citing_paper":"/paper/2506.13191"},"observation_digest":"sha256:f84bedcb506548dfa2efaa17a1b7f8463764dfdb4e824ddf64fc1c62d7742193","observation_id":"aafaef13-8f9f-4138-bc48-4db6b6b60205","resolution":{"observed_at":"2026-08-07T00:47:34.318852Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T00:47:34.047421Z","title":"Fpt approximations for capacitated sum of radii and diameters","venue":null,"work_id":null,"year":2024},"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":13,"source":"pdf_text","source_observed_at":"2026-08-07T00:47:34.047421Z"},"links":{"cited_paper":"/paper/2409.04984","citing_paper":"/paper/2506.13191"},"observation_digest":"sha256:02e47c45ed14c2972da218fd4e353b2515613ad847f4d624ab48d9f50c92b184","observation_id":"6443017c-986f-4c9b-aa3b-f90640a03aba","resolution":{"observed_at":"2026-08-07T00:47:34.047421Z","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":"2026-08-07T00:47:34.298376Z","title":"Improved polynomial-time approximations for clustering with minimum sum of radii or diameters","venue":null,"work_id":"5791d8ec-d8f2-4096-9cc6-03e946a3044b","year":2022},"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":14,"source":"pdf_text","source_observed_at":"2026-08-07T00:47:34.052226Z"},"links":{"citing_paper":"/paper/2506.13191"},"observation_digest":"sha256:97694b0f85359d278b1778cfa5755ae53e0a0c5a0956d211910f2d7ba8eb07df","observation_id":"7d471fba-f79f-4f2b-8c73-4fd451f4e90e","resolution":{"observed_at":"2026-08-07T00:47:34.303717Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T00:47:34.281035Z","title":"An efficient reduction technique for degree-constrained subgraph and bidirected network flow problems","venue":null,"work_id":"d7692e80-69ad-4923-8a48-bd254c1db9d9","year":1983},"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":15,"source":"pdf_text","source_observed_at":"2026-08-07T00:47:34.056301Z"},"links":{"citing_paper":"/paper/2506.13191"},"observation_digest":"sha256:2fc46dc718ca5d1585a8d31c04b5ad6a8c5ac33534643b8e775c45f56c8ca659","observation_id":"fc10c56e-62fb-4b4e-9b9a-b2f55ba0484a","resolution":{"observed_at":"2026-08-07T00:47:34.285820Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T00:47:34.265104Z","title":"Socially fair k-means clustering","venue":null,"work_id":"f0217205-248f-4e7a-a684-85d06674db79","year":2021},"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":16,"source":"pdf_text","source_observed_at":"2026-08-07T00:47:34.060708Z"},"links":{"citing_paper":"/paper/2506.13191"},"observation_digest":"sha256:81177c839d3b2076e76437796964858d3146dc12b03fec7e503db7cd49a7ecf6","observation_id":"681c7057-d300-4eeb-9e9a-2c55ff45821a","resolution":{"observed_at":"2026-08-07T00:47:34.270509Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T00:47:34.246283Z","title":"On metric clustering to minimize the sum of radii","venue":null,"work_id":"cfe45332-1c68-4ae8-b3fa-3d78095e953e","year":2010},"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":17,"source":"pdf_text","source_observed_at":"2026-08-07T00:47:34.064953Z"},"links":{"citing_paper":"/paper/2506.13191"},"observation_digest":"sha256:5fe43481ac3485224bcd2ae997a9a6a23e3e2339a21f8e5a771afa41caba07f2","observation_id":"8b256066-ad13-4574-9db9-0b5e7a67010c","resolution":{"observed_at":"2026-08-07T00:47:34.252108Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T00:47:34.229407Z","title":"Cluster analysis and mathematical programming","venue":null,"work_id":"914311e1-4a95-4e0e-a179-ee6f32d01fc3","year":1997},"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":18,"source":"pdf_text","source_observed_at":"2026-08-07T00:47:34.069184Z"},"links":{"citing_paper":"/paper/2506.13191"},"observation_digest":"sha256:85ff456e4f2d50a3a1ee10aa46579bd7e8ceed99c3ae092a5784b0e2ffaf80e8","observation_id":"294ffcd0-ece6-4040-a0bc-4b1bab471322","resolution":{"observed_at":"2026-08-07T00:47:34.234002Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T00:47:34.212753Z","title":"Capacitated sum-of-radii clustering: An fpt approximation","venue":null,"work_id":"ddfa9eb5-a167-4bb5-b48e-8949359c5992","year":2020},"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":19,"source":"pdf_text","source_observed_at":"2026-08-07T00:47:34.073170Z"},"links":{"citing_paper":"/paper/2506.13191"},"observation_digest":"sha256:38539821b178d834804f58ebf91298cb2b9aede6fc8e686bcd9aa2f8c961cf9c","observation_id":"c0d5f71a-e35f-4e19-b744-d9a231e9808b","resolution":{"observed_at":"2026-08-07T00:47:34.218029Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T00:47:34.197649Z","title":"Fpt approximation for capacitated sum of radii","venue":null,"work_id":"d69c5c71-136c-4b5c-8b1c-afbd0e0ccb79","year":2024},"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":20,"source":"pdf_text","source_observed_at":"2026-08-07T00:47:34.077362Z"},"links":{"citing_paper":"/paper/2506.13191"},"observation_digest":"sha256:201f2081abf2f8f102328ab50f9ddd2ada6cc2e928e738b6786123cd9ae42f28","observation_id":"98857c75-d8c2-493c-878e-fe9190e65905","resolution":{"observed_at":"2026-08-07T00:47:34.202133Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T00:47:34.181963Z","title":"Fair colorful k-center clustering","venue":null,"work_id":"d9d96076-b1c5-41b2-92fa-ef2e3fd2f0a8","year":2022},"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":21,"source":"pdf_text","source_observed_at":"2026-08-07T00:47:34.081530Z"},"links":{"citing_paper":"/paper/2506.13191"},"observation_digest":"sha256:03a6394ea6be0c88051c59fc32f0a3b5f459c030f56365dc6e16e027a32509e2","observation_id":"19b1edbf-da59-460c-bc39-8eb1646b975e","resolution":{"observed_at":"2026-08-07T00:47:34.187379Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-07T00:47:34.166371Z","title":"Partitioning points and graphs to minimize the maximum or the sum of diameters","venue":null,"work_id":"4c169c26-6da0-4357-a6cc-08e541bcdaa9","year":1989},"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":22,"source":"pdf_text","source_observed_at":"2026-08-07T00:47:34.085820Z"},"links":{"citing_paper":"/paper/2506.13191"},"observation_digest":"sha256:3563bd88666af24275e2b1d6957a9c4662f7db6592db0452162fdc2ae377bb9e","observation_id":"e0d701a1-8c1a-4c75-9cf9-0cfb2991cc87","resolution":{"observed_at":"2026-08-07T00:47:34.171039Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"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":"sha256:4c7f28c40f46154db339703c9d4691f63caf4254d3d7b4854c82972fa45f808e","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 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.13191","last_updated":"2025-06-16T07:59:42Z","latest_version":1,"primary_category":"cs.CG","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"},"reference_resolution":{"displayed":23,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":2,"verified_exact":1,"verified_fuzzy":20},"total_outbound_references":23},"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":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 2 inbound Pith citation observations for arXiv:2506.13191."}