{"as_of":"2026-08-16T09:48:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:871aea90e611b99cbffe0bdb1078544ebb91fb83681202e4b15cd64442823b48","coverage":[{"denominator":20,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":20,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T14:20:20.149615Z","state":"measured"},{"denominator":20,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":20,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/1908.06818/citation-record","integrity":"/paper/1908.06818/integrity","json":"/paper/1908.06818/citation-record.json","paper":"/paper/1908.06818"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T14:20:20.365801Z","title":null,"venue":null,"work_id":"37243dcd-abd2-4cc0-aba8-7c887ea8296e","year":null},"citing_paper":{"arxiv_id":"1908.06818","last_updated":"2021-02-22T03:13:45Z","snapshot_observed_at":"2026-08-16T02:25:27.522921Z","submitted_at":"2019-08-09T18:21:00Z","title":"Unexpected Effects of Online no-Substitution k-means Clustering","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T14:20:20.083230Z"},"links":{"citing_paper":"/paper/1908.06818"},"observation_digest":"sha256:70990b50f434422aabb6e2cf14b5870bfe1138961188c507b7f8c1704b09045d","observation_id":"08be0f34-b32b-4a7b-9af5-ab97237aa871","resolution":{"observed_at":"2026-08-14T14:20:20.369066Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:20:20.355986Z","title":"This is proved in Claims 14 and 15","venue":null,"work_id":"1de8b499-e2a7-48fc-9cb7-3b59c55d089b","year":null},"citing_paper":{"arxiv_id":"1908.06818","last_updated":"2021-02-22T03:13:45Z","snapshot_observed_at":"2026-08-16T02:25:27.522921Z","submitted_at":"2019-08-09T18:21:00Z","title":"Unexpected Effects of Online no-Substitution k-means Clustering","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T14:20:20.087004Z"},"links":{"citing_paper":"/paper/1908.06818"},"observation_digest":"sha256:8da3138e40ce55282b5eee43191ec5e211f6fe6563e24c5ff5805caa3e5d2643","observation_id":"c0820617-f340-4b14-b984-54c005bbee1c","resolution":{"observed_at":"2026-08-14T14:20:20.359649Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:20:20.281834Z","title":"We cannot use this deﬁnition in our framework","venue":null,"work_id":"8cf3eeda-72ec-4378-9c45-e0c83e35c987","year":1999},"citing_paper":{"arxiv_id":"1908.06818","last_updated":"2021-02-22T03:13:45Z","snapshot_observed_at":"2026-08-16T02:25:27.522921Z","submitted_at":"2019-08-09T18:21:00Z","title":"Unexpected Effects of Online no-Substitution k-means Clustering","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T14:20:20.114681Z"},"links":{"citing_paper":"/paper/1908.06818"},"observation_digest":"sha256:0a31e2462edf9df9297bc7fc93657991957ab3d6977054f27422efef719bf60b","observation_id":"e34771be-fdd8-46e1-8a6a-bd0fc70df4b5","resolution":{"observed_at":"2026-08-14T14:20:20.285750Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:20:20.346246Z","title":null,"venue":null,"work_id":"d75f3a3f-8962-464f-9af2-ce47d088c20c","year":null},"citing_paper":{"arxiv_id":"1908.06818","last_updated":"2021-02-22T03:13:45Z","snapshot_observed_at":"2026-08-16T02:25:27.522921Z","submitted_at":"2019-08-09T18:21:00Z","title":"Unexpected Effects of Online no-Substitution k-means Clustering","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T14:20:20.090956Z"},"links":{"citing_paper":"/paper/1908.06818"},"observation_digest":"sha256:710fc529780d3653f123d0174726a5fc4298c143285e949383b39d65e965c45a","observation_id":"308b2528-04a5-49cf-893a-8c881c04eacc","resolution":{"observed_at":"2026-08-14T14:20:20.349949Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:20:20.336206Z","title":null,"venue":null,"work_id":"dfea76a9-35ea-41eb-a11b-66d2a6a79b87","year":null},"citing_paper":{"arxiv_id":"1908.06818","last_updated":"2021-02-22T03:13:45Z","snapshot_observed_at":"2026-08-16T02:25:27.522921Z","submitted_at":"2019-08-09T18:21:00Z","title":"Unexpected Effects of Online no-Substitution k-means Clustering","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T14:20:20.095040Z"},"links":{"citing_paper":"/paper/1908.06818"},"observation_digest":"sha256:f9fdcd7b05a1a36c0dd2740bf4faff03fff912282b17d3d24737d0e18606054e","observation_id":"7b1d4abc-41f3-4998-9e74-9517bd83a212","resolution":{"observed_at":"2026-08-14T14:20:20.339545Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:20:20.325176Z","title":null,"venue":null,"work_id":"8637aea4-c4db-4fff-ad3d-0d993f87c4ee","year":null},"citing_paper":{"arxiv_id":"1908.06818","last_updated":"2021-02-22T03:13:45Z","snapshot_observed_at":"2026-08-16T02:25:27.522921Z","submitted_at":"2019-08-09T18:21:00Z","title":"Unexpected Effects of Online no-Substitution k-means Clustering","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T14:20:20.099160Z"},"links":{"citing_paper":"/paper/1908.06818"},"observation_digest":"sha256:c78a38836dcd0762d3bf5cd74016c392dc267707bffda2a4054604c56f264ae0","observation_id":"41f9c72e-e060-48d0-a8bd-a97cf2f4e97c","resolution":{"observed_at":"2026-08-14T14:20:20.328894Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:20:20.314384Z","title":null,"venue":null,"work_id":"38ca7c92-ea4a-4c17-b0b9-ecfc914fe8c8","year":1999},"citing_paper":{"arxiv_id":"1908.06818","last_updated":"2021-02-22T03:13:45Z","snapshot_observed_at":"2026-08-16T02:25:27.522921Z","submitted_at":"2019-08-09T18:21:00Z","title":"Unexpected Effects of Online no-Substitution k-means Clustering","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T14:20:20.102861Z"},"links":{"citing_paper":"/paper/1908.06818"},"observation_digest":"sha256:03920e919285b7013bed6c28acdc41b39e59f59b89efa7a41e4a5fc60bc2f0c5","observation_id":"35ce95bb-1f99-4538-b906-896ae6ffdb5d","resolution":{"observed_at":"2026-08-14T14:20:20.318046Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:20:20.386066Z","title":"Claim 12 F or any c > 1 there is an algorithm that obtains O(c)-approximation with O(logc n) centers, no matter what the order is and even if n is unknown","venue":null,"work_id":"a6b60c68-3552-446b-992e-d0b6b62ce6d0","year":null},"citing_paper":{"arxiv_id":"1908.06818","last_updated":"2021-02-22T03:13:45Z","snapshot_observed_at":"2026-08-16T02:25:27.522921Z","submitted_at":"2019-08-09T18:21:00Z","title":"Unexpected Effects of Online no-Substitution k-means Clustering","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T14:20:20.074338Z"},"links":{"citing_paper":"/paper/1908.06818"},"observation_digest":"sha256:52e319bad36c7b1c0aac6b9e20059d836025c64c04a068d7b799c35a00bcb84b","observation_id":"2da2448b-e3fb-42d1-a6b9-6e54a3392be7","resolution":{"observed_at":"2026-08-14T14:20:20.389806Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:20:20.304276Z","title":"In Indyk (1999), large means O(√n), as they cannot take more points for the algorithm to be with sublinear time","venue":null,"work_id":"3eab00a2-7701-4536-9320-647570a3270a","year":1999},"citing_paper":{"arxiv_id":"1908.06818","last_updated":"2021-02-22T03:13:45Z","snapshot_observed_at":"2026-08-16T02:25:27.522921Z","submitted_at":"2019-08-09T18:21:00Z","title":"Unexpected Effects of Online no-Substitution k-means Clustering","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T14:20:20.107340Z"},"links":{"citing_paper":"/paper/1908.06818"},"observation_digest":"sha256:0a54b2a6db3e7c65917fe89acdf1d29bc08742970ec78e6d1f54e436aadb5727","observation_id":"468c4f74-bb62-4fd7-bbb6-acb87145d956","resolution":{"observed_at":"2026-08-14T14:20:20.307945Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:20:20.375346Z","title":"Once more data is arrived, it increases the value of n to c, and then to c2 and so on","venue":null,"work_id":"0dc2c6b7-c988-4509-ba4d-b9b7fcd494ee","year":null},"citing_paper":{"arxiv_id":"1908.06818","last_updated":"2021-02-22T03:13:45Z","snapshot_observed_at":"2026-08-16T02:25:27.522921Z","submitted_at":"2019-08-09T18:21:00Z","title":"Unexpected Effects of Online no-Substitution k-means Clustering","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T14:20:20.079012Z"},"links":{"citing_paper":"/paper/1908.06818"},"observation_digest":"sha256:b39218ef5ddcbfa02817d3927249f9124b72b912b5affb0759b6053c40959e0c","observation_id":"14aec203-6df0-40f7-8719-0961748af3ce","resolution":{"observed_at":"2026-08-14T14:20:20.378887Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:20:20.293389Z","title":"In our framework this is not allowed since once a center was ob served the algorithm cannot retake it","venue":null,"work_id":"2847cf52-f385-4e77-b767-662c49f98846","year":1999},"citing_paper":{"arxiv_id":"1908.06818","last_updated":"2021-02-22T03:13:45Z","snapshot_observed_at":"2026-08-16T02:25:27.522921Z","submitted_at":"2019-08-09T18:21:00Z","title":"Unexpected Effects of Online no-Substitution k-means Clustering","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T14:20:20.111213Z"},"links":{"citing_paper":"/paper/1908.06818"},"observation_digest":"sha256:4f82335fdd3db66d55b250fb83f17f923b7cecf3515d49ad0973c2a9c56852c3","observation_id":"6b69db39-8ae7-4a2b-af37-923a8ced2502","resolution":{"observed_at":"2026-08-14T14:20:20.297446Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:20:20.271168Z","title":null,"venue":null,"work_id":"ef3cf623-7955-4322-a932-e46e68f3388a","year":null},"citing_paper":{"arxiv_id":"1908.06818","last_updated":"2021-02-22T03:13:45Z","snapshot_observed_at":"2026-08-16T02:25:27.522921Z","submitted_at":"2019-08-09T18:21:00Z","title":"Unexpected Effects of Online no-Substitution k-means Clustering","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T14:20:20.118443Z"},"links":{"citing_paper":"/paper/1908.06818"},"observation_digest":"sha256:7501376b59ff014f234b8d27eb41c5c61a568d24b01c15aefaf44ca9c9f0b8cc","observation_id":"4529d2fc-d637-41a9-8706-f3056a32184a","resolution":{"observed_at":"2026-08-14T14:20:20.274876Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:20:20.260560Z","title":"Once we prove the two steps we are done","venue":null,"work_id":"ea43f6fa-2790-4b81-968e-1fa0e970040d","year":null},"citing_paper":{"arxiv_id":"1908.06818","last_updated":"2021-02-22T03:13:45Z","snapshot_observed_at":"2026-08-16T02:25:27.522921Z","submitted_at":"2019-08-09T18:21:00Z","title":"Unexpected Effects of Online no-Substitution k-means Clustering","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T14:20:20.122093Z"},"links":{"citing_paper":"/paper/1908.06818"},"observation_digest":"sha256:50b5d485405d8c54135248c538b828c0860e28d158d1179ceb60e296b66f5891","observation_id":"77733072-462c-4dca-9730-795d03bf5a11","resolution":{"observed_at":"2026-08-14T14:20:20.264340Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:20:20.248970Z","title":null,"venue":null,"work_id":"ca7c328d-7c57-4c33-9a8a-bbe1d98d5294","year":null},"citing_paper":{"arxiv_id":"1908.06818","last_updated":"2021-02-22T03:13:45Z","snapshot_observed_at":"2026-08-16T02:25:27.522921Z","submitted_at":"2019-08-09T18:21:00Z","title":"Unexpected Effects of Online no-Substitution k-means Clustering","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T14:20:20.126491Z"},"links":{"citing_paper":"/paper/1908.06818"},"observation_digest":"sha256:63b728af232c14c6720befa80adac8a85203dc7134a4f3ad21545b8114b1a6a5","observation_id":"e2a3291f-659c-4d69-ae6e-9f387aab86b6","resolution":{"observed_at":"2026-08-14T14:20:20.253181Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:20:20.236633Z","title":"The two claims follow from similar arguments as the proof of C laim 18","venue":null,"work_id":"a7d3d4c3-3f9f-4e52-a521-f0feb0bdee6d","year":null},"citing_paper":{"arxiv_id":"1908.06818","last_updated":"2021-02-22T03:13:45Z","snapshot_observed_at":"2026-08-16T02:25:27.522921Z","submitted_at":"2019-08-09T18:21:00Z","title":"Unexpected Effects of Online no-Substitution k-means Clustering","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T14:20:20.130228Z"},"links":{"citing_paper":"/paper/1908.06818"},"observation_digest":"sha256:5f431fc2de857a744b45447c86628b9ebcf5cc83f14294a2e4c7b5c3fea49179","observation_id":"ea3f71e5-3f49-4a8c-b526-30d3ce02eb4c","resolution":{"observed_at":"2026-08-14T14:20:20.240658Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:20:20.224978Z","title":"We know that |B| ≤ 0.01|C ∗ 2 | ≤ 0.02|Good2|","venue":null,"work_id":"ec5d3eba-295e-4115-a512-f9aa387547d5","year":null},"citing_paper":{"arxiv_id":"1908.06818","last_updated":"2021-02-22T03:13:45Z","snapshot_observed_at":"2026-08-16T02:25:27.522921Z","submitted_at":"2019-08-09T18:21:00Z","title":"Unexpected Effects of Online no-Substitution k-means Clustering","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T14:20:20.134141Z"},"links":{"citing_paper":"/paper/1908.06818"},"observation_digest":"sha256:1364442880993a2b8ed29647a03594ffbff6f38ffbea0d8fd73974fc822a6b58","observation_id":"51d43eae-d425-4769-b9bd-a74217986849","resolution":{"observed_at":"2026-08-14T14:20:20.228725Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:20:20.214016Z","title":null,"venue":null,"work_id":"68fb954d-9c0a-4dbf-9621-c63e63abdb25","year":null},"citing_paper":{"arxiv_id":"1908.06818","last_updated":"2021-02-22T03:13:45Z","snapshot_observed_at":"2026-08-16T02:25:27.522921Z","submitted_at":"2019-08-09T18:21:00Z","title":"Unexpected Effects of Online no-Substitution k-means Clustering","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-14T14:20:20.138001Z"},"links":{"citing_paper":"/paper/1908.06818"},"observation_digest":"sha256:45846e3ccbbd28312d34c8bd10d684bf2af54ffc101186280d8b672b4514e051","observation_id":"9cab2af4-c50e-4e79-97e7-96c7c2ac03e4","resolution":{"observed_at":"2026-08-14T14:20:20.217709Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:20:20.202672Z","title":null,"venue":null,"work_id":"0b73dfc6-2b1c-442a-9498-39fb80d432bd","year":null},"citing_paper":{"arxiv_id":"1908.06818","last_updated":"2021-02-22T03:13:45Z","snapshot_observed_at":"2026-08-16T02:25:27.522921Z","submitted_at":"2019-08-09T18:21:00Z","title":"Unexpected Effects of Online no-Substitution k-means Clustering","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T14:20:20.141786Z"},"links":{"citing_paper":"/paper/1908.06818"},"observation_digest":"sha256:a26a005907b893a8cecbcaf54db7e8fbaad123345f7b73a5d90f07e456a08670","observation_id":"4602ab4b-38ff-488c-89e9-21c3768ee59d","resolution":{"observed_at":"2026-08-14T14:20:20.206226Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:20:20.191367Z","title":"We prove the claim under the general cost function, see Section 5","venue":null,"work_id":"5a1c6d0f-94f4-4521-8022-bfd19553b4c6","year":2016},"citing_paper":{"arxiv_id":"1908.06818","last_updated":"2021-02-22T03:13:45Z","snapshot_observed_at":"2026-08-16T02:25:27.522921Z","submitted_at":"2019-08-09T18:21:00Z","title":"Unexpected Effects of Online no-Substitution k-means Clustering","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-14T14:20:20.145617Z"},"links":{"citing_paper":"/paper/1908.06818"},"observation_digest":"sha256:418f0fa380740176f637bef24b662438c37f3038f90d30b72e7ac8b8d73b8ffd","observation_id":"5dc80bc1-23e5-4ee5-a1f6-56e0324b33fa","resolution":{"observed_at":"2026-08-14T14:20:20.195202Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:20:20.177323Z","title":"In Section B.2 we connect the optimal clustering and a clustering based on a random sample","venue":null,"work_id":"b669fba2-5fdc-4bb0-b64f-f5c0eb433ab9","year":null},"citing_paper":{"arxiv_id":"1908.06818","last_updated":"2021-02-22T03:13:45Z","snapshot_observed_at":"2026-08-16T02:25:27.522921Z","submitted_at":"2019-08-09T18:21:00Z","title":"Unexpected Effects of Online no-Substitution k-means Clustering","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-14T14:20:20.149615Z"},"links":{"citing_paper":"/paper/1908.06818"},"observation_digest":"sha256:88ec399943db29f4726f54a1b3414ed1cd697c7d1982b50b9750ce66774ede73","observation_id":"19e4a04d-5157-4227-a25b-ee20dc185ac1","resolution":{"observed_at":"2026-08-14T14:20:20.183457Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1908.06818","last_updated":"2021-02-22T03:13:45Z","latest_version":2,"primary_category":"cs.LG","snapshot_observed_at":"2026-08-16T02:25:27.522921Z","submitted_at":"2019-08-09T18:21:00Z","title":"Unexpected Effects of Online no-Substitution k-means Clustering"},"reference_resolution":{"displayed":20,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":9,"verified_exact":0,"verified_fuzzy":11},"total_outbound_references":20},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 0 inbound Pith citation observations for arXiv:1908.06818."}