{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:EHXEOSDRVXBP4K6S3B2LWBUTMD","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a050c1af9659ba8bf919f4a18101c5610670934c89d360f7b0c85c5682bd28b8","cross_cats_sorted":["cs.CG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-02-10T05:22:08Z","title_canon_sha256":"5894889e1e93c27258c6e6c3c797bdc51f092496348e02f8f1d4a1739dfa2639"},"schema_version":"1.0","source":{"id":"2502.06163","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.06163","created_at":"2026-07-05T10:11:48Z"},{"alias_kind":"arxiv_version","alias_value":"2502.06163v1","created_at":"2026-07-05T10:11:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.06163","created_at":"2026-07-05T10:11:48Z"},{"alias_kind":"pith_short_12","alias_value":"EHXEOSDRVXBP","created_at":"2026-07-05T10:11:48Z"},{"alias_kind":"pith_short_16","alias_value":"EHXEOSDRVXBP4K6S","created_at":"2026-07-05T10:11:48Z"},{"alias_kind":"pith_short_8","alias_value":"EHXEOSDR","created_at":"2026-07-05T10:11:48Z"}],"graph_snapshots":[{"event_id":"sha256:234abb66d2f9210abf15d5a5e10516e4e45c45190d72c539e67fdcdc08a83245","target":"graph","created_at":"2026-07-05T10:11:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2502.06163/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For very large values of $k$, we consider methods for fast $k$-means clustering of massive datasets with $10^7\\sim10^9$ points in high-dimensions ($d\\geq100$). All current practical methods for this problem have runtimes at least $\\Omega(k^2)$. We find that initialization routines are not a bottleneck for this case. Instead, it is critical to improve the speed of Lloyd's local-search algorithm, particularly the step that reassigns points to their closest center. Attempting to improve this step naturally leads us to leverage approximate nearest-neighbor search methods, although this alone is no","authors_text":"Da Wei Zheng, Eliot Wong Robson, Jack Spalding-Jamieson","cross_cats":["cs.CG","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-02-10T05:22:08Z","title":"Scalable k-Means Clustering for Large k via Seeded Approximate Nearest-Neighbor Search"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06163","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4239eed1a753f8c971f21322700c0450a5999b3e3eb54a54ec15c057f8f72661","target":"record","created_at":"2026-07-05T10:11:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a050c1af9659ba8bf919f4a18101c5610670934c89d360f7b0c85c5682bd28b8","cross_cats_sorted":["cs.CG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-02-10T05:22:08Z","title_canon_sha256":"5894889e1e93c27258c6e6c3c797bdc51f092496348e02f8f1d4a1739dfa2639"},"schema_version":"1.0","source":{"id":"2502.06163","kind":"arxiv","version":1}},"canonical_sha256":"21ee474871adc2fe2bd2d874bb069360c0c80534093ff93e41a98cb6349901a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21ee474871adc2fe2bd2d874bb069360c0c80534093ff93e41a98cb6349901a2","first_computed_at":"2026-07-05T10:11:48.455242Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:11:48.455242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pqDLokUjepkuIceRUnKhKeaw9vA59TO46IzZS0cGeNLWcdmnsNInjjrlePrjIXzWec3vIbghmnTSzh2NCP8aAA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:11:48.455727Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.06163","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4239eed1a753f8c971f21322700c0450a5999b3e3eb54a54ec15c057f8f72661","sha256:234abb66d2f9210abf15d5a5e10516e4e45c45190d72c539e67fdcdc08a83245"],"state_sha256":"c893b89c7d32e5031137c0f13606e353a6b3c9a681b835199b78cb4f524f8dd7"}