{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:6TNSV4ZPDRKPTFUHANHNEIJRLS","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":"e4e56fd45391df6fe58b1495d08453d05db49c3596ba8add7cb0b9db41e4bb08","cross_cats_sorted":["cs.DS","cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2023-08-18T17:52:12Z","title_canon_sha256":"ed232c7487b1d4bceda76464ff55b9fe57fead12212aaed0c4f03ecbf4f1504b"},"schema_version":"1.0","source":{"id":"2308.09701","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.09701","created_at":"2026-07-05T11:38:47Z"},{"alias_kind":"arxiv_version","alias_value":"2308.09701v3","created_at":"2026-07-05T11:38:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.09701","created_at":"2026-07-05T11:38:47Z"},{"alias_kind":"pith_short_12","alias_value":"6TNSV4ZPDRKP","created_at":"2026-07-05T11:38:47Z"},{"alias_kind":"pith_short_16","alias_value":"6TNSV4ZPDRKPTFUH","created_at":"2026-07-05T11:38:47Z"},{"alias_kind":"pith_short_8","alias_value":"6TNSV4ZP","created_at":"2026-07-05T11:38:47Z"}],"graph_snapshots":[{"event_id":"sha256:f2d625733f6e942da685f31a70355eec400e8f77599da06caa71674d036d628a","target":"graph","created_at":"2026-07-05T11:38:47Z","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/2308.09701/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Clustering is one of the most important tools for analysis of large datasets, and perhaps the most popular clustering algorithm is Lloyd's algorithm for $k$-means. This algorithm takes $n$ vectors $V=[v_1,\\dots,v_n]\\in\\mathbb{R}^{d\\times n}$ and outputs $k$ centroids $c_1,\\dots,c_k\\in\\mathbb{R}^d$; these partition the vectors into clusters based on which centroid is closest to a particular vector. We present a classical $\\varepsilon$-$k$-means algorithm that performs an approximate version of one iteration of Lloyd's algorithm with time complexity $\\tilde{O}\\big(\\frac{\\|V\\|_F^2}{n}\\frac{k^{2}d","authors_text":"Alessandro Luongo, Arjan Cornelissen, Ewin Tang, Joao F. Doriguello","cross_cats":["cs.DS","cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2023-08-18T17:52:12Z","title":"Do you know what q-means?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.09701","kind":"arxiv","version":3},"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":"sha256:490d00baba91b5685630aeec6c4bbe4745d96149a8c3458f230ddc19244c75da","target":"record","created_at":"2026-07-05T11:38:47Z","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":"e4e56fd45391df6fe58b1495d08453d05db49c3596ba8add7cb0b9db41e4bb08","cross_cats_sorted":["cs.DS","cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2023-08-18T17:52:12Z","title_canon_sha256":"ed232c7487b1d4bceda76464ff55b9fe57fead12212aaed0c4f03ecbf4f1504b"},"schema_version":"1.0","source":{"id":"2308.09701","kind":"arxiv","version":3}},"canonical_sha256":"f4db2af32f1c54f99687034ed221315ca639a694d825802b2d8fed66a79e68d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4db2af32f1c54f99687034ed221315ca639a694d825802b2d8fed66a79e68d8","first_computed_at":"2026-07-05T11:38:47.644721Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:38:47.644721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ARMlRTxeRrQPYNIAoQ3SzMegPhLPUZV6z63bfqiGdhcJwH1YWgF29SEhLp+foqyrPK4f7UXNIeiTQa4pgjiHAg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:38:47.645392Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.09701","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:490d00baba91b5685630aeec6c4bbe4745d96149a8c3458f230ddc19244c75da","sha256:f2d625733f6e942da685f31a70355eec400e8f77599da06caa71674d036d628a"],"state_sha256":"2df00dc25dc4374b5cb78d251566bc3a75c88a50c2727a3de36bf8ab40f94dec"}