{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:6TNSV4ZPDRKPTFUHANHNEIJRLS","short_pith_number":"pith:6TNSV4ZP","canonical_record":{"source":{"id":"2308.09701","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2023-08-18T17:52:12Z","cross_cats_sorted":["cs.DS","cs.LG"],"title_canon_sha256":"ed232c7487b1d4bceda76464ff55b9fe57fead12212aaed0c4f03ecbf4f1504b","abstract_canon_sha256":"e4e56fd45391df6fe58b1495d08453d05db49c3596ba8add7cb0b9db41e4bb08"},"schema_version":"1.0"},"canonical_sha256":"f4db2af32f1c54f99687034ed221315ca639a694d825802b2d8fed66a79e68d8","source":{"kind":"arxiv","id":"2308.09701","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:6TNSV4ZPDRKPTFUHANHNEIJRLS","target":"record","payload":{"canonical_record":{"source":{"id":"2308.09701","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2023-08-18T17:52:12Z","cross_cats_sorted":["cs.DS","cs.LG"],"title_canon_sha256":"ed232c7487b1d4bceda76464ff55b9fe57fead12212aaed0c4f03ecbf4f1504b","abstract_canon_sha256":"e4e56fd45391df6fe58b1495d08453d05db49c3596ba8add7cb0b9db41e4bb08"},"schema_version":"1.0"},"canonical_sha256":"f4db2af32f1c54f99687034ed221315ca639a694d825802b2d8fed66a79e68d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:38:47.645392Z","signature_b64":"ARMlRTxeRrQPYNIAoQ3SzMegPhLPUZV6z63bfqiGdhcJwH1YWgF29SEhLp+foqyrPK4f7UXNIeiTQa4pgjiHAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4db2af32f1c54f99687034ed221315ca639a694d825802b2d8fed66a79e68d8","last_reissued_at":"2026-07-05T11:38:47.644721Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:38:47.644721Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2308.09701","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:38:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8+g52mhpQk4lfP2g6nk5q4/y0JPpDx3jY069ppuD0VtZoBM5cyE8CyOr/X6l3OoSrLhAHiNejowVPoI3ckypCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T19:32:31.266836Z"},"content_sha256":"490d00baba91b5685630aeec6c4bbe4745d96149a8c3458f230ddc19244c75da","schema_version":"1.0","event_id":"sha256:490d00baba91b5685630aeec6c4bbe4745d96149a8c3458f230ddc19244c75da"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:6TNSV4ZPDRKPTFUHANHNEIJRLS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Do you know what q-means?","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS","cs.LG"],"primary_cat":"quant-ph","authors_text":"Alessandro Luongo, Arjan Cornelissen, Ewin Tang, Joao F. Doriguello","submitted_at":"2023-08-18T17:52:12Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.09701","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2308.09701/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:38:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UV9vt4uRWkCy1tuLuej1BB6Iq7hvsXgpfhlkGcEVtWDEpj6Ey12LdJKkfMsT7741essjc2qtjnueqeDi86cUAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T19:32:31.267457Z"},"content_sha256":"f2d625733f6e942da685f31a70355eec400e8f77599da06caa71674d036d628a","schema_version":"1.0","event_id":"sha256:f2d625733f6e942da685f31a70355eec400e8f77599da06caa71674d036d628a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6TNSV4ZPDRKPTFUHANHNEIJRLS/bundle.json","state_url":"https://pith.science/pith/6TNSV4ZPDRKPTFUHANHNEIJRLS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6TNSV4ZPDRKPTFUHANHNEIJRLS/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-16T19:32:31Z","links":{"resolver":"https://pith.science/pith/6TNSV4ZPDRKPTFUHANHNEIJRLS","bundle":"https://pith.science/pith/6TNSV4ZPDRKPTFUHANHNEIJRLS/bundle.json","state":"https://pith.science/pith/6TNSV4ZPDRKPTFUHANHNEIJRLS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6TNSV4ZPDRKPTFUHANHNEIJRLS/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Jv0sWhmr+s1sn5Mz8GR5xuMfuJIbNcjJlPTt4Imnivq6Pe+UbYKMp27sTkPFKc1G1D2KSxwort7xsBnSt6eAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T19:32:31.272127Z","bundle_sha256":"9417158c33731c0c752154ed2a2eb1ca669b5d55d7a03a84c2fec93cb5abe2e6"}}