{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:FAHJ2D34JWYYNG3ICP5PVTV5ER","short_pith_number":"pith:FAHJ2D34","canonical_record":{"source":{"id":"2206.08646","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-06-17T09:24:41Z","cross_cats_sorted":["cs.CR","cs.LG"],"title_canon_sha256":"16d756910eb4c2c54674d08c90c49db72661c411b4206b61e9378363314574f1","abstract_canon_sha256":"d56edc730661201333264566ab992baccd538f0bc636ac8be7bc23add6753ad4"},"schema_version":"1.0"},"canonical_sha256":"280e9d0f7c4db1869b6813fafacebd24639afda265e94c7af97c1330e2a4406f","source":{"kind":"arxiv","id":"2206.08646","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.08646","created_at":"2026-07-05T04:32:41Z"},{"alias_kind":"arxiv_version","alias_value":"2206.08646v1","created_at":"2026-07-05T04:32:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.08646","created_at":"2026-07-05T04:32:41Z"},{"alias_kind":"pith_short_12","alias_value":"FAHJ2D34JWYY","created_at":"2026-07-05T04:32:41Z"},{"alias_kind":"pith_short_16","alias_value":"FAHJ2D34JWYYNG3I","created_at":"2026-07-05T04:32:41Z"},{"alias_kind":"pith_short_8","alias_value":"FAHJ2D34","created_at":"2026-07-05T04:32:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:FAHJ2D34JWYYNG3ICP5PVTV5ER","target":"record","payload":{"canonical_record":{"source":{"id":"2206.08646","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-06-17T09:24:41Z","cross_cats_sorted":["cs.CR","cs.LG"],"title_canon_sha256":"16d756910eb4c2c54674d08c90c49db72661c411b4206b61e9378363314574f1","abstract_canon_sha256":"d56edc730661201333264566ab992baccd538f0bc636ac8be7bc23add6753ad4"},"schema_version":"1.0"},"canonical_sha256":"280e9d0f7c4db1869b6813fafacebd24639afda265e94c7af97c1330e2a4406f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:32:41.616147Z","signature_b64":"O1SaGpmp30At+ob8shEkGDIgmHfz6CnK0zArgIDDYJ09JACZbAk/b6Y5MRWp17qPGeeeN/sBhlMyD9ZCpFp6AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"280e9d0f7c4db1869b6813fafacebd24639afda265e94c7af97c1330e2a4406f","last_reissued_at":"2026-07-05T04:32:41.615590Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:32:41.615590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2206.08646","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:32:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BeFVAEQxRxTvb3IpNBUt3Dp5xKPlmQgEEH/LI+05EwzAAVcIrFmzbr2YD+vb/Fd1nI9GrMOi+oP+RdzA1vIMBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T09:12:48.638783Z"},"content_sha256":"7a8abd9cad0440472d6e01c0e1eef7861b3be4b49295e5d1e62c1932543634bc","schema_version":"1.0","event_id":"sha256:7a8abd9cad0440472d6e01c0e1eef7861b3be4b49295e5d1e62c1932543634bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:FAHJ2D34JWYYNG3ICP5PVTV5ER","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Scalable Differentially Private Clustering via Hierarchically Separated Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","cs.LG"],"primary_cat":"cs.DS","authors_text":"Alessandro Epasto, Andres Munoz, Chris Schwiegelshohn, David Saulpic, Sergei Vassilvitskii, Silvio Lattanzi, Vahab Mirrokni, Vincent Cohen-Addad","submitted_at":"2022-06-17T09:24:41Z","abstract_excerpt":"We study the private $k$-median and $k$-means clustering problem in $d$ dimensional Euclidean space. By leveraging tree embeddings, we give an efficient and easy to implement algorithm, that is empirically competitive with state of the art non private methods. We prove that our method computes a solution with cost at most $O(d^{3/2}\\log n)\\cdot OPT + O(k d^2 \\log^2 n / \\epsilon^2)$, where $\\epsilon$ is the privacy guarantee. (The dimension term, $d$, can be replaced with $O(\\log k)$ using standard dimension reduction techniques.) Although the worst-case guarantee is worse than that of state of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.08646","kind":"arxiv","version":1},"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/2206.08646/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":"2026-07-05T04:32:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IuHVyXvpzPS/qNhWfL/hvlwqkT+EqPAhqlxXOE4oY0S673EPtvtKU0I9ErD1c5TuqUB+Fl12yN06j++cn87eAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T09:12:48.639283Z"},"content_sha256":"ab0324795a836473a0057c944f3ed8dee78b14586c3d52e681c9927be70a129a","schema_version":"1.0","event_id":"sha256:ab0324795a836473a0057c944f3ed8dee78b14586c3d52e681c9927be70a129a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FAHJ2D34JWYYNG3ICP5PVTV5ER/bundle.json","state_url":"https://pith.science/pith/FAHJ2D34JWYYNG3ICP5PVTV5ER/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FAHJ2D34JWYYNG3ICP5PVTV5ER/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":"2026-08-22T09:12:48Z","links":{"resolver":"https://pith.science/pith/FAHJ2D34JWYYNG3ICP5PVTV5ER","bundle":"https://pith.science/pith/FAHJ2D34JWYYNG3ICP5PVTV5ER/bundle.json","state":"https://pith.science/pith/FAHJ2D34JWYYNG3ICP5PVTV5ER/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FAHJ2D34JWYYNG3ICP5PVTV5ER/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:FAHJ2D34JWYYNG3ICP5PVTV5ER","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":"d56edc730661201333264566ab992baccd538f0bc636ac8be7bc23add6753ad4","cross_cats_sorted":["cs.CR","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-06-17T09:24:41Z","title_canon_sha256":"16d756910eb4c2c54674d08c90c49db72661c411b4206b61e9378363314574f1"},"schema_version":"1.0","source":{"id":"2206.08646","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.08646","created_at":"2026-07-05T04:32:41Z"},{"alias_kind":"arxiv_version","alias_value":"2206.08646v1","created_at":"2026-07-05T04:32:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.08646","created_at":"2026-07-05T04:32:41Z"},{"alias_kind":"pith_short_12","alias_value":"FAHJ2D34JWYY","created_at":"2026-07-05T04:32:41Z"},{"alias_kind":"pith_short_16","alias_value":"FAHJ2D34JWYYNG3I","created_at":"2026-07-05T04:32:41Z"},{"alias_kind":"pith_short_8","alias_value":"FAHJ2D34","created_at":"2026-07-05T04:32:41Z"}],"graph_snapshots":[{"event_id":"sha256:ab0324795a836473a0057c944f3ed8dee78b14586c3d52e681c9927be70a129a","target":"graph","created_at":"2026-07-05T04:32:41Z","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/2206.08646/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the private $k$-median and $k$-means clustering problem in $d$ dimensional Euclidean space. By leveraging tree embeddings, we give an efficient and easy to implement algorithm, that is empirically competitive with state of the art non private methods. We prove that our method computes a solution with cost at most $O(d^{3/2}\\log n)\\cdot OPT + O(k d^2 \\log^2 n / \\epsilon^2)$, where $\\epsilon$ is the privacy guarantee. (The dimension term, $d$, can be replaced with $O(\\log k)$ using standard dimension reduction techniques.) Although the worst-case guarantee is worse than that of state of","authors_text":"Alessandro Epasto, Andres Munoz, Chris Schwiegelshohn, David Saulpic, Sergei Vassilvitskii, Silvio Lattanzi, Vahab Mirrokni, Vincent Cohen-Addad","cross_cats":["cs.CR","cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-06-17T09:24:41Z","title":"Scalable Differentially Private Clustering via Hierarchically Separated Trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.08646","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":"sha256:7a8abd9cad0440472d6e01c0e1eef7861b3be4b49295e5d1e62c1932543634bc","target":"record","created_at":"2026-07-05T04:32:41Z","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":"d56edc730661201333264566ab992baccd538f0bc636ac8be7bc23add6753ad4","cross_cats_sorted":["cs.CR","cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-06-17T09:24:41Z","title_canon_sha256":"16d756910eb4c2c54674d08c90c49db72661c411b4206b61e9378363314574f1"},"schema_version":"1.0","source":{"id":"2206.08646","kind":"arxiv","version":1}},"canonical_sha256":"280e9d0f7c4db1869b6813fafacebd24639afda265e94c7af97c1330e2a4406f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"280e9d0f7c4db1869b6813fafacebd24639afda265e94c7af97c1330e2a4406f","first_computed_at":"2026-07-05T04:32:41.615590Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:32:41.615590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O1SaGpmp30At+ob8shEkGDIgmHfz6CnK0zArgIDDYJ09JACZbAk/b6Y5MRWp17qPGeeeN/sBhlMyD9ZCpFp6AA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:32:41.616147Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.08646","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a8abd9cad0440472d6e01c0e1eef7861b3be4b49295e5d1e62c1932543634bc","sha256:ab0324795a836473a0057c944f3ed8dee78b14586c3d52e681c9927be70a129a"],"state_sha256":"86aa06280c1a2b01ed327c89f7408b72e53a7857d447b911d94dce11722d3aef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aXvdXMo/5He540T1tr3PMQQotVXmVFBqtcqcUyd8Bz2CDy4WT+NoxDoN0rxJS+yAHxLWjux9JVWic0SxxE8lCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T09:12:48.644103Z","bundle_sha256":"1ec1ae39a3df8726deec2787e12d0b9dc7ffab42da353602c5624ee01ea203d6"}}