{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:HCE7L6OS7P7IX7PCJJVWV5UVX4","short_pith_number":"pith:HCE7L6OS","canonical_record":{"source":{"id":"2606.00342","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-29T20:30:15Z","cross_cats_sorted":["cs.CR","cs.DB"],"title_canon_sha256":"43899e0f47eb3ce414c8632dd5e9aa6ec34fb519f4df518b9330fdf355794497","abstract_canon_sha256":"e028b819cf2eda9c114e48345887e275c84a5dd88cf19c70dcbcace5ebe36e65"},"schema_version":"1.0"},"canonical_sha256":"3889f5f9d2fbfe8bfde24a6b6af695bf16e0fa0938bdaba2af5239e15b6f883b","source":{"kind":"arxiv","id":"2606.00342","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.00342","created_at":"2026-06-02T01:03:52Z"},{"alias_kind":"arxiv_version","alias_value":"2606.00342v1","created_at":"2026-06-02T01:03:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.00342","created_at":"2026-06-02T01:03:52Z"},{"alias_kind":"pith_short_12","alias_value":"HCE7L6OS7P7I","created_at":"2026-06-02T01:03:52Z"},{"alias_kind":"pith_short_16","alias_value":"HCE7L6OS7P7IX7PC","created_at":"2026-06-02T01:03:52Z"},{"alias_kind":"pith_short_8","alias_value":"HCE7L6OS","created_at":"2026-06-02T01:03:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:HCE7L6OS7P7IX7PCJJVWV5UVX4","target":"record","payload":{"canonical_record":{"source":{"id":"2606.00342","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-29T20:30:15Z","cross_cats_sorted":["cs.CR","cs.DB"],"title_canon_sha256":"43899e0f47eb3ce414c8632dd5e9aa6ec34fb519f4df518b9330fdf355794497","abstract_canon_sha256":"e028b819cf2eda9c114e48345887e275c84a5dd88cf19c70dcbcace5ebe36e65"},"schema_version":"1.0"},"canonical_sha256":"3889f5f9d2fbfe8bfde24a6b6af695bf16e0fa0938bdaba2af5239e15b6f883b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T01:03:52.144625Z","signature_b64":"P9Ry6eihHvrEcEPJMxRL4u4ciq3SPei9mJ4kwTuQZ5GgFyjyRrlByIBVZb+LJeJR3Bgje8Fzgp3e4e2uwazZAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3889f5f9d2fbfe8bfde24a6b6af695bf16e0fa0938bdaba2af5239e15b6f883b","last_reissued_at":"2026-06-02T01:03:52.144223Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T01:03:52.144223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.00342","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":"2026-06-02T01:03:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PX0QIOSx4KLAaDkLHLL3gIMhhj0mF6+mIcWZh+awaViLTiT9y8Fmiq0/4Y0EvFIsEKHjyeSk3V/xoIlJnl6pCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T09:07:30.659829Z"},"content_sha256":"18245c30d3c1c5c2c3540292d34db22ace10bc69f012d7faf06897bf1be8c453","schema_version":"1.0","event_id":"sha256:18245c30d3c1c5c2c3540292d34db22ace10bc69f012d7faf06897bf1be8c453"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:HCE7L6OS7P7IX7PCJJVWV5UVX4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"PE-means: Improved Differentially Private $k$-means Clustering through Private Evolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","cs.DB"],"primary_cat":"cs.LG","authors_text":"Sergey Yekhanin, Thomas Humphries, Zinan Lin","submitted_at":"2026-05-29T20:30:15Z","abstract_excerpt":"We study the problem of differentially private (DP) $k$-means clustering in Euclidean space. Previous solutions rely on summing the private data directly, which induces a sensitivity proportional to the domain. We introduce PE-means, an extension of the private evolution (PE) algorithm (an increasingly popular method for synthetic data generation), to the problem of $k$-means clustering. The key advantage of PE is that it only computes a private histogram with constant sensitivity to guide the evolution. Our adaptation of PE includes new evolutionary operators for clustering, as well as other "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00342","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/2606.00342/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":"2026-06-02T01:03:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hA21/6SFMXnbnLTN45r2YC6+/+B/yHbRvwkf6mmURkoIXnmZf66Ej7mNElkWKZUPQs/rMerljQ+nWNT5rqVZAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T09:07:30.660220Z"},"content_sha256":"18a99393f815f6f3d37595ede507d93ede791fa3f29b5cbbb79a57e24dbd5562","schema_version":"1.0","event_id":"sha256:18a99393f815f6f3d37595ede507d93ede791fa3f29b5cbbb79a57e24dbd5562"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HCE7L6OS7P7IX7PCJJVWV5UVX4/bundle.json","state_url":"https://pith.science/pith/HCE7L6OS7P7IX7PCJJVWV5UVX4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HCE7L6OS7P7IX7PCJJVWV5UVX4/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":"2026-07-04T09:07:30Z","links":{"resolver":"https://pith.science/pith/HCE7L6OS7P7IX7PCJJVWV5UVX4","bundle":"https://pith.science/pith/HCE7L6OS7P7IX7PCJJVWV5UVX4/bundle.json","state":"https://pith.science/pith/HCE7L6OS7P7IX7PCJJVWV5UVX4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HCE7L6OS7P7IX7PCJJVWV5UVX4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:HCE7L6OS7P7IX7PCJJVWV5UVX4","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":"e028b819cf2eda9c114e48345887e275c84a5dd88cf19c70dcbcace5ebe36e65","cross_cats_sorted":["cs.CR","cs.DB"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-29T20:30:15Z","title_canon_sha256":"43899e0f47eb3ce414c8632dd5e9aa6ec34fb519f4df518b9330fdf355794497"},"schema_version":"1.0","source":{"id":"2606.00342","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.00342","created_at":"2026-06-02T01:03:52Z"},{"alias_kind":"arxiv_version","alias_value":"2606.00342v1","created_at":"2026-06-02T01:03:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.00342","created_at":"2026-06-02T01:03:52Z"},{"alias_kind":"pith_short_12","alias_value":"HCE7L6OS7P7I","created_at":"2026-06-02T01:03:52Z"},{"alias_kind":"pith_short_16","alias_value":"HCE7L6OS7P7IX7PC","created_at":"2026-06-02T01:03:52Z"},{"alias_kind":"pith_short_8","alias_value":"HCE7L6OS","created_at":"2026-06-02T01:03:52Z"}],"graph_snapshots":[{"event_id":"sha256:18a99393f815f6f3d37595ede507d93ede791fa3f29b5cbbb79a57e24dbd5562","target":"graph","created_at":"2026-06-02T01:03:52Z","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/2606.00342/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the problem of differentially private (DP) $k$-means clustering in Euclidean space. Previous solutions rely on summing the private data directly, which induces a sensitivity proportional to the domain. We introduce PE-means, an extension of the private evolution (PE) algorithm (an increasingly popular method for synthetic data generation), to the problem of $k$-means clustering. The key advantage of PE is that it only computes a private histogram with constant sensitivity to guide the evolution. Our adaptation of PE includes new evolutionary operators for clustering, as well as other ","authors_text":"Sergey Yekhanin, Thomas Humphries, Zinan Lin","cross_cats":["cs.CR","cs.DB"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-29T20:30:15Z","title":"PE-means: Improved Differentially Private $k$-means Clustering through Private Evolution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00342","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":"sha256:18245c30d3c1c5c2c3540292d34db22ace10bc69f012d7faf06897bf1be8c453","target":"record","created_at":"2026-06-02T01:03:52Z","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":"e028b819cf2eda9c114e48345887e275c84a5dd88cf19c70dcbcace5ebe36e65","cross_cats_sorted":["cs.CR","cs.DB"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-05-29T20:30:15Z","title_canon_sha256":"43899e0f47eb3ce414c8632dd5e9aa6ec34fb519f4df518b9330fdf355794497"},"schema_version":"1.0","source":{"id":"2606.00342","kind":"arxiv","version":1}},"canonical_sha256":"3889f5f9d2fbfe8bfde24a6b6af695bf16e0fa0938bdaba2af5239e15b6f883b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3889f5f9d2fbfe8bfde24a6b6af695bf16e0fa0938bdaba2af5239e15b6f883b","first_computed_at":"2026-06-02T01:03:52.144223Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T01:03:52.144223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P9Ry6eihHvrEcEPJMxRL4u4ciq3SPei9mJ4kwTuQZ5GgFyjyRrlByIBVZb+LJeJR3Bgje8Fzgp3e4e2uwazZAw==","signature_status":"signed_v1","signed_at":"2026-06-02T01:03:52.144625Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.00342","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18245c30d3c1c5c2c3540292d34db22ace10bc69f012d7faf06897bf1be8c453","sha256:18a99393f815f6f3d37595ede507d93ede791fa3f29b5cbbb79a57e24dbd5562"],"state_sha256":"4a075b4f800e32fc8cda88525e607e5aa2b3cb7be7a5554d57777523e436861a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r/uLz44w4BORtHL3KRmogZ04vcsnmWkohMnzMLWBtEjkYM+6zZX7YUwmbPFJ3WZO2ZTodBjrkSsGiOMkouKNBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T09:07:30.662292Z","bundle_sha256":"330db22d6b0a1b7d74ef50bf4818f928f78a2b3358bad39e5b24f41ffd10d55c"}}