{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:NNA633ODXRGIRC37X5IJKXPOTY","short_pith_number":"pith:NNA633OD","canonical_record":{"source":{"id":"2409.01688","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2024-09-03T08:01:19Z","cross_cats_sorted":["cs.AI","cs.LG","stat.ML"],"title_canon_sha256":"17e0616ebab547551c5a7ffbd17e23552132e342b51877a0fb19c2df4112bcc8","abstract_canon_sha256":"236fbc1acdaca6b2a13bf2ff2f900c6678fe4664998e267bdcc347f5d32e4b0f"},"schema_version":"1.0"},"canonical_sha256":"6b41ededc3bc4c888b7fbf50955dee9e1ea55e5d44c872abe4f555de8451abab","source":{"kind":"arxiv","id":"2409.01688","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.01688","created_at":"2026-07-05T10:37:32Z"},{"alias_kind":"arxiv_version","alias_value":"2409.01688v3","created_at":"2026-07-05T10:37:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.01688","created_at":"2026-07-05T10:37:32Z"},{"alias_kind":"pith_short_12","alias_value":"NNA633ODXRGI","created_at":"2026-07-05T10:37:32Z"},{"alias_kind":"pith_short_16","alias_value":"NNA633ODXRGIRC37","created_at":"2026-07-05T10:37:32Z"},{"alias_kind":"pith_short_8","alias_value":"NNA633OD","created_at":"2026-07-05T10:37:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:NNA633ODXRGIRC37X5IJKXPOTY","target":"record","payload":{"canonical_record":{"source":{"id":"2409.01688","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2024-09-03T08:01:19Z","cross_cats_sorted":["cs.AI","cs.LG","stat.ML"],"title_canon_sha256":"17e0616ebab547551c5a7ffbd17e23552132e342b51877a0fb19c2df4112bcc8","abstract_canon_sha256":"236fbc1acdaca6b2a13bf2ff2f900c6678fe4664998e267bdcc347f5d32e4b0f"},"schema_version":"1.0"},"canonical_sha256":"6b41ededc3bc4c888b7fbf50955dee9e1ea55e5d44c872abe4f555de8451abab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:37:32.528436Z","signature_b64":"4cXdRN2hf/mLTFf5QD1U3F0a1J5wDomqtvQnKik818QXGlZSEtjSzpWCCnXLmX7OOakT8ODAPxzy2caaeACxAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b41ededc3bc4c888b7fbf50955dee9e1ea55e5d44c872abe4f555de8451abab","last_reissued_at":"2026-07-05T10:37:32.527581Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:37:32.527581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.01688","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":"2026-07-05T10:37:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mhdy0yPEej9ACse3LcudwIDllAXVcvbCZxxRF5mYLY8iY2GcdXMNUI2Hu03pVsQqJ+tC+DEEKzxALjXo2i6lCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-26T21:33:08.593804Z"},"content_sha256":"2890a713e4bec23bc59f76c532a07d6133848733fd301f5d92535a758751f0a0","schema_version":"1.0","event_id":"sha256:2890a713e4bec23bc59f76c532a07d6133848733fd301f5d92535a758751f0a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:NNA633ODXRGIRC37X5IJKXPOTY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Differentially Private Kernel Density Estimation","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.AI","cs.LG","stat.ML"],"primary_cat":"cs.DS","authors_text":"Alex Reneau, Erzhi Liu, Han Liu, Jerry Yao-Chieh Hu, Zhao Song","submitted_at":"2024-09-03T08:01:19Z","abstract_excerpt":"We introduce a refined differentially private (DP) data structure for kernel density estimation (KDE), offering not only improved privacy-utility tradeoff but also better efficiency over prior results. Specifically, we study the mathematical problem: given a similarity function $f$ (or DP KDE) and a private dataset $X \\subset \\mathbb{R}^d$, our goal is to preprocess $X$ so that for any query $y\\in\\mathbb{R}^d$, we approximate $\\sum_{x \\in X} f(x, y)$ in a differentially private fashion. The best previous algorithm for $f(x,y) =\\| x - y \\|_1$ is the node-contaminated balanced binary tree by [Ba"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.01688","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/2409.01688/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":"2026-07-05T10:37:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fzqZLWmrPwtnV2QG5WeOK7l44g/OBA8TE1+noBsuLxJ9fw7gQfU0zKlxpe/ZMRE78sgluQYsxrUIGVsgmcl4Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-26T21:33:08.594184Z"},"content_sha256":"9eece164b13c21838f3d69dc33f26f162b5eeae8eac51bf027150ce8e2922a9b","schema_version":"1.0","event_id":"sha256:9eece164b13c21838f3d69dc33f26f162b5eeae8eac51bf027150ce8e2922a9b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NNA633ODXRGIRC37X5IJKXPOTY/bundle.json","state_url":"https://pith.science/pith/NNA633ODXRGIRC37X5IJKXPOTY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NNA633ODXRGIRC37X5IJKXPOTY/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":"2026-07-26T21:33:08Z","links":{"resolver":"https://pith.science/pith/NNA633ODXRGIRC37X5IJKXPOTY","bundle":"https://pith.science/pith/NNA633ODXRGIRC37X5IJKXPOTY/bundle.json","state":"https://pith.science/pith/NNA633ODXRGIRC37X5IJKXPOTY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NNA633ODXRGIRC37X5IJKXPOTY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:NNA633ODXRGIRC37X5IJKXPOTY","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":"236fbc1acdaca6b2a13bf2ff2f900c6678fe4664998e267bdcc347f5d32e4b0f","cross_cats_sorted":["cs.AI","cs.LG","stat.ML"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2024-09-03T08:01:19Z","title_canon_sha256":"17e0616ebab547551c5a7ffbd17e23552132e342b51877a0fb19c2df4112bcc8"},"schema_version":"1.0","source":{"id":"2409.01688","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.01688","created_at":"2026-07-05T10:37:32Z"},{"alias_kind":"arxiv_version","alias_value":"2409.01688v3","created_at":"2026-07-05T10:37:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.01688","created_at":"2026-07-05T10:37:32Z"},{"alias_kind":"pith_short_12","alias_value":"NNA633ODXRGI","created_at":"2026-07-05T10:37:32Z"},{"alias_kind":"pith_short_16","alias_value":"NNA633ODXRGIRC37","created_at":"2026-07-05T10:37:32Z"},{"alias_kind":"pith_short_8","alias_value":"NNA633OD","created_at":"2026-07-05T10:37:32Z"}],"graph_snapshots":[{"event_id":"sha256:9eece164b13c21838f3d69dc33f26f162b5eeae8eac51bf027150ce8e2922a9b","target":"graph","created_at":"2026-07-05T10:37:32Z","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/2409.01688/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a refined differentially private (DP) data structure for kernel density estimation (KDE), offering not only improved privacy-utility tradeoff but also better efficiency over prior results. Specifically, we study the mathematical problem: given a similarity function $f$ (or DP KDE) and a private dataset $X \\subset \\mathbb{R}^d$, our goal is to preprocess $X$ so that for any query $y\\in\\mathbb{R}^d$, we approximate $\\sum_{x \\in X} f(x, y)$ in a differentially private fashion. The best previous algorithm for $f(x,y) =\\| x - y \\|_1$ is the node-contaminated balanced binary tree by [Ba","authors_text":"Alex Reneau, Erzhi Liu, Han Liu, Jerry Yao-Chieh Hu, Zhao Song","cross_cats":["cs.AI","cs.LG","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2024-09-03T08:01:19Z","title":"Differentially Private Kernel Density Estimation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.01688","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":"sha256:2890a713e4bec23bc59f76c532a07d6133848733fd301f5d92535a758751f0a0","target":"record","created_at":"2026-07-05T10:37:32Z","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":"236fbc1acdaca6b2a13bf2ff2f900c6678fe4664998e267bdcc347f5d32e4b0f","cross_cats_sorted":["cs.AI","cs.LG","stat.ML"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2024-09-03T08:01:19Z","title_canon_sha256":"17e0616ebab547551c5a7ffbd17e23552132e342b51877a0fb19c2df4112bcc8"},"schema_version":"1.0","source":{"id":"2409.01688","kind":"arxiv","version":3}},"canonical_sha256":"6b41ededc3bc4c888b7fbf50955dee9e1ea55e5d44c872abe4f555de8451abab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b41ededc3bc4c888b7fbf50955dee9e1ea55e5d44c872abe4f555de8451abab","first_computed_at":"2026-07-05T10:37:32.527581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:37:32.527581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4cXdRN2hf/mLTFf5QD1U3F0a1J5wDomqtvQnKik818QXGlZSEtjSzpWCCnXLmX7OOakT8ODAPxzy2caaeACxAw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:37:32.528436Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.01688","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2890a713e4bec23bc59f76c532a07d6133848733fd301f5d92535a758751f0a0","sha256:9eece164b13c21838f3d69dc33f26f162b5eeae8eac51bf027150ce8e2922a9b"],"state_sha256":"40d7964c4e82354c361cfc9be916840a4dc3d7de0e4f844ecb3f6e52da5ebb63"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7LAVX7n6q4mUiFb8pk44DzDsYYGtPxRnewkSU5H764PQ/j/seofXYAkuyooiUawPoAnHIAzan+sLp9c/p8b3BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-26T21:33:08.596374Z","bundle_sha256":"f5bdfa2786c6c58a98a813e254b81a97210ac615b5d68a07fb663cc75abeb2fc"}}