{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:7UEFPJ5WFDKKKABRVP42J7BCOJ","short_pith_number":"pith:7UEFPJ5W","canonical_record":{"source":{"id":"2203.15400","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-03-29T09:51:50Z","cross_cats_sorted":[],"title_canon_sha256":"fec251853f040b5b69f13675e78cbd86c563fe2280de7a37c744bb70523023d6","abstract_canon_sha256":"b5a015672f420188bb7238a4839b36da804775ff17445deacfd6622b1760e0c2"},"schema_version":"1.0"},"canonical_sha256":"fd0857a7b628d4a50031abf9a4fc227246acbf525140f2a3a650257b774cae9b","source":{"kind":"arxiv","id":"2203.15400","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.15400","created_at":"2026-07-05T05:38:27Z"},{"alias_kind":"arxiv_version","alias_value":"2203.15400v2","created_at":"2026-07-05T05:38:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.15400","created_at":"2026-07-05T05:38:27Z"},{"alias_kind":"pith_short_12","alias_value":"7UEFPJ5WFDKK","created_at":"2026-07-05T05:38:27Z"},{"alias_kind":"pith_short_16","alias_value":"7UEFPJ5WFDKKKABR","created_at":"2026-07-05T05:38:27Z"},{"alias_kind":"pith_short_8","alias_value":"7UEFPJ5W","created_at":"2026-07-05T05:38:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:7UEFPJ5WFDKKKABRVP42J7BCOJ","target":"record","payload":{"canonical_record":{"source":{"id":"2203.15400","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-03-29T09:51:50Z","cross_cats_sorted":[],"title_canon_sha256":"fec251853f040b5b69f13675e78cbd86c563fe2280de7a37c744bb70523023d6","abstract_canon_sha256":"b5a015672f420188bb7238a4839b36da804775ff17445deacfd6622b1760e0c2"},"schema_version":"1.0"},"canonical_sha256":"fd0857a7b628d4a50031abf9a4fc227246acbf525140f2a3a650257b774cae9b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:38:27.571612Z","signature_b64":"J3lspooHGgxUBNfE+eHcfhzfWG67DDqfGQ5wNyX5WFCr1SXwjW1ghm5m0mYMMGJ21tWxPSR44dfbS2b5AwyABQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd0857a7b628d4a50031abf9a4fc227246acbf525140f2a3a650257b774cae9b","last_reissued_at":"2026-07-05T05:38:27.571131Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:38:27.571131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2203.15400","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:38:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gTbMAiCQroVL2fPDO8CWop6piprOl1yG5nNHhXoXEcSe0e1JXtxsmh7T1l2LBdt/IrDMzSSXXeiMVsNP/NCABg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T15:59:43.676666Z"},"content_sha256":"ee9c8806fa139631b2c987a61adce21b16383c51c8f653558ba7f08189c84617","schema_version":"1.0","event_id":"sha256:ee9c8806fa139631b2c987a61adce21b16383c51c8f653558ba7f08189c84617"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:7UEFPJ5WFDKKKABRVP42J7BCOJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Order-Invariant Cardinality Estimators Are Differentially Private","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Charlie Dickens, Daniel Ting, Justin Thaler","submitted_at":"2022-03-29T09:51:50Z","abstract_excerpt":"We consider privacy in the context of streaming algorithms for cardinality estimation. We show that a large class of algorithms all satisfy $\\epsilon$-differential privacy, so long as (a) the algorithm is combined with a simple down-sampling procedure, and (b) the cardinality of the input stream is $\\Omega(k/\\epsilon)$. Here, $k$ is a certain parameter of the sketch that is always at most the sketch size in bits, but is typically much smaller. We also show that, even with no modification, algorithms in our class satisfy $(\\epsilon, \\delta)$-differential privacy, where $\\delta$ falls exponentia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.15400","kind":"arxiv","version":2},"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/2203.15400/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":"2026-07-05T05:38:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lo1v/Saz4HNI9JNqiMCoaoSuLxypZHa7UkyeBXtFZKOQcZvfhMsKLNnlllxy6XviVsDDWMzWK03Ev71j/8vIDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T15:59:43.677042Z"},"content_sha256":"42bc5cd5c2542e4cc7f3bff5c7f57b9438d458e869b87636c13030d799cc0b90","schema_version":"1.0","event_id":"sha256:42bc5cd5c2542e4cc7f3bff5c7f57b9438d458e869b87636c13030d799cc0b90"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7UEFPJ5WFDKKKABRVP42J7BCOJ/bundle.json","state_url":"https://pith.science/pith/7UEFPJ5WFDKKKABRVP42J7BCOJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7UEFPJ5WFDKKKABRVP42J7BCOJ/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":"2026-07-05T15:59:43Z","links":{"resolver":"https://pith.science/pith/7UEFPJ5WFDKKKABRVP42J7BCOJ","bundle":"https://pith.science/pith/7UEFPJ5WFDKKKABRVP42J7BCOJ/bundle.json","state":"https://pith.science/pith/7UEFPJ5WFDKKKABRVP42J7BCOJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7UEFPJ5WFDKKKABRVP42J7BCOJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:7UEFPJ5WFDKKKABRVP42J7BCOJ","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":"b5a015672f420188bb7238a4839b36da804775ff17445deacfd6622b1760e0c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-03-29T09:51:50Z","title_canon_sha256":"fec251853f040b5b69f13675e78cbd86c563fe2280de7a37c744bb70523023d6"},"schema_version":"1.0","source":{"id":"2203.15400","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.15400","created_at":"2026-07-05T05:38:27Z"},{"alias_kind":"arxiv_version","alias_value":"2203.15400v2","created_at":"2026-07-05T05:38:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.15400","created_at":"2026-07-05T05:38:27Z"},{"alias_kind":"pith_short_12","alias_value":"7UEFPJ5WFDKK","created_at":"2026-07-05T05:38:27Z"},{"alias_kind":"pith_short_16","alias_value":"7UEFPJ5WFDKKKABR","created_at":"2026-07-05T05:38:27Z"},{"alias_kind":"pith_short_8","alias_value":"7UEFPJ5W","created_at":"2026-07-05T05:38:27Z"}],"graph_snapshots":[{"event_id":"sha256:42bc5cd5c2542e4cc7f3bff5c7f57b9438d458e869b87636c13030d799cc0b90","target":"graph","created_at":"2026-07-05T05:38:27Z","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/2203.15400/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider privacy in the context of streaming algorithms for cardinality estimation. We show that a large class of algorithms all satisfy $\\epsilon$-differential privacy, so long as (a) the algorithm is combined with a simple down-sampling procedure, and (b) the cardinality of the input stream is $\\Omega(k/\\epsilon)$. Here, $k$ is a certain parameter of the sketch that is always at most the sketch size in bits, but is typically much smaller. We also show that, even with no modification, algorithms in our class satisfy $(\\epsilon, \\delta)$-differential privacy, where $\\delta$ falls exponentia","authors_text":"Charlie Dickens, Daniel Ting, Justin Thaler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-03-29T09:51:50Z","title":"Order-Invariant Cardinality Estimators Are Differentially Private"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.15400","kind":"arxiv","version":2},"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:ee9c8806fa139631b2c987a61adce21b16383c51c8f653558ba7f08189c84617","target":"record","created_at":"2026-07-05T05:38:27Z","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":"b5a015672f420188bb7238a4839b36da804775ff17445deacfd6622b1760e0c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-03-29T09:51:50Z","title_canon_sha256":"fec251853f040b5b69f13675e78cbd86c563fe2280de7a37c744bb70523023d6"},"schema_version":"1.0","source":{"id":"2203.15400","kind":"arxiv","version":2}},"canonical_sha256":"fd0857a7b628d4a50031abf9a4fc227246acbf525140f2a3a650257b774cae9b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd0857a7b628d4a50031abf9a4fc227246acbf525140f2a3a650257b774cae9b","first_computed_at":"2026-07-05T05:38:27.571131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:38:27.571131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J3lspooHGgxUBNfE+eHcfhzfWG67DDqfGQ5wNyX5WFCr1SXwjW1ghm5m0mYMMGJ21tWxPSR44dfbS2b5AwyABQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:38:27.571612Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.15400","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee9c8806fa139631b2c987a61adce21b16383c51c8f653558ba7f08189c84617","sha256:42bc5cd5c2542e4cc7f3bff5c7f57b9438d458e869b87636c13030d799cc0b90"],"state_sha256":"1e3487b0cbfe1185af51e62b2a6f2ff33dd5ccce83236d673403db66cbe99fa9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vwpaN30mbbXUuK8Wz9wrA6PVm06KuhECQFwbxv5Lf4RP2UGm5GT4LS6oPcBJLOW3Kb/Zviph1mWdan/zwzJeBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T15:59:43.679126Z","bundle_sha256":"e26a9f9c6b50477973058fb88121df8828ee87ce4c5f7bcc95449eb95573be86"}}