{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:CRO2YOLXGF3XG5SRPY2GQKUA4C","short_pith_number":"pith:CRO2YOLX","canonical_record":{"source":{"id":"1504.07553","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2015-04-28T16:15:01Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"515ca12403a950e2ae05b34f71386be47cc04ed56cce87119e51e65671ca0121","abstract_canon_sha256":"ae2e21c133e4f8db781c3003bad0de58c50cde9b6bfba17abb39ab116559bebc"},"schema_version":"1.0"},"canonical_sha256":"145dac397731777376517e34682a80e0830a5e9dea923dcaaf92d2bb8c10ebf0","source":{"kind":"arxiv","id":"1504.07553","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.07553","created_at":"2026-07-05T09:52:05Z"},{"alias_kind":"arxiv_version","alias_value":"1504.07553v2","created_at":"2026-07-05T09:52:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.07553","created_at":"2026-07-05T09:52:05Z"},{"alias_kind":"pith_short_12","alias_value":"CRO2YOLXGF3X","created_at":"2026-07-05T09:52:05Z"},{"alias_kind":"pith_short_16","alias_value":"CRO2YOLXGF3XG5SR","created_at":"2026-07-05T09:52:05Z"},{"alias_kind":"pith_short_8","alias_value":"CRO2YOLX","created_at":"2026-07-05T09:52:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:CRO2YOLXGF3XG5SRPY2GQKUA4C","target":"record","payload":{"canonical_record":{"source":{"id":"1504.07553","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2015-04-28T16:15:01Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"515ca12403a950e2ae05b34f71386be47cc04ed56cce87119e51e65671ca0121","abstract_canon_sha256":"ae2e21c133e4f8db781c3003bad0de58c50cde9b6bfba17abb39ab116559bebc"},"schema_version":"1.0"},"canonical_sha256":"145dac397731777376517e34682a80e0830a5e9dea923dcaaf92d2bb8c10ebf0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:52:05.872303Z","signature_b64":"Ap9qrxBWyv61wl6Kl/vEFGT5M98G0BD3jHNsNXBm7I/MTf0dsBuearIug3nJi4RfnXqoNDGa/LW92SeMl10yDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"145dac397731777376517e34682a80e0830a5e9dea923dcaaf92d2bb8c10ebf0","last_reissued_at":"2026-07-05T09:52:05.871842Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:52:05.871842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.07553","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":"2026-07-05T09:52:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DL6OVEmAi1853gKKclUAzIl8bM5+/C6GvD7ijA12dCYukyY7lM6rf8T7Kn14LSp7PFTfqfZP4uAKQAssnObhDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T15:37:27.205671Z"},"content_sha256":"9d517339c59b358ac789d268fee755038dd280d252034375d122ee0738e2a68a","schema_version":"1.0","event_id":"sha256:9d517339c59b358ac789d268fee755038dd280d252034375d122ee0738e2a68a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:CRO2YOLXGF3XG5SRPY2GQKUA4C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Differentially Private Release and Learning of Threshold Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.CR","authors_text":"Kobbi Nissim, Mark Bun, Salil Vadhan, Uri Stemmer","submitted_at":"2015-04-28T16:15:01Z","abstract_excerpt":"We prove new upper and lower bounds on the sample complexity of $(\\epsilon, \\delta)$ differentially private algorithms for releasing approximate answers to threshold functions. A threshold function $c_x$ over a totally ordered domain $X$ evaluates to $c_x(y) = 1$ if $y \\le x$, and evaluates to $0$ otherwise. We give the first nontrivial lower bound for releasing thresholds with $(\\epsilon,\\delta)$ differential privacy, showing that the task is impossible over an infinite domain $X$, and moreover requires sample complexity $n \\ge \\Omega(\\log^*|X|)$, which grows with the size of the domain. Insp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07553","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/1504.07553/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":"2026-07-05T09:52:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2C72mhE5h0fk7VyYHeBQ/6wUxbDGPxX1MD/00Y8GTfxBJobPzeOhTRqTJ8aehs5Jc5EkCBo3Ysy6PWO5FR+1AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T15:37:27.206335Z"},"content_sha256":"3dd3bc1c6f07c590a6afef3ac7bb88b0a3f0de4e71bc2f8e6dc725c77f3d9b46","schema_version":"1.0","event_id":"sha256:3dd3bc1c6f07c590a6afef3ac7bb88b0a3f0de4e71bc2f8e6dc725c77f3d9b46"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CRO2YOLXGF3XG5SRPY2GQKUA4C/bundle.json","state_url":"https://pith.science/pith/CRO2YOLXGF3XG5SRPY2GQKUA4C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CRO2YOLXGF3XG5SRPY2GQKUA4C/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":"2026-07-05T15:37:27Z","links":{"resolver":"https://pith.science/pith/CRO2YOLXGF3XG5SRPY2GQKUA4C","bundle":"https://pith.science/pith/CRO2YOLXGF3XG5SRPY2GQKUA4C/bundle.json","state":"https://pith.science/pith/CRO2YOLXGF3XG5SRPY2GQKUA4C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CRO2YOLXGF3XG5SRPY2GQKUA4C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CRO2YOLXGF3XG5SRPY2GQKUA4C","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":"ae2e21c133e4f8db781c3003bad0de58c50cde9b6bfba17abb39ab116559bebc","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2015-04-28T16:15:01Z","title_canon_sha256":"515ca12403a950e2ae05b34f71386be47cc04ed56cce87119e51e65671ca0121"},"schema_version":"1.0","source":{"id":"1504.07553","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.07553","created_at":"2026-07-05T09:52:05Z"},{"alias_kind":"arxiv_version","alias_value":"1504.07553v2","created_at":"2026-07-05T09:52:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.07553","created_at":"2026-07-05T09:52:05Z"},{"alias_kind":"pith_short_12","alias_value":"CRO2YOLXGF3X","created_at":"2026-07-05T09:52:05Z"},{"alias_kind":"pith_short_16","alias_value":"CRO2YOLXGF3XG5SR","created_at":"2026-07-05T09:52:05Z"},{"alias_kind":"pith_short_8","alias_value":"CRO2YOLX","created_at":"2026-07-05T09:52:05Z"}],"graph_snapshots":[{"event_id":"sha256:3dd3bc1c6f07c590a6afef3ac7bb88b0a3f0de4e71bc2f8e6dc725c77f3d9b46","target":"graph","created_at":"2026-07-05T09:52:05Z","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/1504.07553/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove new upper and lower bounds on the sample complexity of $(\\epsilon, \\delta)$ differentially private algorithms for releasing approximate answers to threshold functions. A threshold function $c_x$ over a totally ordered domain $X$ evaluates to $c_x(y) = 1$ if $y \\le x$, and evaluates to $0$ otherwise. We give the first nontrivial lower bound for releasing thresholds with $(\\epsilon,\\delta)$ differential privacy, showing that the task is impossible over an infinite domain $X$, and moreover requires sample complexity $n \\ge \\Omega(\\log^*|X|)$, which grows with the size of the domain. Insp","authors_text":"Kobbi Nissim, Mark Bun, Salil Vadhan, Uri Stemmer","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2015-04-28T16:15:01Z","title":"Differentially Private Release and Learning of Threshold Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07553","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":"sha256:9d517339c59b358ac789d268fee755038dd280d252034375d122ee0738e2a68a","target":"record","created_at":"2026-07-05T09:52:05Z","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":"ae2e21c133e4f8db781c3003bad0de58c50cde9b6bfba17abb39ab116559bebc","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2015-04-28T16:15:01Z","title_canon_sha256":"515ca12403a950e2ae05b34f71386be47cc04ed56cce87119e51e65671ca0121"},"schema_version":"1.0","source":{"id":"1504.07553","kind":"arxiv","version":2}},"canonical_sha256":"145dac397731777376517e34682a80e0830a5e9dea923dcaaf92d2bb8c10ebf0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"145dac397731777376517e34682a80e0830a5e9dea923dcaaf92d2bb8c10ebf0","first_computed_at":"2026-07-05T09:52:05.871842Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:52:05.871842Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ap9qrxBWyv61wl6Kl/vEFGT5M98G0BD3jHNsNXBm7I/MTf0dsBuearIug3nJi4RfnXqoNDGa/LW92SeMl10yDg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:52:05.872303Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.07553","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d517339c59b358ac789d268fee755038dd280d252034375d122ee0738e2a68a","sha256:3dd3bc1c6f07c590a6afef3ac7bb88b0a3f0de4e71bc2f8e6dc725c77f3d9b46"],"state_sha256":"5f0bbe2848f6a58896a52d561258636bb0420e7f7f0793fdddda49b9f2f5658c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XzCkKTol0Jz4ujqgrSIvCRHdp2ibI+PGsV2EaeHnEVkCxxeQXlxlZYii0LfMjwU9E+nVF+hoVA/KdEm3kTkrAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T15:37:27.211069Z","bundle_sha256":"90cf096f0341140573f9e90294e4b61eac8af5aa4703037c211370b09b9a9b8a"}}