{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:5NJWK2VCL6ARRYCR6JRDQZHTEP","short_pith_number":"pith:5NJWK2VC","canonical_record":{"source":{"id":"1311.3158","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2013-11-13T15:09:48Z","cross_cats_sorted":[],"title_canon_sha256":"70714cb7ddf026dc4118b1e21cbd6343e1d5dc2cb8e87cae5079f53ea0095f2a","abstract_canon_sha256":"17e518f108c9c0c70d48f25b0aeefe18f87093c1dbd1896e8404590b3362bd96"},"schema_version":"1.0"},"canonical_sha256":"eb53656aa25f8118e051f2623864f323f4e7e66c8984e87e1ba1478aa7c28d1b","source":{"kind":"arxiv","id":"1311.3158","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.3158","created_at":"2026-05-18T00:02:28Z"},{"alias_kind":"arxiv_version","alias_value":"1311.3158v3","created_at":"2026-05-18T00:02:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.3158","created_at":"2026-05-18T00:02:28Z"},{"alias_kind":"pith_short_12","alias_value":"5NJWK2VCL6AR","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5NJWK2VCL6ARRYCR","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5NJWK2VC","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:5NJWK2VCL6ARRYCR6JRDQZHTEP","target":"record","payload":{"canonical_record":{"source":{"id":"1311.3158","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2013-11-13T15:09:48Z","cross_cats_sorted":[],"title_canon_sha256":"70714cb7ddf026dc4118b1e21cbd6343e1d5dc2cb8e87cae5079f53ea0095f2a","abstract_canon_sha256":"17e518f108c9c0c70d48f25b0aeefe18f87093c1dbd1896e8404590b3362bd96"},"schema_version":"1.0"},"canonical_sha256":"eb53656aa25f8118e051f2623864f323f4e7e66c8984e87e1ba1478aa7c28d1b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:28.581612Z","signature_b64":"tMJZmrpNF0qVkgbznnjsdLfTrEhfDuteTHRg8ZQRow6UTWrWkC1V7Wv2jIvh2LqAib7gJNxxjbdQk6P10pwBBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb53656aa25f8118e051f2623864f323f4e7e66c8984e87e1ba1478aa7c28d1b","last_reissued_at":"2026-05-18T00:02:28.580993Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:28.580993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.3158","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":"2026-05-18T00:02:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ScX7fiOKloWfAUwHvUgEgG0K5vDVBAQPkHD7dW2PuogWLT+rjwOfdtmnLrANgdg0Pc2iw3I9zWiDKBhAq0uDCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T06:01:01.687760Z"},"content_sha256":"fc919e398808c4f10cc67c22a7c1f805adc23616cf9c74eb4096505b3c9d4163","schema_version":"1.0","event_id":"sha256:fc919e398808c4f10cc67c22a7c1f805adc23616cf9c74eb4096505b3c9d4163"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:5NJWK2VCL6ARRYCR6JRDQZHTEP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fingerprinting Codes and the Price of Approximate Differential Privacy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CR","authors_text":"Jonathan Ullman, Mark Bun, Salil Vadhan","submitted_at":"2013-11-13T15:09:48Z","abstract_excerpt":"We show new lower bounds on the sample complexity of $(\\varepsilon, \\delta)$-differentially private algorithms that accurately answer large sets of counting queries. A counting query on a database $D \\in (\\{0,1\\}^d)^n$ has the form \"What fraction of the individual records in the database satisfy the property $q$?\" We show that in order to answer an arbitrary set $\\mathcal{Q}$ of $\\gg nd$ counting queries on $D$ to within error $\\pm \\alpha$ it is necessary that $$ n \\geq \\tilde{\\Omega}\\Bigg(\\frac{\\sqrt{d} \\log |\\mathcal{Q}|}{\\alpha^2 \\varepsilon} \\Bigg). $$ This bound is optimal up to poly-loga"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3158","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":""},"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":"2026-05-18T00:02:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DFsmbA4IlRvxPxHzJYZ09Vn2Pz/zFhDRUHAEjciHGDLbE8BkwMczAsam/t6KyAb2Z4cCnxXnUFITTABeU9cDCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T06:01:01.688653Z"},"content_sha256":"204d723e169d44bc611019db1fcc774a64c43133037b9b32b865d3bc0a593872","schema_version":"1.0","event_id":"sha256:204d723e169d44bc611019db1fcc774a64c43133037b9b32b865d3bc0a593872"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5NJWK2VCL6ARRYCR6JRDQZHTEP/bundle.json","state_url":"https://pith.science/pith/5NJWK2VCL6ARRYCR6JRDQZHTEP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5NJWK2VCL6ARRYCR6JRDQZHTEP/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":"2026-08-13T06:01:01Z","links":{"resolver":"https://pith.science/pith/5NJWK2VCL6ARRYCR6JRDQZHTEP","bundle":"https://pith.science/pith/5NJWK2VCL6ARRYCR6JRDQZHTEP/bundle.json","state":"https://pith.science/pith/5NJWK2VCL6ARRYCR6JRDQZHTEP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5NJWK2VCL6ARRYCR6JRDQZHTEP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5NJWK2VCL6ARRYCR6JRDQZHTEP","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":"17e518f108c9c0c70d48f25b0aeefe18f87093c1dbd1896e8404590b3362bd96","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2013-11-13T15:09:48Z","title_canon_sha256":"70714cb7ddf026dc4118b1e21cbd6343e1d5dc2cb8e87cae5079f53ea0095f2a"},"schema_version":"1.0","source":{"id":"1311.3158","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.3158","created_at":"2026-05-18T00:02:28Z"},{"alias_kind":"arxiv_version","alias_value":"1311.3158v3","created_at":"2026-05-18T00:02:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.3158","created_at":"2026-05-18T00:02:28Z"},{"alias_kind":"pith_short_12","alias_value":"5NJWK2VCL6AR","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5NJWK2VCL6ARRYCR","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5NJWK2VC","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:204d723e169d44bc611019db1fcc774a64c43133037b9b32b865d3bc0a593872","target":"graph","created_at":"2026-05-18T00:02:28Z","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"},"paper":{"abstract_excerpt":"We show new lower bounds on the sample complexity of $(\\varepsilon, \\delta)$-differentially private algorithms that accurately answer large sets of counting queries. A counting query on a database $D \\in (\\{0,1\\}^d)^n$ has the form \"What fraction of the individual records in the database satisfy the property $q$?\" We show that in order to answer an arbitrary set $\\mathcal{Q}$ of $\\gg nd$ counting queries on $D$ to within error $\\pm \\alpha$ it is necessary that $$ n \\geq \\tilde{\\Omega}\\Bigg(\\frac{\\sqrt{d} \\log |\\mathcal{Q}|}{\\alpha^2 \\varepsilon} \\Bigg). $$ This bound is optimal up to poly-loga","authors_text":"Jonathan Ullman, Mark Bun, Salil Vadhan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2013-11-13T15:09:48Z","title":"Fingerprinting Codes and the Price of Approximate Differential Privacy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3158","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:fc919e398808c4f10cc67c22a7c1f805adc23616cf9c74eb4096505b3c9d4163","target":"record","created_at":"2026-05-18T00:02:28Z","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":"17e518f108c9c0c70d48f25b0aeefe18f87093c1dbd1896e8404590b3362bd96","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2013-11-13T15:09:48Z","title_canon_sha256":"70714cb7ddf026dc4118b1e21cbd6343e1d5dc2cb8e87cae5079f53ea0095f2a"},"schema_version":"1.0","source":{"id":"1311.3158","kind":"arxiv","version":3}},"canonical_sha256":"eb53656aa25f8118e051f2623864f323f4e7e66c8984e87e1ba1478aa7c28d1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb53656aa25f8118e051f2623864f323f4e7e66c8984e87e1ba1478aa7c28d1b","first_computed_at":"2026-05-18T00:02:28.580993Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:28.580993Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tMJZmrpNF0qVkgbznnjsdLfTrEhfDuteTHRg8ZQRow6UTWrWkC1V7Wv2jIvh2LqAib7gJNxxjbdQk6P10pwBBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:28.581612Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.3158","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc919e398808c4f10cc67c22a7c1f805adc23616cf9c74eb4096505b3c9d4163","sha256:204d723e169d44bc611019db1fcc774a64c43133037b9b32b865d3bc0a593872"],"state_sha256":"2392199771b608a365af85ad05070e603025e29e0fa2c2f5e3abb35b177028ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QrWMeAkAaZyQe8FXh5V2Ho/LOFYDHz4eaTlsxmjlkja/02VFWMbVZFCEh8uE9LzhK95FvG/nsGvRxLLvWp8IAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T06:01:01.762193Z","bundle_sha256":"8b952c9ae5c79c3538a4830d1f7b83d9d4c28084dc145306ac5c6086c1d2e6cb"}}