{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:CUW74UP3QAOY22YQ2GIAOM35BK","short_pith_number":"pith:CUW74UP3","canonical_record":{"source":{"id":"2102.05172","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2021-02-09T22:57:57Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"bf1ad742c8ded7ce0d978f1ae11bf48c1f2a1789aac355d4b61704fd4d537be2","abstract_canon_sha256":"515e37e029d37991aeda22801325ff8d8d3bf104b5079fd0a24b367e4d77c38d"},"schema_version":"1.0"},"canonical_sha256":"152dfe51fb801d8d6b10d19007337d0a86464504017aaa6781ca43a40efcfacc","source":{"kind":"arxiv","id":"2102.05172","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.05172","created_at":"2026-07-05T02:14:15Z"},{"alias_kind":"arxiv_version","alias_value":"2102.05172v1","created_at":"2026-07-05T02:14:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.05172","created_at":"2026-07-05T02:14:15Z"},{"alias_kind":"pith_short_12","alias_value":"CUW74UP3QAOY","created_at":"2026-07-05T02:14:15Z"},{"alias_kind":"pith_short_16","alias_value":"CUW74UP3QAOY22YQ","created_at":"2026-07-05T02:14:15Z"},{"alias_kind":"pith_short_8","alias_value":"CUW74UP3","created_at":"2026-07-05T02:14:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:CUW74UP3QAOY22YQ2GIAOM35BK","target":"record","payload":{"canonical_record":{"source":{"id":"2102.05172","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2021-02-09T22:57:57Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"bf1ad742c8ded7ce0d978f1ae11bf48c1f2a1789aac355d4b61704fd4d537be2","abstract_canon_sha256":"515e37e029d37991aeda22801325ff8d8d3bf104b5079fd0a24b367e4d77c38d"},"schema_version":"1.0"},"canonical_sha256":"152dfe51fb801d8d6b10d19007337d0a86464504017aaa6781ca43a40efcfacc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:14:15.644409Z","signature_b64":"xSi792S+j9OobfMfDGu3OPzEDgjcKxLPSpl1G5PqHMR+6t5gfe5o2kIjrp660IqdopYVA4BxgIBGuUJe/kf+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"152dfe51fb801d8d6b10d19007337d0a86464504017aaa6781ca43a40efcfacc","last_reissued_at":"2026-07-05T02:14:15.644017Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:14:15.644017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2102.05172","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":"2026-07-05T02:14:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K+4RFiVx795q/nFPVzKhnjxm55GeZMhzS3G2+6AMuSigNqMuHTSIQd9wKt86oFxEMSOiiMNdv/kPg+T2ftA1DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T11:27:42.806033Z"},"content_sha256":"b70bb27b344fb9cbad473d6ec411991988f5d0eb0ddb881970a0f895d56c27ac","schema_version":"1.0","event_id":"sha256:b70bb27b344fb9cbad473d6ec411991988f5d0eb0ddb881970a0f895d56c27ac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:CUW74UP3QAOY22YQ2GIAOM35BK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Differential Privacy for Binary Functions via Randomized Graph Colorings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Muriel Medard, Parastoo Sadeghi, Rafael G. L. D'Oliveira","submitted_at":"2021-02-09T22:57:57Z","abstract_excerpt":"We present a framework for designing differentially private (DP) mechanisms for binary functions via a graph representation of datasets. Datasets are nodes in the graph and any two neighboring datasets are connected by an edge. The true binary function we want to approximate assigns a value (or true color) to a dataset. Randomized DP mechanisms are then equivalent to randomized colorings of the graph. A key notion we use is that of the boundary of the graph. Any two neighboring datasets assigned a different true color belong to the boundary.\n  Under this framework, we show that fixing the mech"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.05172","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/2102.05172/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":"2026-07-05T02:14:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MRYH5x/SEDGkGS4nFVecXa5+8JSytEUV6fVJqrO0r4QVJktaFMwpEUXmhu2sW/TD0/c+t5GH05jtfAeA3GnyBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T11:27:42.807062Z"},"content_sha256":"9d0d2876cd676269413a18c73716aa5e3086c1cfc16e14800642031b14fb2bb5","schema_version":"1.0","event_id":"sha256:9d0d2876cd676269413a18c73716aa5e3086c1cfc16e14800642031b14fb2bb5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CUW74UP3QAOY22YQ2GIAOM35BK/bundle.json","state_url":"https://pith.science/pith/CUW74UP3QAOY22YQ2GIAOM35BK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CUW74UP3QAOY22YQ2GIAOM35BK/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":"2026-08-06T11:27:42Z","links":{"resolver":"https://pith.science/pith/CUW74UP3QAOY22YQ2GIAOM35BK","bundle":"https://pith.science/pith/CUW74UP3QAOY22YQ2GIAOM35BK/bundle.json","state":"https://pith.science/pith/CUW74UP3QAOY22YQ2GIAOM35BK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CUW74UP3QAOY22YQ2GIAOM35BK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:CUW74UP3QAOY22YQ2GIAOM35BK","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":"515e37e029d37991aeda22801325ff8d8d3bf104b5079fd0a24b367e4d77c38d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2021-02-09T22:57:57Z","title_canon_sha256":"bf1ad742c8ded7ce0d978f1ae11bf48c1f2a1789aac355d4b61704fd4d537be2"},"schema_version":"1.0","source":{"id":"2102.05172","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.05172","created_at":"2026-07-05T02:14:15Z"},{"alias_kind":"arxiv_version","alias_value":"2102.05172v1","created_at":"2026-07-05T02:14:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.05172","created_at":"2026-07-05T02:14:15Z"},{"alias_kind":"pith_short_12","alias_value":"CUW74UP3QAOY","created_at":"2026-07-05T02:14:15Z"},{"alias_kind":"pith_short_16","alias_value":"CUW74UP3QAOY22YQ","created_at":"2026-07-05T02:14:15Z"},{"alias_kind":"pith_short_8","alias_value":"CUW74UP3","created_at":"2026-07-05T02:14:15Z"}],"graph_snapshots":[{"event_id":"sha256:9d0d2876cd676269413a18c73716aa5e3086c1cfc16e14800642031b14fb2bb5","target":"graph","created_at":"2026-07-05T02:14:15Z","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/2102.05172/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a framework for designing differentially private (DP) mechanisms for binary functions via a graph representation of datasets. Datasets are nodes in the graph and any two neighboring datasets are connected by an edge. The true binary function we want to approximate assigns a value (or true color) to a dataset. Randomized DP mechanisms are then equivalent to randomized colorings of the graph. A key notion we use is that of the boundary of the graph. Any two neighboring datasets assigned a different true color belong to the boundary.\n  Under this framework, we show that fixing the mech","authors_text":"Muriel Medard, Parastoo Sadeghi, Rafael G. L. D'Oliveira","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2021-02-09T22:57:57Z","title":"Differential Privacy for Binary Functions via Randomized Graph Colorings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.05172","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:b70bb27b344fb9cbad473d6ec411991988f5d0eb0ddb881970a0f895d56c27ac","target":"record","created_at":"2026-07-05T02:14:15Z","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":"515e37e029d37991aeda22801325ff8d8d3bf104b5079fd0a24b367e4d77c38d","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2021-02-09T22:57:57Z","title_canon_sha256":"bf1ad742c8ded7ce0d978f1ae11bf48c1f2a1789aac355d4b61704fd4d537be2"},"schema_version":"1.0","source":{"id":"2102.05172","kind":"arxiv","version":1}},"canonical_sha256":"152dfe51fb801d8d6b10d19007337d0a86464504017aaa6781ca43a40efcfacc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"152dfe51fb801d8d6b10d19007337d0a86464504017aaa6781ca43a40efcfacc","first_computed_at":"2026-07-05T02:14:15.644017Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:14:15.644017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xSi792S+j9OobfMfDGu3OPzEDgjcKxLPSpl1G5PqHMR+6t5gfe5o2kIjrp660IqdopYVA4BxgIBGuUJe/kf+CA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:14:15.644409Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.05172","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b70bb27b344fb9cbad473d6ec411991988f5d0eb0ddb881970a0f895d56c27ac","sha256:9d0d2876cd676269413a18c73716aa5e3086c1cfc16e14800642031b14fb2bb5"],"state_sha256":"48be762a86d811fe2fde62f699eb4fe70adb25c1c4b237d7baf806de31e33e67"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CwmvE4MENgOgfd7FlHdIpxKHT4LMR2DLktvYaGn+S7Nr8fEii8VVSSwo+/rRDYLarEMnlXGBQQlp/OseFm4qBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T11:27:42.812603Z","bundle_sha256":"6f0ef0e1aaaec17533fa9ce7bf6cfae48290e4da59becb05ae1294fc2c9f4999"}}