{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:7QGCPDDUKXMFGC6TQBZTM4NY25","short_pith_number":"pith:7QGCPDDU","canonical_record":{"source":{"id":"2109.10528","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CR","submitted_at":"2021-09-22T06:20:01Z","cross_cats_sorted":["cs.IT","cs.LG","math.IT"],"title_canon_sha256":"8902a48f1164aef26dc43d6430165cf93399116212e2d89ca7ccd740828caaee","abstract_canon_sha256":"cd069b0708c66027f02361a4e8ca1f2792f9568657ef2ab70ffceb5a4eed0d77"},"schema_version":"1.0"},"canonical_sha256":"fc0c278c7455d8530bd380733671b8d7505f2e6c5c7628c686f22c668eeb0526","source":{"kind":"arxiv","id":"2109.10528","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.10528","created_at":"2026-07-05T03:16:37Z"},{"alias_kind":"arxiv_version","alias_value":"2109.10528v1","created_at":"2026-07-05T03:16:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.10528","created_at":"2026-07-05T03:16:37Z"},{"alias_kind":"pith_short_12","alias_value":"7QGCPDDUKXMF","created_at":"2026-07-05T03:16:37Z"},{"alias_kind":"pith_short_16","alias_value":"7QGCPDDUKXMFGC6T","created_at":"2026-07-05T03:16:37Z"},{"alias_kind":"pith_short_8","alias_value":"7QGCPDDU","created_at":"2026-07-05T03:16:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:7QGCPDDUKXMFGC6TQBZTM4NY25","target":"record","payload":{"canonical_record":{"source":{"id":"2109.10528","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CR","submitted_at":"2021-09-22T06:20:01Z","cross_cats_sorted":["cs.IT","cs.LG","math.IT"],"title_canon_sha256":"8902a48f1164aef26dc43d6430165cf93399116212e2d89ca7ccd740828caaee","abstract_canon_sha256":"cd069b0708c66027f02361a4e8ca1f2792f9568657ef2ab70ffceb5a4eed0d77"},"schema_version":"1.0"},"canonical_sha256":"fc0c278c7455d8530bd380733671b8d7505f2e6c5c7628c686f22c668eeb0526","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:16:37.376392Z","signature_b64":"5EL/OLRH1lqmBbQDs/UGBU4eisTjqQubKAquYhddCT1UPBAuaQ3gml7LOra8BbYGKo8A3hvU2OlbfgXzH1esDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc0c278c7455d8530bd380733671b8d7505f2e6c5c7628c686f22c668eeb0526","last_reissued_at":"2026-07-05T03:16:37.375879Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:16:37.375879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.10528","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":"2026-07-05T03:16:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"isxWo6Z7dR5XtwEq1P/0fQwGJUFm/HykjGiFvYuNvzgS3sDwDlOCwo0pSAUmTwTvHeX1txTGeT8qH85AeRV9Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-13T11:48:35.902494Z"},"content_sha256":"5374c218de93f62d0fe5a9afd509b72fd5064f1ef0ff0c1db1582e94635e7c76","schema_version":"1.0","event_id":"sha256:5374c218de93f62d0fe5a9afd509b72fd5064f1ef0ff0c1db1582e94635e7c76"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:7QGCPDDUKXMFGC6TQBZTM4NY25","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A unified interpretation of the Gaussian mechanism for differential privacy through the sensitivity index","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT"],"primary_cat":"cs.CR","authors_text":"Alexander Ziller, Daniel Rueckert, Dmitrii Usynin, Friederike Jungmann, Georgios Kaissis, Moritz Knolle","submitted_at":"2021-09-22T06:20:01Z","abstract_excerpt":"The Gaussian mechanism (GM) represents a universally employed tool for achieving differential privacy (DP), and a large body of work has been devoted to its analysis. We argue that the three prevailing interpretations of the GM, namely $(\\varepsilon, \\delta)$-DP, f-DP and R\\'enyi DP can be expressed by using a single parameter $\\psi$, which we term the sensitivity index. $\\psi$ uniquely characterises the GM and its properties by encapsulating its two fundamental quantities: the sensitivity of the query and the magnitude of the noise perturbation. With strong links to the ROC curve and the hypo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.10528","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/2109.10528/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":"2026-07-05T03:16:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pn93LZRKabW3+yz/nZBoIxrVUQWjZJOSNapOjjbb8iJpM2Hu9lzcIFmZHGAPmfRh+8i7IMwg1oZ4u8Y6/xNJDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-13T11:48:35.902873Z"},"content_sha256":"70e9ff718a479d182f1398475c52c520d7311266b9a078fd392f2df9928c6654","schema_version":"1.0","event_id":"sha256:70e9ff718a479d182f1398475c52c520d7311266b9a078fd392f2df9928c6654"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7QGCPDDUKXMFGC6TQBZTM4NY25/bundle.json","state_url":"https://pith.science/pith/7QGCPDDUKXMFGC6TQBZTM4NY25/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7QGCPDDUKXMFGC6TQBZTM4NY25/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":"2026-07-13T11:48:35Z","links":{"resolver":"https://pith.science/pith/7QGCPDDUKXMFGC6TQBZTM4NY25","bundle":"https://pith.science/pith/7QGCPDDUKXMFGC6TQBZTM4NY25/bundle.json","state":"https://pith.science/pith/7QGCPDDUKXMFGC6TQBZTM4NY25/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7QGCPDDUKXMFGC6TQBZTM4NY25/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:7QGCPDDUKXMFGC6TQBZTM4NY25","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":"cd069b0708c66027f02361a4e8ca1f2792f9568657ef2ab70ffceb5a4eed0d77","cross_cats_sorted":["cs.IT","cs.LG","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CR","submitted_at":"2021-09-22T06:20:01Z","title_canon_sha256":"8902a48f1164aef26dc43d6430165cf93399116212e2d89ca7ccd740828caaee"},"schema_version":"1.0","source":{"id":"2109.10528","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.10528","created_at":"2026-07-05T03:16:37Z"},{"alias_kind":"arxiv_version","alias_value":"2109.10528v1","created_at":"2026-07-05T03:16:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.10528","created_at":"2026-07-05T03:16:37Z"},{"alias_kind":"pith_short_12","alias_value":"7QGCPDDUKXMF","created_at":"2026-07-05T03:16:37Z"},{"alias_kind":"pith_short_16","alias_value":"7QGCPDDUKXMFGC6T","created_at":"2026-07-05T03:16:37Z"},{"alias_kind":"pith_short_8","alias_value":"7QGCPDDU","created_at":"2026-07-05T03:16:37Z"}],"graph_snapshots":[{"event_id":"sha256:70e9ff718a479d182f1398475c52c520d7311266b9a078fd392f2df9928c6654","target":"graph","created_at":"2026-07-05T03:16:37Z","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/2109.10528/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Gaussian mechanism (GM) represents a universally employed tool for achieving differential privacy (DP), and a large body of work has been devoted to its analysis. We argue that the three prevailing interpretations of the GM, namely $(\\varepsilon, \\delta)$-DP, f-DP and R\\'enyi DP can be expressed by using a single parameter $\\psi$, which we term the sensitivity index. $\\psi$ uniquely characterises the GM and its properties by encapsulating its two fundamental quantities: the sensitivity of the query and the magnitude of the noise perturbation. With strong links to the ROC curve and the hypo","authors_text":"Alexander Ziller, Daniel Rueckert, Dmitrii Usynin, Friederike Jungmann, Georgios Kaissis, Moritz Knolle","cross_cats":["cs.IT","cs.LG","math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CR","submitted_at":"2021-09-22T06:20:01Z","title":"A unified interpretation of the Gaussian mechanism for differential privacy through the sensitivity index"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.10528","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":"sha256:5374c218de93f62d0fe5a9afd509b72fd5064f1ef0ff0c1db1582e94635e7c76","target":"record","created_at":"2026-07-05T03:16:37Z","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":"cd069b0708c66027f02361a4e8ca1f2792f9568657ef2ab70ffceb5a4eed0d77","cross_cats_sorted":["cs.IT","cs.LG","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CR","submitted_at":"2021-09-22T06:20:01Z","title_canon_sha256":"8902a48f1164aef26dc43d6430165cf93399116212e2d89ca7ccd740828caaee"},"schema_version":"1.0","source":{"id":"2109.10528","kind":"arxiv","version":1}},"canonical_sha256":"fc0c278c7455d8530bd380733671b8d7505f2e6c5c7628c686f22c668eeb0526","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc0c278c7455d8530bd380733671b8d7505f2e6c5c7628c686f22c668eeb0526","first_computed_at":"2026-07-05T03:16:37.375879Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:16:37.375879Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5EL/OLRH1lqmBbQDs/UGBU4eisTjqQubKAquYhddCT1UPBAuaQ3gml7LOra8BbYGKo8A3hvU2OlbfgXzH1esDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:16:37.376392Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.10528","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5374c218de93f62d0fe5a9afd509b72fd5064f1ef0ff0c1db1582e94635e7c76","sha256:70e9ff718a479d182f1398475c52c520d7311266b9a078fd392f2df9928c6654"],"state_sha256":"d09e51dc7484518e3362bb41d7186ad67ac934aaf79a0fae07316831a5c58466"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qDtOFBXzfUXO0CRvaS5J/5NglKzMJ9SQWlwIeQYB/PkVD4H/MmfzooATAIBvVrQRtwQhxYOoeL5HwD0HGq0KBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-13T11:48:35.904981Z","bundle_sha256":"15d6957e44b9b792f5798906478c4a08e60e5b8bfd9d2f7ec6d2523b481e06b5"}}