{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:X7UPUGQ4XZ5RO4DEFBWKKBZJD3","short_pith_number":"pith:X7UPUGQ4","canonical_record":{"source":{"id":"1511.05680","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2015-11-18T07:34:23Z","cross_cats_sorted":["cs.DS","stat.ML"],"title_canon_sha256":"9c60ab7ec07bf2a6f5c152ffeb24954021f90898c1f175d1b0d0e1dbbca1e18f","abstract_canon_sha256":"af2f540d17275bdb69264e226ac397113568beba61efa40d2408c797c6d4614c"},"schema_version":"1.0"},"canonical_sha256":"bfe8fa1a1cbe7b177064286ca507291ee8fa2d5d097b48de0f88bb92b245c305","source":{"kind":"arxiv","id":"1511.05680","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.05680","created_at":"2026-05-18T01:26:30Z"},{"alias_kind":"arxiv_version","alias_value":"1511.05680v2","created_at":"2026-05-18T01:26:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.05680","created_at":"2026-05-18T01:26:30Z"},{"alias_kind":"pith_short_12","alias_value":"X7UPUGQ4XZ5R","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"X7UPUGQ4XZ5RO4DE","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"X7UPUGQ4","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:X7UPUGQ4XZ5RO4DEFBWKKBZJD3","target":"record","payload":{"canonical_record":{"source":{"id":"1511.05680","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2015-11-18T07:34:23Z","cross_cats_sorted":["cs.DS","stat.ML"],"title_canon_sha256":"9c60ab7ec07bf2a6f5c152ffeb24954021f90898c1f175d1b0d0e1dbbca1e18f","abstract_canon_sha256":"af2f540d17275bdb69264e226ac397113568beba61efa40d2408c797c6d4614c"},"schema_version":"1.0"},"canonical_sha256":"bfe8fa1a1cbe7b177064286ca507291ee8fa2d5d097b48de0f88bb92b245c305","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:30.941638Z","signature_b64":"5IrRua9AiRYDvPP4VJn4uXKEhhnRd3Hajt7HfBYFvPuQDL7PaMVwcBv5HfoQL/U8NZbjkKAzTMGic+T6XNBkAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bfe8fa1a1cbe7b177064286ca507291ee8fa2d5d097b48de0f88bb92b245c305","last_reissued_at":"2026-05-18T01:26:30.941053Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:30.941053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.05680","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":"2026-05-18T01:26:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"niLlW8nEdN98nl3cqXmk4BE40PFh//v8Q9u5+VpUJOfDyaF7eKOKrwPNkakv5nmDXwC00RfZkrGdEWVe1TOQBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:50:59.826806Z"},"content_sha256":"5c4ca4013ac122751e59de2b485fb4526b08b91e7a4638b57d867bf7bb68c3dc","schema_version":"1.0","event_id":"sha256:5c4ca4013ac122751e59de2b485fb4526b08b91e7a4638b57d867bf7bb68c3dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:X7UPUGQ4XZ5RO4DEFBWKKBZJD3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wishart Mechanism for Differentially Private Principal Components Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","stat.ML"],"primary_cat":"cs.CR","authors_text":"Cong Xie, Wuxuan Jiang, Zhihua Zhang","submitted_at":"2015-11-18T07:34:23Z","abstract_excerpt":"We propose a new input perturbation mechanism for publishing a covariance matrix to achieve $(\\epsilon,0)$-differential privacy. Our mechanism uses a Wishart distribution to generate matrix noise. In particular, We apply this mechanism to principal component analysis. Our mechanism is able to keep the positive semi-definiteness of the published covariance matrix. Thus, our approach gives rise to a general publishing framework for input perturbation of a symmetric positive semidefinite matrix. Moreover, compared with the classic Laplace mechanism, our method has better utility guarantee. To the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05680","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":""},"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":"2026-05-18T01:26:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oumiqhTWKLn7kX4zCeK8gKAsy3sABDn/PobJqFFxwVvb9152QyRjijp11aa4Lcx0nP0fZwr+54ZHQywRfo2+Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:50:59.827494Z"},"content_sha256":"90d24d4c4bfe62e0c3c1a09c455e73d47a3f104c271887d09493bf5b4841bb1b","schema_version":"1.0","event_id":"sha256:90d24d4c4bfe62e0c3c1a09c455e73d47a3f104c271887d09493bf5b4841bb1b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X7UPUGQ4XZ5RO4DEFBWKKBZJD3/bundle.json","state_url":"https://pith.science/pith/X7UPUGQ4XZ5RO4DEFBWKKBZJD3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X7UPUGQ4XZ5RO4DEFBWKKBZJD3/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":"2026-05-26T09:50:59Z","links":{"resolver":"https://pith.science/pith/X7UPUGQ4XZ5RO4DEFBWKKBZJD3","bundle":"https://pith.science/pith/X7UPUGQ4XZ5RO4DEFBWKKBZJD3/bundle.json","state":"https://pith.science/pith/X7UPUGQ4XZ5RO4DEFBWKKBZJD3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X7UPUGQ4XZ5RO4DEFBWKKBZJD3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:X7UPUGQ4XZ5RO4DEFBWKKBZJD3","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":"af2f540d17275bdb69264e226ac397113568beba61efa40d2408c797c6d4614c","cross_cats_sorted":["cs.DS","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2015-11-18T07:34:23Z","title_canon_sha256":"9c60ab7ec07bf2a6f5c152ffeb24954021f90898c1f175d1b0d0e1dbbca1e18f"},"schema_version":"1.0","source":{"id":"1511.05680","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.05680","created_at":"2026-05-18T01:26:30Z"},{"alias_kind":"arxiv_version","alias_value":"1511.05680v2","created_at":"2026-05-18T01:26:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.05680","created_at":"2026-05-18T01:26:30Z"},{"alias_kind":"pith_short_12","alias_value":"X7UPUGQ4XZ5R","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"X7UPUGQ4XZ5RO4DE","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"X7UPUGQ4","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:90d24d4c4bfe62e0c3c1a09c455e73d47a3f104c271887d09493bf5b4841bb1b","target":"graph","created_at":"2026-05-18T01:26:30Z","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 propose a new input perturbation mechanism for publishing a covariance matrix to achieve $(\\epsilon,0)$-differential privacy. Our mechanism uses a Wishart distribution to generate matrix noise. In particular, We apply this mechanism to principal component analysis. Our mechanism is able to keep the positive semi-definiteness of the published covariance matrix. Thus, our approach gives rise to a general publishing framework for input perturbation of a symmetric positive semidefinite matrix. Moreover, compared with the classic Laplace mechanism, our method has better utility guarantee. To the","authors_text":"Cong Xie, Wuxuan Jiang, Zhihua Zhang","cross_cats":["cs.DS","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2015-11-18T07:34:23Z","title":"Wishart Mechanism for Differentially Private Principal Components Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05680","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":"sha256:5c4ca4013ac122751e59de2b485fb4526b08b91e7a4638b57d867bf7bb68c3dc","target":"record","created_at":"2026-05-18T01:26:30Z","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":"af2f540d17275bdb69264e226ac397113568beba61efa40d2408c797c6d4614c","cross_cats_sorted":["cs.DS","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CR","submitted_at":"2015-11-18T07:34:23Z","title_canon_sha256":"9c60ab7ec07bf2a6f5c152ffeb24954021f90898c1f175d1b0d0e1dbbca1e18f"},"schema_version":"1.0","source":{"id":"1511.05680","kind":"arxiv","version":2}},"canonical_sha256":"bfe8fa1a1cbe7b177064286ca507291ee8fa2d5d097b48de0f88bb92b245c305","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfe8fa1a1cbe7b177064286ca507291ee8fa2d5d097b48de0f88bb92b245c305","first_computed_at":"2026-05-18T01:26:30.941053Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:30.941053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5IrRua9AiRYDvPP4VJn4uXKEhhnRd3Hajt7HfBYFvPuQDL7PaMVwcBv5HfoQL/U8NZbjkKAzTMGic+T6XNBkAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:30.941638Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.05680","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c4ca4013ac122751e59de2b485fb4526b08b91e7a4638b57d867bf7bb68c3dc","sha256:90d24d4c4bfe62e0c3c1a09c455e73d47a3f104c271887d09493bf5b4841bb1b"],"state_sha256":"df4829f4f805560c5b22beaf82a6f044a442a9fff433e3cab8d0f9f447e42d0c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6WpuH+qU90UW3Dfj/iIoM6P0Rgp8i62VWBXh7Aql2FWLHWGIjyyJQx5OZ3ah5c2It1kPq2rJEU/GcFFsZlwFCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T09:50:59.831309Z","bundle_sha256":"24e3c97c916c56deeb4a02581faac7163310c8abd26a241d565c1e00c1df3673"}}