{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:VSO5PHSBTYPDAYOA2DP7WKO2IP","short_pith_number":"pith:VSO5PHSB","canonical_record":{"source":{"id":"1604.01429","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-04-05T21:12:01Z","cross_cats_sorted":[],"title_canon_sha256":"b346c2ffb67c16384b647b59ae03ffaca6269ad3a1cdacaac6a32d56611abb30","abstract_canon_sha256":"4cef5d4ea835d05da4fd79436b432d8039ef1ef8b32b04cb54efc0403a9d6b7b"},"schema_version":"1.0"},"canonical_sha256":"ac9dd79e419e1e3061c0d0dffb29da43f739ca35c122da9339611705d8872af3","source":{"kind":"arxiv","id":"1604.01429","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.01429","created_at":"2026-05-18T00:18:09Z"},{"alias_kind":"arxiv_version","alias_value":"1604.01429v5","created_at":"2026-05-18T00:18:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.01429","created_at":"2026-05-18T00:18:09Z"},{"alias_kind":"pith_short_12","alias_value":"VSO5PHSBTYPD","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VSO5PHSBTYPDAYOA","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VSO5PHSB","created_at":"2026-05-18T12:30:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:VSO5PHSBTYPDAYOA2DP7WKO2IP","target":"record","payload":{"canonical_record":{"source":{"id":"1604.01429","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-04-05T21:12:01Z","cross_cats_sorted":[],"title_canon_sha256":"b346c2ffb67c16384b647b59ae03ffaca6269ad3a1cdacaac6a32d56611abb30","abstract_canon_sha256":"4cef5d4ea835d05da4fd79436b432d8039ef1ef8b32b04cb54efc0403a9d6b7b"},"schema_version":"1.0"},"canonical_sha256":"ac9dd79e419e1e3061c0d0dffb29da43f739ca35c122da9339611705d8872af3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:09.956234Z","signature_b64":"tVvAZXgxIeeDR7PToMgrmN6Nse8jQwC6RTspAKIF0CuQVTdzBEeRxMDngMDdCzLc/9aZ7V5Vrolrb3DzOgQQAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac9dd79e419e1e3061c0d0dffb29da43f739ca35c122da9339611705d8872af3","last_reissued_at":"2026-05-18T00:18:09.955728Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:09.955728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.01429","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:18:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mo5Q0p4Wrq1YCm58eHXP0wTOp80KZmbUclIkECCK57Sx7jKVjxNFx2PrrhyRFgMNlXAKYAf/LANrBcgwLS94CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T11:31:50.549083Z"},"content_sha256":"3837dd6fd9b7bccc6779ac01034e73c4cba06eb8da2ef0c0ee050540d3182c3b","schema_version":"1.0","event_id":"sha256:3837dd6fd9b7bccc6779ac01034e73c4cba06eb8da2ef0c0ee050540d3182c3b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:VSO5PHSBTYPDAYOA2DP7WKO2IP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Price of Differential Privacy for Low-Rank Factorization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Jalaj Upadhyay","submitted_at":"2016-04-05T21:12:01Z","abstract_excerpt":"In this paper, we study what price one has to pay to release {\\em differentially private low-rank factorization} of a matrix. We consider various settings that are close to the real world applications of low-rank factorization: (i) the manner in which matrices are updated (row by row or in an arbitrary manner), (ii) whether matrices are distributed or not, and (iii) how the output is produced (once at the end of all updates, also known as {\\em one-shot algorithms} or continually). Even though these settings are well studied without privacy, surprisingly, there are no private algorithm for thes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01429","kind":"arxiv","version":5},"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":"2026-05-18T00:18:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1kIqZhctHTUg0+pjUw9NgKEbWE9UyxsPjcu60lT6V7kqyR453magE6jCxKJAzDwVGa118FjZ4F9yg9Lq17K5Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T11:31:50.549449Z"},"content_sha256":"1753aa10ed0c86c8c28ba7d2b1a7eff2c77dc0011cd55daf983babcd93c0e890","schema_version":"1.0","event_id":"sha256:1753aa10ed0c86c8c28ba7d2b1a7eff2c77dc0011cd55daf983babcd93c0e890"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VSO5PHSBTYPDAYOA2DP7WKO2IP/bundle.json","state_url":"https://pith.science/pith/VSO5PHSBTYPDAYOA2DP7WKO2IP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VSO5PHSBTYPDAYOA2DP7WKO2IP/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":"2026-06-20T11:31:50Z","links":{"resolver":"https://pith.science/pith/VSO5PHSBTYPDAYOA2DP7WKO2IP","bundle":"https://pith.science/pith/VSO5PHSBTYPDAYOA2DP7WKO2IP/bundle.json","state":"https://pith.science/pith/VSO5PHSBTYPDAYOA2DP7WKO2IP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VSO5PHSBTYPDAYOA2DP7WKO2IP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VSO5PHSBTYPDAYOA2DP7WKO2IP","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":"4cef5d4ea835d05da4fd79436b432d8039ef1ef8b32b04cb54efc0403a9d6b7b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-04-05T21:12:01Z","title_canon_sha256":"b346c2ffb67c16384b647b59ae03ffaca6269ad3a1cdacaac6a32d56611abb30"},"schema_version":"1.0","source":{"id":"1604.01429","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.01429","created_at":"2026-05-18T00:18:09Z"},{"alias_kind":"arxiv_version","alias_value":"1604.01429v5","created_at":"2026-05-18T00:18:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.01429","created_at":"2026-05-18T00:18:09Z"},{"alias_kind":"pith_short_12","alias_value":"VSO5PHSBTYPD","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VSO5PHSBTYPDAYOA","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VSO5PHSB","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:1753aa10ed0c86c8c28ba7d2b1a7eff2c77dc0011cd55daf983babcd93c0e890","target":"graph","created_at":"2026-05-18T00:18:09Z","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":"In this paper, we study what price one has to pay to release {\\em differentially private low-rank factorization} of a matrix. We consider various settings that are close to the real world applications of low-rank factorization: (i) the manner in which matrices are updated (row by row or in an arbitrary manner), (ii) whether matrices are distributed or not, and (iii) how the output is produced (once at the end of all updates, also known as {\\em one-shot algorithms} or continually). Even though these settings are well studied without privacy, surprisingly, there are no private algorithm for thes","authors_text":"Jalaj Upadhyay","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-04-05T21:12:01Z","title":"The Price of Differential Privacy for Low-Rank Factorization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01429","kind":"arxiv","version":5},"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":"sha256:3837dd6fd9b7bccc6779ac01034e73c4cba06eb8da2ef0c0ee050540d3182c3b","target":"record","created_at":"2026-05-18T00:18:09Z","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":"4cef5d4ea835d05da4fd79436b432d8039ef1ef8b32b04cb54efc0403a9d6b7b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-04-05T21:12:01Z","title_canon_sha256":"b346c2ffb67c16384b647b59ae03ffaca6269ad3a1cdacaac6a32d56611abb30"},"schema_version":"1.0","source":{"id":"1604.01429","kind":"arxiv","version":5}},"canonical_sha256":"ac9dd79e419e1e3061c0d0dffb29da43f739ca35c122da9339611705d8872af3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac9dd79e419e1e3061c0d0dffb29da43f739ca35c122da9339611705d8872af3","first_computed_at":"2026-05-18T00:18:09.955728Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:09.955728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tVvAZXgxIeeDR7PToMgrmN6Nse8jQwC6RTspAKIF0CuQVTdzBEeRxMDngMDdCzLc/9aZ7V5Vrolrb3DzOgQQAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:09.956234Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.01429","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3837dd6fd9b7bccc6779ac01034e73c4cba06eb8da2ef0c0ee050540d3182c3b","sha256:1753aa10ed0c86c8c28ba7d2b1a7eff2c77dc0011cd55daf983babcd93c0e890"],"state_sha256":"8fb5d02587188eba300a8bab9a25095ccee6c0505ba51af965d666bcc3e181ed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oaqT5WLmx91FVbtoNLdTj7eIKXCXzJpk8Gs1lNB5a+rsD/NY6fwHuKk3HZ/OzvZ+gRq3QWaIVIYMjnq02SjJBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T11:31:50.551447Z","bundle_sha256":"6f52708474f8cc63a50bfa1fab43c65c52d7da403cdb022a5379e59e1ea8239d"}}