{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:UYCCZJMOULE6BRHKXHJGVJ47AN","short_pith_number":"pith:UYCCZJMO","canonical_record":{"source":{"id":"1611.08954","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-28T01:57:53Z","cross_cats_sorted":["cs.CR"],"title_canon_sha256":"cc1f65ea574ba65b0bacb8fac8db469ae2122a8ee9f918f83ddc0380dab3fe4a","abstract_canon_sha256":"ccaf187166a9c46754e800264b77be898e9395d03390a001913ff5b234149ae3"},"schema_version":"1.0"},"canonical_sha256":"a6042ca58ea2c9e0c4eab9d26aa79f035c97c44f7e2f0f4272d554be26037354","source":{"kind":"arxiv","id":"1611.08954","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.08954","created_at":"2026-05-18T00:56:29Z"},{"alias_kind":"arxiv_version","alias_value":"1611.08954v1","created_at":"2026-05-18T00:56:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08954","created_at":"2026-05-18T00:56:29Z"},{"alias_kind":"pith_short_12","alias_value":"UYCCZJMOULE6","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UYCCZJMOULE6BRHK","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UYCCZJMO","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:UYCCZJMOULE6BRHKXHJGVJ47AN","target":"record","payload":{"canonical_record":{"source":{"id":"1611.08954","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-28T01:57:53Z","cross_cats_sorted":["cs.CR"],"title_canon_sha256":"cc1f65ea574ba65b0bacb8fac8db469ae2122a8ee9f918f83ddc0380dab3fe4a","abstract_canon_sha256":"ccaf187166a9c46754e800264b77be898e9395d03390a001913ff5b234149ae3"},"schema_version":"1.0"},"canonical_sha256":"a6042ca58ea2c9e0c4eab9d26aa79f035c97c44f7e2f0f4272d554be26037354","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:29.755311Z","signature_b64":"dYWEK6Y9khKM1y1DLsNGOKl7m8ppIVAabsYPIQ0SSTiSRpmKcCLz+yZwHmcVZvWTuHdfMdYqKXOGBZoaF6MoBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6042ca58ea2c9e0c4eab9d26aa79f035c97c44f7e2f0f4272d554be26037354","last_reissued_at":"2026-05-18T00:56:29.754642Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:29.754642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.08954","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":"2026-05-18T00:56:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b70YLLxHaNKEDJ7SrHTGyNQEL48RYcTZ1NBMSMxPFqX0iF4IOFD//o5Q9Mv4sD5BOWPojP2fmqU3ctFNWshSBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:52:37.626595Z"},"content_sha256":"bcfe06b6e0ed8fbf8be2e7df4f2bd4609705cbfcff0badbc13e1ae0ba371808d","schema_version":"1.0","event_id":"sha256:bcfe06b6e0ed8fbf8be2e7df4f2bd4609705cbfcff0badbc13e1ae0ba371808d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:UYCCZJMOULE6BRHKXHJGVJ47AN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Low-Space Differentially Private Low-rank Factorization in the Spectral Norm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR"],"primary_cat":"cs.DS","authors_text":"Jalaj Upadhyay","submitted_at":"2016-11-28T01:57:53Z","abstract_excerpt":"Low-rank factorization is used in many areas of computer science where one performs spectral analysis on large sensitive data stored in the form of matrices. In this paper, we study differentially private low-rank factorization of a matrix with respect to the spectral norm in the turnstile update model. In this problem, given an input matrix $\\mathbf{A} \\in \\mathbb{R}^{m \\times n}$ updated in the turnstile manner and a target rank $k$, the goal is to find two rank-$k$ orthogonal matrices $\\mathbf{U}_k \\in \\mathbb{R}^{m \\times k}$ and $\\mathbf{V}_k \\in \\mathbb{R}^{n \\times k}$, and one positive"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08954","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":""},"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":"2026-05-18T00:56:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8QRV2i+7q/eTGI4AT1QyIVWhXGu55LRPJK6dYn+4SPu7VQhG7FDO9Zxx/R6nsMP3jhSbKjqDWehFLkORLhX2AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:52:37.626936Z"},"content_sha256":"89a4e746af478d68a8fdea89efd666b6939d5dd0fde5c6cca03436312138183d","schema_version":"1.0","event_id":"sha256:89a4e746af478d68a8fdea89efd666b6939d5dd0fde5c6cca03436312138183d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UYCCZJMOULE6BRHKXHJGVJ47AN/bundle.json","state_url":"https://pith.science/pith/UYCCZJMOULE6BRHKXHJGVJ47AN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UYCCZJMOULE6BRHKXHJGVJ47AN/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":"2026-06-20T07:52:37Z","links":{"resolver":"https://pith.science/pith/UYCCZJMOULE6BRHKXHJGVJ47AN","bundle":"https://pith.science/pith/UYCCZJMOULE6BRHKXHJGVJ47AN/bundle.json","state":"https://pith.science/pith/UYCCZJMOULE6BRHKXHJGVJ47AN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UYCCZJMOULE6BRHKXHJGVJ47AN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UYCCZJMOULE6BRHKXHJGVJ47AN","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":"ccaf187166a9c46754e800264b77be898e9395d03390a001913ff5b234149ae3","cross_cats_sorted":["cs.CR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-28T01:57:53Z","title_canon_sha256":"cc1f65ea574ba65b0bacb8fac8db469ae2122a8ee9f918f83ddc0380dab3fe4a"},"schema_version":"1.0","source":{"id":"1611.08954","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.08954","created_at":"2026-05-18T00:56:29Z"},{"alias_kind":"arxiv_version","alias_value":"1611.08954v1","created_at":"2026-05-18T00:56:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.08954","created_at":"2026-05-18T00:56:29Z"},{"alias_kind":"pith_short_12","alias_value":"UYCCZJMOULE6","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UYCCZJMOULE6BRHK","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UYCCZJMO","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:89a4e746af478d68a8fdea89efd666b6939d5dd0fde5c6cca03436312138183d","target":"graph","created_at":"2026-05-18T00:56:29Z","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":"Low-rank factorization is used in many areas of computer science where one performs spectral analysis on large sensitive data stored in the form of matrices. In this paper, we study differentially private low-rank factorization of a matrix with respect to the spectral norm in the turnstile update model. In this problem, given an input matrix $\\mathbf{A} \\in \\mathbb{R}^{m \\times n}$ updated in the turnstile manner and a target rank $k$, the goal is to find two rank-$k$ orthogonal matrices $\\mathbf{U}_k \\in \\mathbb{R}^{m \\times k}$ and $\\mathbf{V}_k \\in \\mathbb{R}^{n \\times k}$, and one positive","authors_text":"Jalaj Upadhyay","cross_cats":["cs.CR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-28T01:57:53Z","title":"On Low-Space Differentially Private Low-rank Factorization in the Spectral Norm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.08954","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:bcfe06b6e0ed8fbf8be2e7df4f2bd4609705cbfcff0badbc13e1ae0ba371808d","target":"record","created_at":"2026-05-18T00:56:29Z","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":"ccaf187166a9c46754e800264b77be898e9395d03390a001913ff5b234149ae3","cross_cats_sorted":["cs.CR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-11-28T01:57:53Z","title_canon_sha256":"cc1f65ea574ba65b0bacb8fac8db469ae2122a8ee9f918f83ddc0380dab3fe4a"},"schema_version":"1.0","source":{"id":"1611.08954","kind":"arxiv","version":1}},"canonical_sha256":"a6042ca58ea2c9e0c4eab9d26aa79f035c97c44f7e2f0f4272d554be26037354","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6042ca58ea2c9e0c4eab9d26aa79f035c97c44f7e2f0f4272d554be26037354","first_computed_at":"2026-05-18T00:56:29.754642Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:29.754642Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dYWEK6Y9khKM1y1DLsNGOKl7m8ppIVAabsYPIQ0SSTiSRpmKcCLz+yZwHmcVZvWTuHdfMdYqKXOGBZoaF6MoBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:29.755311Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.08954","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bcfe06b6e0ed8fbf8be2e7df4f2bd4609705cbfcff0badbc13e1ae0ba371808d","sha256:89a4e746af478d68a8fdea89efd666b6939d5dd0fde5c6cca03436312138183d"],"state_sha256":"eb21150b0ca9ff3577f9f731f3dcd135b0b535ca5b81c1403d6f8b0bee0fc607"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9mW5tkBhdkGQaNGfFqRefF1TGAuDa3nyym8tYspnzl4T3CMDLQSM77+qekUtsKUmIvpfauqjUn7MkUaUTUYCCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T07:52:37.628776Z","bundle_sha256":"29b260b3f19714ce08aad400ed4dc9f24121e1c554e3f41c876466d7e4a68e10"}}