{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:TDJMRZQUXH4Q33TM6ENTVSEUR6","short_pith_number":"pith:TDJMRZQU","canonical_record":{"source":{"id":"1011.1518","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2010-11-05T21:43:02Z","cross_cats_sorted":["cs.LG","math.NA"],"title_canon_sha256":"176866b13a6a51b353bbe0086bd5994bf66d10b6b6d2f2ecfd1cb8182d182602","abstract_canon_sha256":"7e0851b9b6b4adae534ce5173110d38721afec50f980ce43aa2eb4ae40a8f78e"},"schema_version":"1.0"},"canonical_sha256":"98d2c8e614b9f90dee6cf11b3ac8948fa5dc0f4c32d6bbbff8a21704c7442e57","source":{"kind":"arxiv","id":"1011.1518","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.1518","created_at":"2026-05-18T04:34:08Z"},{"alias_kind":"arxiv_version","alias_value":"1011.1518v3","created_at":"2026-05-18T04:34:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1518","created_at":"2026-05-18T04:34:08Z"},{"alias_kind":"pith_short_12","alias_value":"TDJMRZQUXH4Q","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"TDJMRZQUXH4Q33TM","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"TDJMRZQU","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:TDJMRZQUXH4Q33TM6ENTVSEUR6","target":"record","payload":{"canonical_record":{"source":{"id":"1011.1518","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2010-11-05T21:43:02Z","cross_cats_sorted":["cs.LG","math.NA"],"title_canon_sha256":"176866b13a6a51b353bbe0086bd5994bf66d10b6b6d2f2ecfd1cb8182d182602","abstract_canon_sha256":"7e0851b9b6b4adae534ce5173110d38721afec50f980ce43aa2eb4ae40a8f78e"},"schema_version":"1.0"},"canonical_sha256":"98d2c8e614b9f90dee6cf11b3ac8948fa5dc0f4c32d6bbbff8a21704c7442e57","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:08.635709Z","signature_b64":"fr2bvKzXgNG9clmPDctn9zu49RS9zLnf+8zEj7/Ni3gjGhViTT3luAihT1WQ4r8V2osx/Yt0Qgnhf8ozbMTHBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98d2c8e614b9f90dee6cf11b3ac8948fa5dc0f4c32d6bbbff8a21704c7442e57","last_reissued_at":"2026-05-18T04:34:08.635121Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:08.635121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.1518","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:34:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GEGxbg41YJ/d7Xt6y3Q4WUnBQEDe6r+3aM2eBEKs/BSzPsxFZha4SXaA34hw4mReFIxJbspyyBRkRkitCDzDCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:31:15.192413Z"},"content_sha256":"2826954d8b716a56cee1fa25f2eb3f6b40fa02221ac5e1c1a602f773f8970183","schema_version":"1.0","event_id":"sha256:2826954d8b716a56cee1fa25f2eb3f6b40fa02221ac5e1c1a602f773f8970183"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:TDJMRZQUXH4Q33TM6ENTVSEUR6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Robust Matrix Decomposition with Outliers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.NA"],"primary_cat":"stat.ML","authors_text":"Daniel Hsu, Sham M. Kakade, Tong Zhang","submitted_at":"2010-11-05T21:43:02Z","abstract_excerpt":"Suppose a given observation matrix can be decomposed as the sum of a low-rank matrix and a sparse matrix (outliers), and the goal is to recover these individual components from the observed sum. Such additive decompositions have applications in a variety of numerical problems including system identification, latent variable graphical modeling, and principal components analysis. We study conditions under which recovering such a decomposition is possible via a combination of $\\ell_1$ norm and trace norm minimization. We are specifically interested in the question of how many outliers are allowed"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1518","kind":"arxiv","version":3},"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":"2026-05-18T04:34:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bbxhKcTHRLoWWgACmtUGEW4ScJ909FNd9rPAXPal9WHciP8rGRAfeky9EJMI0kxqVzbyifhm7urNMQLt+DeAAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:31:15.192902Z"},"content_sha256":"4fd5fccbdb278b42892e8afcbead224caf27e2e45168ab6a9235612636aa78fa","schema_version":"1.0","event_id":"sha256:4fd5fccbdb278b42892e8afcbead224caf27e2e45168ab6a9235612636aa78fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TDJMRZQUXH4Q33TM6ENTVSEUR6/bundle.json","state_url":"https://pith.science/pith/TDJMRZQUXH4Q33TM6ENTVSEUR6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TDJMRZQUXH4Q33TM6ENTVSEUR6/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":"2026-05-30T15:31:15Z","links":{"resolver":"https://pith.science/pith/TDJMRZQUXH4Q33TM6ENTVSEUR6","bundle":"https://pith.science/pith/TDJMRZQUXH4Q33TM6ENTVSEUR6/bundle.json","state":"https://pith.science/pith/TDJMRZQUXH4Q33TM6ENTVSEUR6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TDJMRZQUXH4Q33TM6ENTVSEUR6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:TDJMRZQUXH4Q33TM6ENTVSEUR6","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":"7e0851b9b6b4adae534ce5173110d38721afec50f980ce43aa2eb4ae40a8f78e","cross_cats_sorted":["cs.LG","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2010-11-05T21:43:02Z","title_canon_sha256":"176866b13a6a51b353bbe0086bd5994bf66d10b6b6d2f2ecfd1cb8182d182602"},"schema_version":"1.0","source":{"id":"1011.1518","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.1518","created_at":"2026-05-18T04:34:08Z"},{"alias_kind":"arxiv_version","alias_value":"1011.1518v3","created_at":"2026-05-18T04:34:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1518","created_at":"2026-05-18T04:34:08Z"},{"alias_kind":"pith_short_12","alias_value":"TDJMRZQUXH4Q","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"TDJMRZQUXH4Q33TM","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"TDJMRZQU","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:4fd5fccbdb278b42892e8afcbead224caf27e2e45168ab6a9235612636aa78fa","target":"graph","created_at":"2026-05-18T04:34:08Z","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":"Suppose a given observation matrix can be decomposed as the sum of a low-rank matrix and a sparse matrix (outliers), and the goal is to recover these individual components from the observed sum. Such additive decompositions have applications in a variety of numerical problems including system identification, latent variable graphical modeling, and principal components analysis. We study conditions under which recovering such a decomposition is possible via a combination of $\\ell_1$ norm and trace norm minimization. We are specifically interested in the question of how many outliers are allowed","authors_text":"Daniel Hsu, Sham M. Kakade, Tong Zhang","cross_cats":["cs.LG","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2010-11-05T21:43:02Z","title":"Robust Matrix Decomposition with Outliers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1518","kind":"arxiv","version":3},"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":"sha256:2826954d8b716a56cee1fa25f2eb3f6b40fa02221ac5e1c1a602f773f8970183","target":"record","created_at":"2026-05-18T04:34:08Z","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":"7e0851b9b6b4adae534ce5173110d38721afec50f980ce43aa2eb4ae40a8f78e","cross_cats_sorted":["cs.LG","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2010-11-05T21:43:02Z","title_canon_sha256":"176866b13a6a51b353bbe0086bd5994bf66d10b6b6d2f2ecfd1cb8182d182602"},"schema_version":"1.0","source":{"id":"1011.1518","kind":"arxiv","version":3}},"canonical_sha256":"98d2c8e614b9f90dee6cf11b3ac8948fa5dc0f4c32d6bbbff8a21704c7442e57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98d2c8e614b9f90dee6cf11b3ac8948fa5dc0f4c32d6bbbff8a21704c7442e57","first_computed_at":"2026-05-18T04:34:08.635121Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:08.635121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fr2bvKzXgNG9clmPDctn9zu49RS9zLnf+8zEj7/Ni3gjGhViTT3luAihT1WQ4r8V2osx/Yt0Qgnhf8ozbMTHBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:08.635709Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.1518","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2826954d8b716a56cee1fa25f2eb3f6b40fa02221ac5e1c1a602f773f8970183","sha256:4fd5fccbdb278b42892e8afcbead224caf27e2e45168ab6a9235612636aa78fa"],"state_sha256":"506740c4c9755ddfca25dccc1c3e95bfe43e917e4cb359340b6a3ca21a39773b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3KktaPAtpjYgyCxM1lKeQB3bsVQy445Vp8i6G+s9ZDOIoulujXolx3jIyTtrwKIesJXBuwlHDS+hDOrvHDfYDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T15:31:15.196399Z","bundle_sha256":"7aaac68f8f8c6edf09f380bef45aeccabeb73474fe545dd8caa909ef094ac509"}}