{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:NVMJXTFXGVLYHOSDWQFGPTBOYS","short_pith_number":"pith:NVMJXTFX","canonical_record":{"source":{"id":"0906.2027","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2009-06-11T00:22:58Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"a0c3f2fa189b189b710861d79e4fa161a38b75a9012e7819db8de5439be0464c","abstract_canon_sha256":"351cc02ef7341f28fac41054ddc5c8a2719ef3ec4606936b7dc0d0dd28dbe28c"},"schema_version":"1.0"},"canonical_sha256":"6d589bccb7355783ba43b40a67cc2ec4a0600789217bbf9db86cf52ad257141c","source":{"kind":"arxiv","id":"0906.2027","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.2027","created_at":"2026-05-18T03:58:25Z"},{"alias_kind":"arxiv_version","alias_value":"0906.2027v2","created_at":"2026-05-18T03:58:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.2027","created_at":"2026-05-18T03:58:25Z"},{"alias_kind":"pith_short_12","alias_value":"NVMJXTFXGVLY","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"NVMJXTFXGVLYHOSD","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"NVMJXTFX","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:NVMJXTFXGVLYHOSDWQFGPTBOYS","target":"record","payload":{"canonical_record":{"source":{"id":"0906.2027","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2009-06-11T00:22:58Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"a0c3f2fa189b189b710861d79e4fa161a38b75a9012e7819db8de5439be0464c","abstract_canon_sha256":"351cc02ef7341f28fac41054ddc5c8a2719ef3ec4606936b7dc0d0dd28dbe28c"},"schema_version":"1.0"},"canonical_sha256":"6d589bccb7355783ba43b40a67cc2ec4a0600789217bbf9db86cf52ad257141c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:25.105222Z","signature_b64":"2qQtbvzYTdIIilOnKNWwNx4Uf70ZtIHIZhvFGUboQ8CdwUAcAYcWFUyXU4za3jFG8WyW44J6wCiuHTg/F7tHBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d589bccb7355783ba43b40a67cc2ec4a0600789217bbf9db86cf52ad257141c","last_reissued_at":"2026-05-18T03:58:25.104634Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:25.104634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0906.2027","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":"2026-05-18T03:58:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xIysApPX0iRCr4l3RdVKUmEIicQYUfz1NmcMYBBBy86bDgKrTk6uFqwcsB8dqtecMdzAcV1tOLGNYMBDyyzeDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T03:50:54.493129Z"},"content_sha256":"831e8f386002f55a6062e1c1ef8e85e52cf20db8a66c93826a6cfa3f43e411a4","schema_version":"1.0","event_id":"sha256:831e8f386002f55a6062e1c1ef8e85e52cf20db8a66c93826a6cfa3f43e411a4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:NVMJXTFXGVLYHOSDWQFGPTBOYS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Matrix Completion from Noisy Entries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Andrea Montanari, Raghunandan H. Keshavan, Sewoong Oh","submitted_at":"2009-06-11T00:22:58Z","abstract_excerpt":"Given a matrix M of low-rank, we consider the problem of reconstructing it from noisy observations of a small, random subset of its entries. The problem arises in a variety of applications, from collaborative filtering (the `Netflix problem') to structure-from-motion and positioning. We study a low complexity algorithm introduced by Keshavan et al.(2009), based on a combination of spectral techniques and manifold optimization, that we call here OptSpace. We prove performance guarantees that are order-optimal in a number of circumstances."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.2027","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":"2026-05-18T03:58:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8LQXM2moUbi7Oyo/N5bkgyLU8gc7DpaVqCv1VfPJOPRlQV2yGxNIvL6U+5ws9yeXUiETUc7ZJqH4SF6Ig+4wBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T03:50:54.493795Z"},"content_sha256":"62513e41f540f8a04c4a79cdd62d051c0b03fb9b8582c5279d19c4455cc8cf45","schema_version":"1.0","event_id":"sha256:62513e41f540f8a04c4a79cdd62d051c0b03fb9b8582c5279d19c4455cc8cf45"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NVMJXTFXGVLYHOSDWQFGPTBOYS/bundle.json","state_url":"https://pith.science/pith/NVMJXTFXGVLYHOSDWQFGPTBOYS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NVMJXTFXGVLYHOSDWQFGPTBOYS/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":"2026-06-10T03:50:54Z","links":{"resolver":"https://pith.science/pith/NVMJXTFXGVLYHOSDWQFGPTBOYS","bundle":"https://pith.science/pith/NVMJXTFXGVLYHOSDWQFGPTBOYS/bundle.json","state":"https://pith.science/pith/NVMJXTFXGVLYHOSDWQFGPTBOYS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NVMJXTFXGVLYHOSDWQFGPTBOYS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:NVMJXTFXGVLYHOSDWQFGPTBOYS","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":"351cc02ef7341f28fac41054ddc5c8a2719ef3ec4606936b7dc0d0dd28dbe28c","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2009-06-11T00:22:58Z","title_canon_sha256":"a0c3f2fa189b189b710861d79e4fa161a38b75a9012e7819db8de5439be0464c"},"schema_version":"1.0","source":{"id":"0906.2027","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.2027","created_at":"2026-05-18T03:58:25Z"},{"alias_kind":"arxiv_version","alias_value":"0906.2027v2","created_at":"2026-05-18T03:58:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.2027","created_at":"2026-05-18T03:58:25Z"},{"alias_kind":"pith_short_12","alias_value":"NVMJXTFXGVLY","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"NVMJXTFXGVLYHOSD","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"NVMJXTFX","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:62513e41f540f8a04c4a79cdd62d051c0b03fb9b8582c5279d19c4455cc8cf45","target":"graph","created_at":"2026-05-18T03:58:25Z","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":"Given a matrix M of low-rank, we consider the problem of reconstructing it from noisy observations of a small, random subset of its entries. The problem arises in a variety of applications, from collaborative filtering (the `Netflix problem') to structure-from-motion and positioning. We study a low complexity algorithm introduced by Keshavan et al.(2009), based on a combination of spectral techniques and manifold optimization, that we call here OptSpace. We prove performance guarantees that are order-optimal in a number of circumstances.","authors_text":"Andrea Montanari, Raghunandan H. Keshavan, Sewoong Oh","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2009-06-11T00:22:58Z","title":"Matrix Completion from Noisy Entries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.2027","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":"sha256:831e8f386002f55a6062e1c1ef8e85e52cf20db8a66c93826a6cfa3f43e411a4","target":"record","created_at":"2026-05-18T03:58:25Z","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":"351cc02ef7341f28fac41054ddc5c8a2719ef3ec4606936b7dc0d0dd28dbe28c","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2009-06-11T00:22:58Z","title_canon_sha256":"a0c3f2fa189b189b710861d79e4fa161a38b75a9012e7819db8de5439be0464c"},"schema_version":"1.0","source":{"id":"0906.2027","kind":"arxiv","version":2}},"canonical_sha256":"6d589bccb7355783ba43b40a67cc2ec4a0600789217bbf9db86cf52ad257141c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d589bccb7355783ba43b40a67cc2ec4a0600789217bbf9db86cf52ad257141c","first_computed_at":"2026-05-18T03:58:25.104634Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:25.104634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2qQtbvzYTdIIilOnKNWwNx4Uf70ZtIHIZhvFGUboQ8CdwUAcAYcWFUyXU4za3jFG8WyW44J6wCiuHTg/F7tHBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:25.105222Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.2027","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:831e8f386002f55a6062e1c1ef8e85e52cf20db8a66c93826a6cfa3f43e411a4","sha256:62513e41f540f8a04c4a79cdd62d051c0b03fb9b8582c5279d19c4455cc8cf45"],"state_sha256":"0df602e11c5ac5f6fcfa1d51aaaf0f34857db0435ae9b88bb07133336f4893be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lWNhSeWb0HlN08sDqgLYO2b3yFLGYszuesYPJ5NpQPqGOVbSxjMJbkYRHwqNz+lzcWIuIZkSlQUOUwaBkGBCCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T03:50:54.497659Z","bundle_sha256":"5d5f79c96844b2406f8d659a0a013cbe2e0411aea03b60f4f9f841e5e2ddeb37"}}