{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:ULSBTZJHJ2KGGY2IOERYDSIDPB","short_pith_number":"pith:ULSBTZJH","schema_version":"1.0","canonical_sha256":"a2e419e5274e94636348712381c9037856acd5b1651a3025ff5c5917f19fbb26","source":{"kind":"arxiv","id":"0805.4471","version":1},"attestation_state":"computed","paper":{"title":"Exact Matrix Completion via Convex Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Benjamin Recht, Emmanuel J. Candes","submitted_at":"2008-05-29T05:29:56Z","abstract_excerpt":"We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen?\n  We show that one can perfectly recover most low-rank matrices from what appears to be an incomplete set of entries. We prove that if the number m of sampled entries obeys m >= C n^{1.2} r log n for some positive numerical constant C, then with very high probability, most n by n matrices of rank r can be perfectly recovered"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0805.4471","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2008-05-29T05:29:56Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"a82750c6f51beadf51e331d8feb3d4d494c78389fc709b0894807330b965e608","abstract_canon_sha256":"d92c4bf75ecd47fcb6a6741314db36a22a3c9fc90cdd01858bda7a163157b902"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:11:52.167134Z","signature_b64":"JC4eVKGKTnpc5qGi8RU47MEUgFfrYx+FzCL0d++o8TawZT5g317qSux6tmQKdsLsohgUxsevGECg2hKu/7yhDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2e419e5274e94636348712381c9037856acd5b1651a3025ff5c5917f19fbb26","last_reissued_at":"2026-07-04T15:11:52.166680Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:11:52.166680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact Matrix Completion via Convex Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Benjamin Recht, Emmanuel J. Candes","submitted_at":"2008-05-29T05:29:56Z","abstract_excerpt":"We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen?\n  We show that one can perfectly recover most low-rank matrices from what appears to be an incomplete set of entries. We prove that if the number m of sampled entries obeys m >= C n^{1.2} r log n for some positive numerical constant C, then with very high probability, most n by n matrices of rank r can be perfectly recovered"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.4471","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0805.4471/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0805.4471","created_at":"2026-07-04T15:11:52.166773+00:00"},{"alias_kind":"arxiv_version","alias_value":"0805.4471v1","created_at":"2026-07-04T15:11:52.166773+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.4471","created_at":"2026-07-04T15:11:52.166773+00:00"},{"alias_kind":"pith_short_12","alias_value":"ULSBTZJHJ2KG","created_at":"2026-07-04T15:11:52.166773+00:00"},{"alias_kind":"pith_short_16","alias_value":"ULSBTZJHJ2KGGY2I","created_at":"2026-07-04T15:11:52.166773+00:00"},{"alias_kind":"pith_short_8","alias_value":"ULSBTZJH","created_at":"2026-07-04T15:11:52.166773+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.07096","citing_title":"Query-efficient model evaluation using cached responses","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ULSBTZJHJ2KGGY2IOERYDSIDPB","json":"https://pith.science/pith/ULSBTZJHJ2KGGY2IOERYDSIDPB.json","graph_json":"https://pith.science/api/pith-number/ULSBTZJHJ2KGGY2IOERYDSIDPB/graph.json","events_json":"https://pith.science/api/pith-number/ULSBTZJHJ2KGGY2IOERYDSIDPB/events.json","paper":"https://pith.science/paper/ULSBTZJH"},"agent_actions":{"view_html":"https://pith.science/pith/ULSBTZJHJ2KGGY2IOERYDSIDPB","download_json":"https://pith.science/pith/ULSBTZJHJ2KGGY2IOERYDSIDPB.json","view_paper":"https://pith.science/paper/ULSBTZJH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0805.4471&json=true","fetch_graph":"https://pith.science/api/pith-number/ULSBTZJHJ2KGGY2IOERYDSIDPB/graph.json","fetch_events":"https://pith.science/api/pith-number/ULSBTZJHJ2KGGY2IOERYDSIDPB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ULSBTZJHJ2KGGY2IOERYDSIDPB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ULSBTZJHJ2KGGY2IOERYDSIDPB/action/storage_attestation","attest_author":"https://pith.science/pith/ULSBTZJHJ2KGGY2IOERYDSIDPB/action/author_attestation","sign_citation":"https://pith.science/pith/ULSBTZJHJ2KGGY2IOERYDSIDPB/action/citation_signature","submit_replication":"https://pith.science/pith/ULSBTZJHJ2KGGY2IOERYDSIDPB/action/replication_record"}},"created_at":"2026-07-04T15:11:52.166773+00:00","updated_at":"2026-07-04T15:11:52.166773+00:00"}