{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:3C2YLOVQRVYYBZHKKEPUQFJCFR","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":"e6881f531ba1f2b54d18784a15768099da305dc9831b5abaa85205ed7fe116c6","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-06-11T04:22:13Z","title_canon_sha256":"6e22b124bfd016be4ea9a049bfcb7bd340441a857f78277d8ba8261aa817f01e"},"schema_version":"1.0","source":{"id":"1006.2195","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.2195","created_at":"2026-05-18T02:06:54Z"},{"alias_kind":"arxiv_version","alias_value":"1006.2195v1","created_at":"2026-05-18T02:06:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.2195","created_at":"2026-05-18T02:06:54Z"},{"alias_kind":"pith_short_12","alias_value":"3C2YLOVQRVYY","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3C2YLOVQRVYYBZHK","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3C2YLOVQ","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:91fa99a58da856d3249826b7373d6d9acb1473a54cc997636bd70516e2c6b9a3","target":"graph","created_at":"2026-05-18T02:06:54Z","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":"We describe a new algorithm, termed subspace evolution and transfer (SET), for solving low-rank matrix completion problems. The algorithm takes as its input a subset of entries of a low-rank matrix, and outputs one low-rank matrix consistent with the given observations. The completion task is accomplished by searching for a column space on the Grassmann manifold that matches the incomplete observations. The SET algorithm consists of two parts -- subspace evolution and subspace transfer. In the evolution part, we use a gradient descent method on the Grassmann manifold to refine our estimate of ","authors_text":"Ely Kerman, Olgica Milenkovic, Wei Dai","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-06-11T04:22:13Z","title":"Subspace Evolution and Transfer (SET) for Low-Rank Matrix Completion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.2195","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:a8d30f2adcd2158e5ab465a552bb2a40ebd37b5f97fd267918c22c3f9f5e57a6","target":"record","created_at":"2026-05-18T02:06:54Z","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":"e6881f531ba1f2b54d18784a15768099da305dc9831b5abaa85205ed7fe116c6","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-06-11T04:22:13Z","title_canon_sha256":"6e22b124bfd016be4ea9a049bfcb7bd340441a857f78277d8ba8261aa817f01e"},"schema_version":"1.0","source":{"id":"1006.2195","kind":"arxiv","version":1}},"canonical_sha256":"d8b585bab08d7180e4ea511f4815222c69f1242948659972a3d59864ec1c86ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8b585bab08d7180e4ea511f4815222c69f1242948659972a3d59864ec1c86ee","first_computed_at":"2026-05-18T02:06:54.772388Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:06:54.772388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+Cssq/tlneY4R9idQAh+UzOgKgeH+9mO+9jLvDUS1nje+dZ30qB25Hns/KAxq60G3aI3NeY9yxDnJyvm52twCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:06:54.773215Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.2195","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8d30f2adcd2158e5ab465a552bb2a40ebd37b5f97fd267918c22c3f9f5e57a6","sha256:91fa99a58da856d3249826b7373d6d9acb1473a54cc997636bd70516e2c6b9a3"],"state_sha256":"a320eb32fbcd2cf96e52ddee74f521cc3b2fed080f483c24abe55cdffc908db9"}