{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BWSG3LQ3EH3HDKJVROMZCREJG7","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":"3570bf17e9c154df795e7d29b80c4f2991bf7d377028c3fe4ac3391e2a1889c8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-10-31T16:09:37Z","title_canon_sha256":"5a84e07f57d932956f03d31cfbb64fccf851ab09d442a7a3c275eb259110da01"},"schema_version":"1.0","source":{"id":"1610.09993","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.09993","created_at":"2026-05-18T01:00:46Z"},{"alias_kind":"arxiv_version","alias_value":"1610.09993v1","created_at":"2026-05-18T01:00:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.09993","created_at":"2026-05-18T01:00:46Z"},{"alias_kind":"pith_short_12","alias_value":"BWSG3LQ3EH3H","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"BWSG3LQ3EH3HDKJV","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"BWSG3LQ3","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:58bb777f940802fdbc009946e27135ddfa02937c0a1733e7c5a753fee8a59cb1","target":"graph","created_at":"2026-05-18T01:00:46Z","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 study the closure of the projection of the (nonconvex) cone of rank restricted positive semidefinite matrices onto subsets of the matrix entries. This defines the feasible sets for semidefinite completion problems with restrictions on the ranks. Applications include conditions for low-rank completions using the nuclear norm heuristic.","authors_text":"Henry Wolkowicz, Ian Davidson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-10-31T16:09:37Z","title":"Rank Restricted Semidefinite Matrices and Image Closedness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09993","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:cd02f033d5af6e364d4066f1acb948368e241737f0f978576257a1df0985bdd6","target":"record","created_at":"2026-05-18T01:00:46Z","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":"3570bf17e9c154df795e7d29b80c4f2991bf7d377028c3fe4ac3391e2a1889c8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-10-31T16:09:37Z","title_canon_sha256":"5a84e07f57d932956f03d31cfbb64fccf851ab09d442a7a3c275eb259110da01"},"schema_version":"1.0","source":{"id":"1610.09993","kind":"arxiv","version":1}},"canonical_sha256":"0da46dae1b21f671a9358b9991448937d5ca18c1d16bc19726d39cb8a71ceb95","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0da46dae1b21f671a9358b9991448937d5ca18c1d16bc19726d39cb8a71ceb95","first_computed_at":"2026-05-18T01:00:46.775865Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:46.775865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7kBOs2k3ALdMUUFf+yS6eMbg5KxKhtyp/oxIFHbdDy/UbEea9kVXW0RveUXJzUCx9Bxw9GpG+Rmn48y71ymZAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:46.776357Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.09993","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd02f033d5af6e364d4066f1acb948368e241737f0f978576257a1df0985bdd6","sha256:58bb777f940802fdbc009946e27135ddfa02937c0a1733e7c5a753fee8a59cb1"],"state_sha256":"c99890f60501223d504f7dc1e6cf591d6ffeebadcb6c70978468fa44af0568b4"}