{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:EYYIZV3ZHZAWYTEH2XKCBLKRGE","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":"0e33a6c327188ea499bb126d5d5be2a31f7de7b2b4c529f2e2706a831b64f517","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-03-18T09:32:06Z","title_canon_sha256":"bfe2f177ebb49d28f7b21a92f67ad5f82b661b84cddf82d794c270bb5815e73f"},"schema_version":"1.0","source":{"id":"1903.07325","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.07325","created_at":"2026-05-17T23:51:01Z"},{"alias_kind":"arxiv_version","alias_value":"1903.07325v1","created_at":"2026-05-17T23:51:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.07325","created_at":"2026-05-17T23:51:01Z"},{"alias_kind":"pith_short_12","alias_value":"EYYIZV3ZHZAW","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"EYYIZV3ZHZAWYTEH","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"EYYIZV3Z","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:e71a8cc7509aba679593dfef5734d44113b1e1e5da44d5a87773bca0827773e6","target":"graph","created_at":"2026-05-17T23:51:01Z","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 equivalence among a nonconvex QOP, its CPP and DNN relaxations under the assumption that the aggregated and correlative sparsity of the data matrices of the CPP relaxation is represented by a block-clique graph $G$. By exploiting the correlative sparsity, we decompose the CPP relaxation problem into a clique-tree structured family of smaller subproblems. Each subproblem is associated with a node of a clique tree of $G$. The optimal value can be obtained by applying an algorithm that we propose for solving the subproblems recursively from leaf nodes to the root node of the clique-t","authors_text":"Kim-Chuan Toh, Masakazu Kojima, Sunyoung Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-03-18T09:32:06Z","title":"Doubly nonnegative relaxations are equivalent to completely positive reformulations of quadratic optimization problems with block-clique graph structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07325","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":"sha256:2595af10557852d919e718d1ea78275d1463abb823addd9ae414965364bdf342","target":"record","created_at":"2026-05-17T23:51:01Z","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":"0e33a6c327188ea499bb126d5d5be2a31f7de7b2b4c529f2e2706a831b64f517","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-03-18T09:32:06Z","title_canon_sha256":"bfe2f177ebb49d28f7b21a92f67ad5f82b661b84cddf82d794c270bb5815e73f"},"schema_version":"1.0","source":{"id":"1903.07325","kind":"arxiv","version":1}},"canonical_sha256":"26308cd7793e416c4c87d5d420ad5131132cc0660cf049dec44c0b9429360f81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26308cd7793e416c4c87d5d420ad5131132cc0660cf049dec44c0b9429360f81","first_computed_at":"2026-05-17T23:51:01.710805Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:01.710805Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tMpmgHo/eKp7eHJ5LlAHhG070C+mZ7ZwxbYCqyNXtdyKmZpsOrXKf8lkSmINlgPTi8vxkTQKSwsrfX/wHVPmDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:01.711277Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.07325","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2595af10557852d919e718d1ea78275d1463abb823addd9ae414965364bdf342","sha256:e71a8cc7509aba679593dfef5734d44113b1e1e5da44d5a87773bca0827773e6"],"state_sha256":"55681cade2521868bdd190c95f039e988695147ccd86f22f8db1fc4c3d12e8ab"}