{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:DDNL74XWGCJMYH2432D6S4YZKF","short_pith_number":"pith:DDNL74XW","schema_version":"1.0","canonical_sha256":"18dabff2f63092cc1f5cde87e973195176f0e8c34119c34fb84075508f40b0dd","source":{"kind":"arxiv","id":"1205.2040","version":2},"attestation_state":"computed","paper":{"title":"Forbidden minor characterizations for low-rank optimal solutions to semidefinite programs over the elliptope","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.OC"],"primary_cat":"math.CO","authors_text":"Antonios Varvitsiotis, Marianna Eisenberg-Nagy, Monique Laurent","submitted_at":"2012-05-09T17:20:59Z","abstract_excerpt":"We study a new geometric graph parameter $\\egd(G)$, defined as the smallest integer $r\\ge 1$ for which any partial symmetric matrix which is completable to a correlation matrix and whose entries are specified at the positions of the edges of $G$, can be completed to a matrix in the convex hull of correlation matrices of $\\rank $ at most $r$. This graph parameter is motivated by its relevance to the problem of finding low rank solutions to semidefinite programs over the elliptope, and also by its relevance to the bounded rank Grothendieck constant. Indeed, $\\egd(G)\\le r$ if and only if the rank"},"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":"1205.2040","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-09T17:20:59Z","cross_cats_sorted":["cs.DM","math.OC"],"title_canon_sha256":"a7e0ef21e630203cb92b1924cafa40047185b68393a7e2297e9b7800cd3bfcb3","abstract_canon_sha256":"87aacc8f96dbe826b1b41037db355a55ff16ff3b866d3fe0a468455f897be3f0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:57.501934Z","signature_b64":"+gTrodstT/g63TEuRHfHrOPSIn37u2EWyisqcWJDq1oDFyEodU8zv5Iz1oy8cozO0PFY7wgIzYr97OvBgl/1Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18dabff2f63092cc1f5cde87e973195176f0e8c34119c34fb84075508f40b0dd","last_reissued_at":"2026-05-18T03:02:57.501276Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:57.501276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Forbidden minor characterizations for low-rank optimal solutions to semidefinite programs over the elliptope","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.OC"],"primary_cat":"math.CO","authors_text":"Antonios Varvitsiotis, Marianna Eisenberg-Nagy, Monique Laurent","submitted_at":"2012-05-09T17:20:59Z","abstract_excerpt":"We study a new geometric graph parameter $\\egd(G)$, defined as the smallest integer $r\\ge 1$ for which any partial symmetric matrix which is completable to a correlation matrix and whose entries are specified at the positions of the edges of $G$, can be completed to a matrix in the convex hull of correlation matrices of $\\rank $ at most $r$. This graph parameter is motivated by its relevance to the problem of finding low rank solutions to semidefinite programs over the elliptope, and also by its relevance to the bounded rank Grothendieck constant. Indeed, $\\egd(G)\\le r$ if and only if the rank"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2040","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1205.2040","created_at":"2026-05-18T03:02:57.501382+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.2040v2","created_at":"2026-05-18T03:02:57.501382+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2040","created_at":"2026-05-18T03:02:57.501382+00:00"},{"alias_kind":"pith_short_12","alias_value":"DDNL74XWGCJM","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"DDNL74XWGCJMYH24","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"DDNL74XW","created_at":"2026-05-18T12:27:01.376967+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DDNL74XWGCJMYH2432D6S4YZKF","json":"https://pith.science/pith/DDNL74XWGCJMYH2432D6S4YZKF.json","graph_json":"https://pith.science/api/pith-number/DDNL74XWGCJMYH2432D6S4YZKF/graph.json","events_json":"https://pith.science/api/pith-number/DDNL74XWGCJMYH2432D6S4YZKF/events.json","paper":"https://pith.science/paper/DDNL74XW"},"agent_actions":{"view_html":"https://pith.science/pith/DDNL74XWGCJMYH2432D6S4YZKF","download_json":"https://pith.science/pith/DDNL74XWGCJMYH2432D6S4YZKF.json","view_paper":"https://pith.science/paper/DDNL74XW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.2040&json=true","fetch_graph":"https://pith.science/api/pith-number/DDNL74XWGCJMYH2432D6S4YZKF/graph.json","fetch_events":"https://pith.science/api/pith-number/DDNL74XWGCJMYH2432D6S4YZKF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DDNL74XWGCJMYH2432D6S4YZKF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DDNL74XWGCJMYH2432D6S4YZKF/action/storage_attestation","attest_author":"https://pith.science/pith/DDNL74XWGCJMYH2432D6S4YZKF/action/author_attestation","sign_citation":"https://pith.science/pith/DDNL74XWGCJMYH2432D6S4YZKF/action/citation_signature","submit_replication":"https://pith.science/pith/DDNL74XWGCJMYH2432D6S4YZKF/action/replication_record"}},"created_at":"2026-05-18T03:02:57.501382+00:00","updated_at":"2026-05-18T03:02:57.501382+00:00"}