{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:Z33OAHMTNJROJF3MOSZGAYF2MO","short_pith_number":"pith:Z33OAHMT","schema_version":"1.0","canonical_sha256":"cef6e01d936a62e4976c74b26060ba63a9dc9d12e4060ed78bd7489587644bb2","source":{"kind":"arxiv","id":"1306.0057","version":1},"attestation_state":"computed","paper":{"title":"Decomposition in conic optimization with partially separable structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Lieven Vandenberghe, Martin S. Andersen, Yifan Sun","submitted_at":"2013-06-01T01:26:55Z","abstract_excerpt":"Decomposition techniques for linear programming are difficult to extend to conic optimization problems with general non-polyhedral convex cones because the conic inequalities introduce an additional nonlinear coupling between the variables. However in many applications the convex cones have a partially separable structure that allows them to be characterized in terms of simpler lower-dimensional cones. The most important example is sparse semidefinite programming with a chordal sparsity pattern. Here partial separability derives from the clique decomposition theorems that characterize positive"},"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":"1306.0057","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-06-01T01:26:55Z","cross_cats_sorted":[],"title_canon_sha256":"843980c35fc35b085a400b346b5928da886af7efbee2385d90bf7424e2b700e4","abstract_canon_sha256":"9d74e00981e5365a64ffa57a8edc8fc5c7473efdc0a81bcd848c56d191eeed8e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:22:04.764839Z","signature_b64":"aSAAVpvS8oNvarLMCwpGg5HkduCLmc0lcA+d1/sQYVK/EIzs1MtJkIinpv0ocoTxuPEcBAOgpAnwNdlzrHRyCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cef6e01d936a62e4976c74b26060ba63a9dc9d12e4060ed78bd7489587644bb2","last_reissued_at":"2026-05-18T03:22:04.764374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:22:04.764374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Decomposition in conic optimization with partially separable structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Lieven Vandenberghe, Martin S. Andersen, Yifan Sun","submitted_at":"2013-06-01T01:26:55Z","abstract_excerpt":"Decomposition techniques for linear programming are difficult to extend to conic optimization problems with general non-polyhedral convex cones because the conic inequalities introduce an additional nonlinear coupling between the variables. However in many applications the convex cones have a partially separable structure that allows them to be characterized in terms of simpler lower-dimensional cones. The most important example is sparse semidefinite programming with a chordal sparsity pattern. Here partial separability derives from the clique decomposition theorems that characterize positive"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0057","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":""},"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":"1306.0057","created_at":"2026-05-18T03:22:04.764436+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.0057v1","created_at":"2026-05-18T03:22:04.764436+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.0057","created_at":"2026-05-18T03:22:04.764436+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z33OAHMTNJRO","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z33OAHMTNJROJF3M","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z33OAHMT","created_at":"2026-05-18T12:28:09.283467+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/Z33OAHMTNJROJF3MOSZGAYF2MO","json":"https://pith.science/pith/Z33OAHMTNJROJF3MOSZGAYF2MO.json","graph_json":"https://pith.science/api/pith-number/Z33OAHMTNJROJF3MOSZGAYF2MO/graph.json","events_json":"https://pith.science/api/pith-number/Z33OAHMTNJROJF3MOSZGAYF2MO/events.json","paper":"https://pith.science/paper/Z33OAHMT"},"agent_actions":{"view_html":"https://pith.science/pith/Z33OAHMTNJROJF3MOSZGAYF2MO","download_json":"https://pith.science/pith/Z33OAHMTNJROJF3MOSZGAYF2MO.json","view_paper":"https://pith.science/paper/Z33OAHMT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.0057&json=true","fetch_graph":"https://pith.science/api/pith-number/Z33OAHMTNJROJF3MOSZGAYF2MO/graph.json","fetch_events":"https://pith.science/api/pith-number/Z33OAHMTNJROJF3MOSZGAYF2MO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z33OAHMTNJROJF3MOSZGAYF2MO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z33OAHMTNJROJF3MOSZGAYF2MO/action/storage_attestation","attest_author":"https://pith.science/pith/Z33OAHMTNJROJF3MOSZGAYF2MO/action/author_attestation","sign_citation":"https://pith.science/pith/Z33OAHMTNJROJF3MOSZGAYF2MO/action/citation_signature","submit_replication":"https://pith.science/pith/Z33OAHMTNJROJF3MOSZGAYF2MO/action/replication_record"}},"created_at":"2026-05-18T03:22:04.764436+00:00","updated_at":"2026-05-18T03:22:04.764436+00:00"}