{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:Z33OAHMTNJROJF3MOSZGAYF2MO","short_pith_number":"pith:Z33OAHMT","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"},"canonical_sha256":"cef6e01d936a62e4976c74b26060ba63a9dc9d12e4060ed78bd7489587644bb2","source":{"kind":"arxiv","id":"1306.0057","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.0057","created_at":"2026-05-18T03:22:04Z"},{"alias_kind":"arxiv_version","alias_value":"1306.0057v1","created_at":"2026-05-18T03:22:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.0057","created_at":"2026-05-18T03:22:04Z"},{"alias_kind":"pith_short_12","alias_value":"Z33OAHMTNJRO","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"Z33OAHMTNJROJF3M","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"Z33OAHMT","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:Z33OAHMTNJROJF3MOSZGAYF2MO","target":"record","payload":{"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"},"canonical_sha256":"cef6e01d936a62e4976c74b26060ba63a9dc9d12e4060ed78bd7489587644bb2","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"},"source_kind":"arxiv","source_id":"1306.0057","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:22:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bVVON5lccLWzVmmwvYCSJPyTH1Ob+uUbmEatji7wQwkr8b6wbzxJN575bWsOCvivQe9yQIpwxyBWyW9uc+2cAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T17:32:20.957967Z"},"content_sha256":"27375e34a317ed11ad98fad8596d3956517ad18effe21c69c9c4f0a2fcaf6aab","schema_version":"1.0","event_id":"sha256:27375e34a317ed11ad98fad8596d3956517ad18effe21c69c9c4f0a2fcaf6aab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:Z33OAHMTNJROJF3MOSZGAYF2MO","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:22:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YtvK+cfN8MeQ2JL5IFkS6qdSMKKxFnASV3qKb5KsfsneiqNx+pDsVXkDsAAJMAZBMQ4I2Knb2dDJOaEPnmq9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T17:32:20.958327Z"},"content_sha256":"cf77c923b6585bf3d73a16861145183d0cf43f6fd4e346a866da08c6b8d89e25","schema_version":"1.0","event_id":"sha256:cf77c923b6585bf3d73a16861145183d0cf43f6fd4e346a866da08c6b8d89e25"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z33OAHMTNJROJF3MOSZGAYF2MO/bundle.json","state_url":"https://pith.science/pith/Z33OAHMTNJROJF3MOSZGAYF2MO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z33OAHMTNJROJF3MOSZGAYF2MO/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T17:32:20Z","links":{"resolver":"https://pith.science/pith/Z33OAHMTNJROJF3MOSZGAYF2MO","bundle":"https://pith.science/pith/Z33OAHMTNJROJF3MOSZGAYF2MO/bundle.json","state":"https://pith.science/pith/Z33OAHMTNJROJF3MOSZGAYF2MO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z33OAHMTNJROJF3MOSZGAYF2MO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Z33OAHMTNJROJF3MOSZGAYF2MO","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":"9d74e00981e5365a64ffa57a8edc8fc5c7473efdc0a81bcd848c56d191eeed8e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-06-01T01:26:55Z","title_canon_sha256":"843980c35fc35b085a400b346b5928da886af7efbee2385d90bf7424e2b700e4"},"schema_version":"1.0","source":{"id":"1306.0057","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.0057","created_at":"2026-05-18T03:22:04Z"},{"alias_kind":"arxiv_version","alias_value":"1306.0057v1","created_at":"2026-05-18T03:22:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.0057","created_at":"2026-05-18T03:22:04Z"},{"alias_kind":"pith_short_12","alias_value":"Z33OAHMTNJRO","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"Z33OAHMTNJROJF3M","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"Z33OAHMT","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:cf77c923b6585bf3d73a16861145183d0cf43f6fd4e346a866da08c6b8d89e25","target":"graph","created_at":"2026-05-18T03:22:04Z","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":"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","authors_text":"Lieven Vandenberghe, Martin S. Andersen, Yifan Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-06-01T01:26:55Z","title":"Decomposition in conic optimization with partially separable structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0057","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":"sha256:27375e34a317ed11ad98fad8596d3956517ad18effe21c69c9c4f0a2fcaf6aab","target":"record","created_at":"2026-05-18T03:22:04Z","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":"9d74e00981e5365a64ffa57a8edc8fc5c7473efdc0a81bcd848c56d191eeed8e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-06-01T01:26:55Z","title_canon_sha256":"843980c35fc35b085a400b346b5928da886af7efbee2385d90bf7424e2b700e4"},"schema_version":"1.0","source":{"id":"1306.0057","kind":"arxiv","version":1}},"canonical_sha256":"cef6e01d936a62e4976c74b26060ba63a9dc9d12e4060ed78bd7489587644bb2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cef6e01d936a62e4976c74b26060ba63a9dc9d12e4060ed78bd7489587644bb2","first_computed_at":"2026-05-18T03:22:04.764374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:22:04.764374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aSAAVpvS8oNvarLMCwpGg5HkduCLmc0lcA+d1/sQYVK/EIzs1MtJkIinpv0ocoTxuPEcBAOgpAnwNdlzrHRyCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:22:04.764839Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.0057","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27375e34a317ed11ad98fad8596d3956517ad18effe21c69c9c4f0a2fcaf6aab","sha256:cf77c923b6585bf3d73a16861145183d0cf43f6fd4e346a866da08c6b8d89e25"],"state_sha256":"1db0af798bfb24aa2858e0a84684b4a591f44fd22f16d3877457a77896da782a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kUobf661HSSzlWE/jIsjhzck9fzSsBIUZPhJtZfKjTVCfFc9gnRu7i1kY9Z1bdq98Q/M40gjWdj5R3jp7zK4Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T17:32:20.960571Z","bundle_sha256":"1aff5f582505223786e43d3eef6c58dd748f0b9b95f6a070c99c6dff897be27b"}}