{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:R4C55ZN4HHCUZO4PP76MB2FG3O","short_pith_number":"pith:R4C55ZN4","canonical_record":{"source":{"id":"1609.05054","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-16T13:58:06Z","cross_cats_sorted":[],"title_canon_sha256":"3fe994dfcecd6f0aa9b738486e968615ab034e51bb4bc56e8f16edbc62706fff","abstract_canon_sha256":"6eee401d48bb6d1baed8f6c016d0fb6f93cfa3d38b26b1ede22240963e3aceab"},"schema_version":"1.0"},"canonical_sha256":"8f05dee5bc39c54cbb8f7ffcc0e8a6db8e05b7eed5c06f6b787072a708552353","source":{"kind":"arxiv","id":"1609.05054","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.05054","created_at":"2026-05-18T00:18:32Z"},{"alias_kind":"arxiv_version","alias_value":"1609.05054v1","created_at":"2026-05-18T00:18:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.05054","created_at":"2026-05-18T00:18:32Z"},{"alias_kind":"pith_short_12","alias_value":"R4C55ZN4HHCU","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"R4C55ZN4HHCUZO4P","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"R4C55ZN4","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:R4C55ZN4HHCUZO4PP76MB2FG3O","target":"record","payload":{"canonical_record":{"source":{"id":"1609.05054","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-16T13:58:06Z","cross_cats_sorted":[],"title_canon_sha256":"3fe994dfcecd6f0aa9b738486e968615ab034e51bb4bc56e8f16edbc62706fff","abstract_canon_sha256":"6eee401d48bb6d1baed8f6c016d0fb6f93cfa3d38b26b1ede22240963e3aceab"},"schema_version":"1.0"},"canonical_sha256":"8f05dee5bc39c54cbb8f7ffcc0e8a6db8e05b7eed5c06f6b787072a708552353","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:32.083929Z","signature_b64":"AI4Z7GZcjuZNTC2fPOZbt6+p5W46EQxuBfLDHzcLPAMdp13bwcnMz58t3dCi5cofjCTYEz0oOuMwvRCCZwkRCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f05dee5bc39c54cbb8f7ffcc0e8a6db8e05b7eed5c06f6b787072a708552353","last_reissued_at":"2026-05-18T00:18:32.083229Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:32.083229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.05054","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":"2026-05-18T00:18:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ML1mufV2VlTrZY00ZLjIqeVtq2EzIFg2sCWtdEJ17HNzCGuWHPjNA/BSGcWdBRU6/dweHxyFJX6c1pG09v8/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T14:25:39.729043Z"},"content_sha256":"ee2760828d302499aded00397a9d99c32dca19d28756584bfb761c520d7abae5","schema_version":"1.0","event_id":"sha256:ee2760828d302499aded00397a9d99c32dca19d28756584bfb761c520d7abae5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:R4C55ZN4HHCUZO4PP76MB2FG3O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Least Square Estimation-Based SDP Cuts for SOCP Relaxation of AC OPF","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bo Zeng, Hossein Ghassempour, Lingling Fan, Zhixin Miao","submitted_at":"2016-09-16T13:58:06Z","abstract_excerpt":"This paper presents a method that generates affine inequalities to strengthen the second-order conic programming (SOCP) relaxation of an alternating current optimal power flow (AC OPF) problem. The affine inequalities serve as cuts to get rid of points outside of the feasible region of AC OPF with semi-definite programming (SDP) relaxation. Hence, the affine inequalities are names as SDP cuts. While AC OPF with SDP relaxation has a high computational complexity, AC OPF with SOCP has a much lower computational complexity. Recent research has found that the feasible region of SDP relaxation is c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05054","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":"2026-05-18T00:18:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NRtdVslVSrEQ1HQBmOnJGUqrfQlVDvalf0E5iDH3+mE2sDfdcnX+Cxj7dIVme3oa1Q0KSDoW+hnxyauKYxVVCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T14:25:39.729403Z"},"content_sha256":"5a84813fa1f4ccea97eaa03dea6816e3c1e64d1ab5569a2279af1492b198365a","schema_version":"1.0","event_id":"sha256:5a84813fa1f4ccea97eaa03dea6816e3c1e64d1ab5569a2279af1492b198365a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R4C55ZN4HHCUZO4PP76MB2FG3O/bundle.json","state_url":"https://pith.science/pith/R4C55ZN4HHCUZO4PP76MB2FG3O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R4C55ZN4HHCUZO4PP76MB2FG3O/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":"2026-06-05T14:25:39Z","links":{"resolver":"https://pith.science/pith/R4C55ZN4HHCUZO4PP76MB2FG3O","bundle":"https://pith.science/pith/R4C55ZN4HHCUZO4PP76MB2FG3O/bundle.json","state":"https://pith.science/pith/R4C55ZN4HHCUZO4PP76MB2FG3O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R4C55ZN4HHCUZO4PP76MB2FG3O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:R4C55ZN4HHCUZO4PP76MB2FG3O","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":"6eee401d48bb6d1baed8f6c016d0fb6f93cfa3d38b26b1ede22240963e3aceab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-16T13:58:06Z","title_canon_sha256":"3fe994dfcecd6f0aa9b738486e968615ab034e51bb4bc56e8f16edbc62706fff"},"schema_version":"1.0","source":{"id":"1609.05054","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.05054","created_at":"2026-05-18T00:18:32Z"},{"alias_kind":"arxiv_version","alias_value":"1609.05054v1","created_at":"2026-05-18T00:18:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.05054","created_at":"2026-05-18T00:18:32Z"},{"alias_kind":"pith_short_12","alias_value":"R4C55ZN4HHCU","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"R4C55ZN4HHCUZO4P","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"R4C55ZN4","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:5a84813fa1f4ccea97eaa03dea6816e3c1e64d1ab5569a2279af1492b198365a","target":"graph","created_at":"2026-05-18T00:18:32Z","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":"This paper presents a method that generates affine inequalities to strengthen the second-order conic programming (SOCP) relaxation of an alternating current optimal power flow (AC OPF) problem. The affine inequalities serve as cuts to get rid of points outside of the feasible region of AC OPF with semi-definite programming (SDP) relaxation. Hence, the affine inequalities are names as SDP cuts. While AC OPF with SDP relaxation has a high computational complexity, AC OPF with SOCP has a much lower computational complexity. Recent research has found that the feasible region of SDP relaxation is c","authors_text":"Bo Zeng, Hossein Ghassempour, Lingling Fan, Zhixin Miao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-16T13:58:06Z","title":"Least Square Estimation-Based SDP Cuts for SOCP Relaxation of AC OPF"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05054","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:ee2760828d302499aded00397a9d99c32dca19d28756584bfb761c520d7abae5","target":"record","created_at":"2026-05-18T00:18:32Z","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":"6eee401d48bb6d1baed8f6c016d0fb6f93cfa3d38b26b1ede22240963e3aceab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-16T13:58:06Z","title_canon_sha256":"3fe994dfcecd6f0aa9b738486e968615ab034e51bb4bc56e8f16edbc62706fff"},"schema_version":"1.0","source":{"id":"1609.05054","kind":"arxiv","version":1}},"canonical_sha256":"8f05dee5bc39c54cbb8f7ffcc0e8a6db8e05b7eed5c06f6b787072a708552353","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f05dee5bc39c54cbb8f7ffcc0e8a6db8e05b7eed5c06f6b787072a708552353","first_computed_at":"2026-05-18T00:18:32.083229Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:32.083229Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AI4Z7GZcjuZNTC2fPOZbt6+p5W46EQxuBfLDHzcLPAMdp13bwcnMz58t3dCi5cofjCTYEz0oOuMwvRCCZwkRCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:32.083929Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.05054","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee2760828d302499aded00397a9d99c32dca19d28756584bfb761c520d7abae5","sha256:5a84813fa1f4ccea97eaa03dea6816e3c1e64d1ab5569a2279af1492b198365a"],"state_sha256":"76b2277cb09dd99045d7a566395828483ee2fd53ae501cf3c8d324263aeb834a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/xtmHiP8sEM7wnIRGeS/ZxweTd+J0uothYX0HHE16Wociy7bfrBEwQjQ+kA8Thb4StdP5UjTkImPuL0e6HhSBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T14:25:39.731352Z","bundle_sha256":"f3386cda2ced4c55439129c71052ad2f6509a0ae3d21d4bc1a7828e77d1e1441"}}