{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:P4RUAAGOYSFA65WVZZ33UVYVTQ","short_pith_number":"pith:P4RUAAGO","canonical_record":{"source":{"id":"1807.08785","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-07-23T18:54:32Z","cross_cats_sorted":[],"title_canon_sha256":"c5e65746a3cf19fc0fd4603f00365a9025f0aac9bef9fa760a3f95db08874776","abstract_canon_sha256":"c06d9eaf7c12f87265a2d42eb2fcc9250cbe42fb9fb0de54aaf9ef553e62ca3f"},"schema_version":"1.0"},"canonical_sha256":"7f234000cec48a0f76d5ce77ba57159c2681988bcbb753a27aabb1803a357908","source":{"kind":"arxiv","id":"1807.08785","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.08785","created_at":"2026-05-18T00:09:57Z"},{"alias_kind":"arxiv_version","alias_value":"1807.08785v1","created_at":"2026-05-18T00:09:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.08785","created_at":"2026-05-18T00:09:57Z"},{"alias_kind":"pith_short_12","alias_value":"P4RUAAGOYSFA","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"P4RUAAGOYSFA65WV","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"P4RUAAGO","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:P4RUAAGOYSFA65WVZZ33UVYVTQ","target":"record","payload":{"canonical_record":{"source":{"id":"1807.08785","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-07-23T18:54:32Z","cross_cats_sorted":[],"title_canon_sha256":"c5e65746a3cf19fc0fd4603f00365a9025f0aac9bef9fa760a3f95db08874776","abstract_canon_sha256":"c06d9eaf7c12f87265a2d42eb2fcc9250cbe42fb9fb0de54aaf9ef553e62ca3f"},"schema_version":"1.0"},"canonical_sha256":"7f234000cec48a0f76d5ce77ba57159c2681988bcbb753a27aabb1803a357908","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:57.867382Z","signature_b64":"Y2nZl/e42PbGtbe86hCsgSj6UNX3Wo7mSUWw9kt6ez0IbgW8h8vLJRwx4Cj6shKSR05obEU64JAyg0gloxAFAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f234000cec48a0f76d5ce77ba57159c2681988bcbb753a27aabb1803a357908","last_reissued_at":"2026-05-18T00:09:57.866649Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:57.866649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.08785","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":"2026-05-18T00:09:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A4VuV14qpJtLm6sdNQu71cBd0s3HbkmlusZS7YzeU5J5DmVLkpxKbfyGTOG7TuCxeeIRFBfPHiDKNgYOmmTwAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:32:44.102240Z"},"content_sha256":"00a9fa11749eaa68a4c5fc49afc27c064840905e0b7884bf9d09044868801fd8","schema_version":"1.0","event_id":"sha256:00a9fa11749eaa68a4c5fc49afc27c064840905e0b7884bf9d09044868801fd8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:P4RUAAGOYSFA65WVZZ33UVYVTQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Study on the Strong Duality of Conic Relaxation of AC Optimal Power Flow in Radial Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bo Zeng, Jianxue Wang, Xiaoyu Cao","submitted_at":"2018-07-23T18:54:32Z","abstract_excerpt":"This paper proposes a set of closed-form conditions to ensure the strong duality of second-order cone program (SOCP) formulation for AC power flow in radial power networks. In addition, numerical evaluations on IEEE 33-bus test networks and a real-world distribution network are performed to demonstrate the validity of the proposed conditions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08785","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":"2026-05-18T00:09:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"stqS4VBrHWpkTnWNdqzdEFtajvWp+XG5IytEWHJAbUMCFhn2ql8OETjhVrA7j807eF0mHo1WTXMibiBmw98QCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:32:44.102727Z"},"content_sha256":"474fe0683c6e4be3b67e821152459636555d463c8da3e81d32b714c74d3e11ed","schema_version":"1.0","event_id":"sha256:474fe0683c6e4be3b67e821152459636555d463c8da3e81d32b714c74d3e11ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P4RUAAGOYSFA65WVZZ33UVYVTQ/bundle.json","state_url":"https://pith.science/pith/P4RUAAGOYSFA65WVZZ33UVYVTQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P4RUAAGOYSFA65WVZZ33UVYVTQ/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":"2026-06-01T09:32:44Z","links":{"resolver":"https://pith.science/pith/P4RUAAGOYSFA65WVZZ33UVYVTQ","bundle":"https://pith.science/pith/P4RUAAGOYSFA65WVZZ33UVYVTQ/bundle.json","state":"https://pith.science/pith/P4RUAAGOYSFA65WVZZ33UVYVTQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P4RUAAGOYSFA65WVZZ33UVYVTQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:P4RUAAGOYSFA65WVZZ33UVYVTQ","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":"c06d9eaf7c12f87265a2d42eb2fcc9250cbe42fb9fb0de54aaf9ef553e62ca3f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-07-23T18:54:32Z","title_canon_sha256":"c5e65746a3cf19fc0fd4603f00365a9025f0aac9bef9fa760a3f95db08874776"},"schema_version":"1.0","source":{"id":"1807.08785","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.08785","created_at":"2026-05-18T00:09:57Z"},{"alias_kind":"arxiv_version","alias_value":"1807.08785v1","created_at":"2026-05-18T00:09:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.08785","created_at":"2026-05-18T00:09:57Z"},{"alias_kind":"pith_short_12","alias_value":"P4RUAAGOYSFA","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"P4RUAAGOYSFA65WV","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"P4RUAAGO","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:474fe0683c6e4be3b67e821152459636555d463c8da3e81d32b714c74d3e11ed","target":"graph","created_at":"2026-05-18T00:09:57Z","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 proposes a set of closed-form conditions to ensure the strong duality of second-order cone program (SOCP) formulation for AC power flow in radial power networks. In addition, numerical evaluations on IEEE 33-bus test networks and a real-world distribution network are performed to demonstrate the validity of the proposed conditions.","authors_text":"Bo Zeng, Jianxue Wang, Xiaoyu Cao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-07-23T18:54:32Z","title":"A Study on the Strong Duality of Conic Relaxation of AC Optimal Power Flow in Radial Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08785","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":"sha256:00a9fa11749eaa68a4c5fc49afc27c064840905e0b7884bf9d09044868801fd8","target":"record","created_at":"2026-05-18T00:09:57Z","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":"c06d9eaf7c12f87265a2d42eb2fcc9250cbe42fb9fb0de54aaf9ef553e62ca3f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-07-23T18:54:32Z","title_canon_sha256":"c5e65746a3cf19fc0fd4603f00365a9025f0aac9bef9fa760a3f95db08874776"},"schema_version":"1.0","source":{"id":"1807.08785","kind":"arxiv","version":1}},"canonical_sha256":"7f234000cec48a0f76d5ce77ba57159c2681988bcbb753a27aabb1803a357908","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f234000cec48a0f76d5ce77ba57159c2681988bcbb753a27aabb1803a357908","first_computed_at":"2026-05-18T00:09:57.866649Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:57.866649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y2nZl/e42PbGtbe86hCsgSj6UNX3Wo7mSUWw9kt6ez0IbgW8h8vLJRwx4Cj6shKSR05obEU64JAyg0gloxAFAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:57.867382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.08785","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00a9fa11749eaa68a4c5fc49afc27c064840905e0b7884bf9d09044868801fd8","sha256:474fe0683c6e4be3b67e821152459636555d463c8da3e81d32b714c74d3e11ed"],"state_sha256":"9ae7a5529947704a15bd283a897190b0c6eaf46686378e142e0837d7dcb16325"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5D3Z0Xmk7TyDVQy4i7352qSQ1cSB4HC7VXjsPm08DKfPeiJL+ENLmnUppGEFPhIPH0ylVRL9R30Rt2ym5ziiCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T09:32:44.105199Z","bundle_sha256":"26921870cc90ed7ec6547a179432c3312522f41d3cf7206f4a44f45a69aa7f85"}}