{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:AKVFB7Z2HUZZNYXPFXWWLN2ZV4","short_pith_number":"pith:AKVFB7Z2","canonical_record":{"source":{"id":"1706.06622","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2017-06-20T18:58:11Z","cross_cats_sorted":["cs.CE"],"title_canon_sha256":"13ab059ca1e8ed0a67a26277b7e0c0d5c204eb715b7604b739486a83f0f6ca60","abstract_canon_sha256":"4a4f62ab4eee59e3495934504100e455d53749a4751bc8ed51ea0b56cab9e9f8"},"schema_version":"1.0"},"canonical_sha256":"02aa50ff3a3d3396e2ef2ded65b759af028b9aab42f2e6f008399fad253f28cd","source":{"kind":"arxiv","id":"1706.06622","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.06622","created_at":"2026-05-17T23:50:38Z"},{"alias_kind":"arxiv_version","alias_value":"1706.06622v2","created_at":"2026-05-17T23:50:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06622","created_at":"2026-05-17T23:50:38Z"},{"alias_kind":"pith_short_12","alias_value":"AKVFB7Z2HUZZ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AKVFB7Z2HUZZNYXP","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AKVFB7Z2","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:AKVFB7Z2HUZZNYXPFXWWLN2ZV4","target":"record","payload":{"canonical_record":{"source":{"id":"1706.06622","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2017-06-20T18:58:11Z","cross_cats_sorted":["cs.CE"],"title_canon_sha256":"13ab059ca1e8ed0a67a26277b7e0c0d5c204eb715b7604b739486a83f0f6ca60","abstract_canon_sha256":"4a4f62ab4eee59e3495934504100e455d53749a4751bc8ed51ea0b56cab9e9f8"},"schema_version":"1.0"},"canonical_sha256":"02aa50ff3a3d3396e2ef2ded65b759af028b9aab42f2e6f008399fad253f28cd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:38.930534Z","signature_b64":"9nyUMnx4IW5ynJchbF+lezTO5gyLoWw0+YrkZPs8Dv/VN4IyvP/3s9x4eZpSDqZ2Oxxh7l7LS+NwCxfTpzegAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02aa50ff3a3d3396e2ef2ded65b759af028b9aab42f2e6f008399fad253f28cd","last_reissued_at":"2026-05-17T23:50:38.929981Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:38.929981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.06622","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:50:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sR22EzRawr6YFAZVgUtrFR+dS9sotKcL/MgMekF7SYu9hJU/nwps959FSHQ7IhRfNR4tSF1bKrtlpjjU9kYAAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T12:24:17.919303Z"},"content_sha256":"4cf752a9df85dd70c8a0fefc7ab9274f502c60cf6a71a9ef4245e01007b94fce","schema_version":"1.0","event_id":"sha256:4cf752a9df85dd70c8a0fefc7ab9274f502c60cf6a71a9ef4245e01007b94fce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:AKVFB7Z2HUZZNYXPFXWWLN2ZV4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximate Analytical Solutions of Power Flow Equations Based on Multi-Dimensional Holomorphic Embedding Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CE"],"primary_cat":"cs.SY","authors_text":"Bin Wang, Chengxi Liu, Claus Leth Bak, Kai Sun, Xin Xu","submitted_at":"2017-06-20T18:58:11Z","abstract_excerpt":"It is well known that closed-form analytical solutions for AC power flow equations do not exist in general. This paper proposes a multi-dimensional holomorphic embedding method (MDHEM) to obtain an explicit approximate analytical AC power-flow solution by finding a physical germ solution and arbitrarily embedding each power, each load or groups of loads with respective scales. Based on the MDHEM, the complete approximate analytical solutions to the power flow equations in the high-dimensional space become achievable, since the voltage vector of each bus can be explicitly expressed by a converg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06622","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:50:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PeveMY4T4LpTyewI51cJO9LSCFyBnv5WpxwDjHmPgYzddm8tkaCcsaIecuO8vTq8cIsRsiDcjUy+pLAsLRBsAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T12:24:17.919671Z"},"content_sha256":"6acebe683ce75bb9af818f56701b4e10f91c36c640d947572021411f9dfa8441","schema_version":"1.0","event_id":"sha256:6acebe683ce75bb9af818f56701b4e10f91c36c640d947572021411f9dfa8441"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AKVFB7Z2HUZZNYXPFXWWLN2ZV4/bundle.json","state_url":"https://pith.science/pith/AKVFB7Z2HUZZNYXPFXWWLN2ZV4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AKVFB7Z2HUZZNYXPFXWWLN2ZV4/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":"2026-06-21T12:24:17Z","links":{"resolver":"https://pith.science/pith/AKVFB7Z2HUZZNYXPFXWWLN2ZV4","bundle":"https://pith.science/pith/AKVFB7Z2HUZZNYXPFXWWLN2ZV4/bundle.json","state":"https://pith.science/pith/AKVFB7Z2HUZZNYXPFXWWLN2ZV4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AKVFB7Z2HUZZNYXPFXWWLN2ZV4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AKVFB7Z2HUZZNYXPFXWWLN2ZV4","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":"4a4f62ab4eee59e3495934504100e455d53749a4751bc8ed51ea0b56cab9e9f8","cross_cats_sorted":["cs.CE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2017-06-20T18:58:11Z","title_canon_sha256":"13ab059ca1e8ed0a67a26277b7e0c0d5c204eb715b7604b739486a83f0f6ca60"},"schema_version":"1.0","source":{"id":"1706.06622","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.06622","created_at":"2026-05-17T23:50:38Z"},{"alias_kind":"arxiv_version","alias_value":"1706.06622v2","created_at":"2026-05-17T23:50:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.06622","created_at":"2026-05-17T23:50:38Z"},{"alias_kind":"pith_short_12","alias_value":"AKVFB7Z2HUZZ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AKVFB7Z2HUZZNYXP","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AKVFB7Z2","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:6acebe683ce75bb9af818f56701b4e10f91c36c640d947572021411f9dfa8441","target":"graph","created_at":"2026-05-17T23:50:38Z","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":"It is well known that closed-form analytical solutions for AC power flow equations do not exist in general. This paper proposes a multi-dimensional holomorphic embedding method (MDHEM) to obtain an explicit approximate analytical AC power-flow solution by finding a physical germ solution and arbitrarily embedding each power, each load or groups of loads with respective scales. Based on the MDHEM, the complete approximate analytical solutions to the power flow equations in the high-dimensional space become achievable, since the voltage vector of each bus can be explicitly expressed by a converg","authors_text":"Bin Wang, Chengxi Liu, Claus Leth Bak, Kai Sun, Xin Xu","cross_cats":["cs.CE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2017-06-20T18:58:11Z","title":"Approximate Analytical Solutions of Power Flow Equations Based on Multi-Dimensional Holomorphic Embedding Method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06622","kind":"arxiv","version":2},"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":"sha256:4cf752a9df85dd70c8a0fefc7ab9274f502c60cf6a71a9ef4245e01007b94fce","target":"record","created_at":"2026-05-17T23:50:38Z","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":"4a4f62ab4eee59e3495934504100e455d53749a4751bc8ed51ea0b56cab9e9f8","cross_cats_sorted":["cs.CE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2017-06-20T18:58:11Z","title_canon_sha256":"13ab059ca1e8ed0a67a26277b7e0c0d5c204eb715b7604b739486a83f0f6ca60"},"schema_version":"1.0","source":{"id":"1706.06622","kind":"arxiv","version":2}},"canonical_sha256":"02aa50ff3a3d3396e2ef2ded65b759af028b9aab42f2e6f008399fad253f28cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02aa50ff3a3d3396e2ef2ded65b759af028b9aab42f2e6f008399fad253f28cd","first_computed_at":"2026-05-17T23:50:38.929981Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:38.929981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9nyUMnx4IW5ynJchbF+lezTO5gyLoWw0+YrkZPs8Dv/VN4IyvP/3s9x4eZpSDqZ2Oxxh7l7LS+NwCxfTpzegAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:38.930534Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.06622","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4cf752a9df85dd70c8a0fefc7ab9274f502c60cf6a71a9ef4245e01007b94fce","sha256:6acebe683ce75bb9af818f56701b4e10f91c36c640d947572021411f9dfa8441"],"state_sha256":"79ee19b61854bcd266579fb5173a0bab11717b45258ab5a10170e5b64571db99"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OQPS8DLed8BQVKOiSVjlW9NeEua+YsSEbs7wMU9q2nhz0pkMo820CSU349Q40OZCWVus7pRI9E6QpEqRSHv9Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T12:24:17.921510Z","bundle_sha256":"d53d6616cc250f012a4f18d7c09a5b6cbce57dbf90ad334cc8487e572a09de0b"}}