{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:PS55MVWUEKHVTWQUUMAFLPRMQB","short_pith_number":"pith:PS55MVWU","canonical_record":{"source":{"id":"1605.08511","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-05-27T05:48:52Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"aedcf7c939e6c2cbeafa1ef9b2004b39a391950dde70d1add9781b475d312066","abstract_canon_sha256":"098123eb82f7c7c84c70b7f1b4da4ad3a6cebcde4fc3c6b097f7d05fd0fb6079"},"schema_version":"1.0"},"canonical_sha256":"7cbbd656d4228f59da14a30055be2c806f10bec34e70861606aa6bb92085192b","source":{"kind":"arxiv","id":"1605.08511","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.08511","created_at":"2026-05-18T00:44:52Z"},{"alias_kind":"arxiv_version","alias_value":"1605.08511v3","created_at":"2026-05-18T00:44:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08511","created_at":"2026-05-18T00:44:52Z"},{"alias_kind":"pith_short_12","alias_value":"PS55MVWUEKHV","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PS55MVWUEKHVTWQU","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PS55MVWU","created_at":"2026-05-18T12:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:PS55MVWUEKHVTWQUUMAFLPRMQB","target":"record","payload":{"canonical_record":{"source":{"id":"1605.08511","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-05-27T05:48:52Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"aedcf7c939e6c2cbeafa1ef9b2004b39a391950dde70d1add9781b475d312066","abstract_canon_sha256":"098123eb82f7c7c84c70b7f1b4da4ad3a6cebcde4fc3c6b097f7d05fd0fb6079"},"schema_version":"1.0"},"canonical_sha256":"7cbbd656d4228f59da14a30055be2c806f10bec34e70861606aa6bb92085192b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:52.481776Z","signature_b64":"b3YQtcej/n6N9moX0u+0SzLpcWTNHPu+FxebtJNUOhR3RvqrWu+tiR5knsO4tUqjWco5kmKe3YgNFHlE9cAyCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7cbbd656d4228f59da14a30055be2c806f10bec34e70861606aa6bb92085192b","last_reissued_at":"2026-05-18T00:44:52.481075Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:52.481075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.08511","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:44:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jqCUK0LZu+wf0H1PHZWNL9Ldta60FQrtjJZbEv8BjOHEafglDrlRoWUzbqz8BujgotrRs1oFUTLvFimV8irkDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:41:34.167253Z"},"content_sha256":"30d187bd55d5029e4bf0ea01a3564aae04b0d5a5a342621940540ae9f43c6a29","schema_version":"1.0","event_id":"sha256:30d187bd55d5029e4bf0ea01a3564aae04b0d5a5a342621940540ae9f43c6a29"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:PS55MVWUEKHVTWQUUMAFLPRMQB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence of the Z-Bus Method for Three-Phase Distribution Load-Flow with ZIP Loads","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY"],"primary_cat":"math.OC","authors_text":"Mohammadhafez Bazrafshan, Nikolaos Gatsis","submitted_at":"2016-05-27T05:48:52Z","abstract_excerpt":"This paper derives a set of sufficient conditions guaranteeing that the load-flow problem in unbalanced three-phase distribution networks with wye and delta ZIP loads has a unique solution over a region that can be explicitly calculated from the network parameters. It is also proved that the well-known Z-Bus iterative method is a contraction over the defined region, and hence converges to the unique solution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08511","kind":"arxiv","version":3},"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":"2026-05-18T00:44:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fAaOFqmZFsEnyINGECfUB3X76n/hG11H121DLG/LlBv8WptJQ7DRVeTYQthvNd9jWsLVSO+/qi+qGavWCQtgDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:41:34.167611Z"},"content_sha256":"bd3b1763803e147bd830c572d7edf2104d8837c5707e535490fde8aba9fc3959","schema_version":"1.0","event_id":"sha256:bd3b1763803e147bd830c572d7edf2104d8837c5707e535490fde8aba9fc3959"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PS55MVWUEKHVTWQUUMAFLPRMQB/bundle.json","state_url":"https://pith.science/pith/PS55MVWUEKHVTWQUUMAFLPRMQB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PS55MVWUEKHVTWQUUMAFLPRMQB/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":"2026-06-03T05:41:34Z","links":{"resolver":"https://pith.science/pith/PS55MVWUEKHVTWQUUMAFLPRMQB","bundle":"https://pith.science/pith/PS55MVWUEKHVTWQUUMAFLPRMQB/bundle.json","state":"https://pith.science/pith/PS55MVWUEKHVTWQUUMAFLPRMQB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PS55MVWUEKHVTWQUUMAFLPRMQB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PS55MVWUEKHVTWQUUMAFLPRMQB","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":"098123eb82f7c7c84c70b7f1b4da4ad3a6cebcde4fc3c6b097f7d05fd0fb6079","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-05-27T05:48:52Z","title_canon_sha256":"aedcf7c939e6c2cbeafa1ef9b2004b39a391950dde70d1add9781b475d312066"},"schema_version":"1.0","source":{"id":"1605.08511","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.08511","created_at":"2026-05-18T00:44:52Z"},{"alias_kind":"arxiv_version","alias_value":"1605.08511v3","created_at":"2026-05-18T00:44:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08511","created_at":"2026-05-18T00:44:52Z"},{"alias_kind":"pith_short_12","alias_value":"PS55MVWUEKHV","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PS55MVWUEKHVTWQU","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PS55MVWU","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:bd3b1763803e147bd830c572d7edf2104d8837c5707e535490fde8aba9fc3959","target":"graph","created_at":"2026-05-18T00:44:52Z","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 derives a set of sufficient conditions guaranteeing that the load-flow problem in unbalanced three-phase distribution networks with wye and delta ZIP loads has a unique solution over a region that can be explicitly calculated from the network parameters. It is also proved that the well-known Z-Bus iterative method is a contraction over the defined region, and hence converges to the unique solution.","authors_text":"Mohammadhafez Bazrafshan, Nikolaos Gatsis","cross_cats":["cs.SY"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-05-27T05:48:52Z","title":"Convergence of the Z-Bus Method for Three-Phase Distribution Load-Flow with ZIP Loads"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08511","kind":"arxiv","version":3},"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":"sha256:30d187bd55d5029e4bf0ea01a3564aae04b0d5a5a342621940540ae9f43c6a29","target":"record","created_at":"2026-05-18T00:44:52Z","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":"098123eb82f7c7c84c70b7f1b4da4ad3a6cebcde4fc3c6b097f7d05fd0fb6079","cross_cats_sorted":["cs.SY"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-05-27T05:48:52Z","title_canon_sha256":"aedcf7c939e6c2cbeafa1ef9b2004b39a391950dde70d1add9781b475d312066"},"schema_version":"1.0","source":{"id":"1605.08511","kind":"arxiv","version":3}},"canonical_sha256":"7cbbd656d4228f59da14a30055be2c806f10bec34e70861606aa6bb92085192b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7cbbd656d4228f59da14a30055be2c806f10bec34e70861606aa6bb92085192b","first_computed_at":"2026-05-18T00:44:52.481075Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:52.481075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b3YQtcej/n6N9moX0u+0SzLpcWTNHPu+FxebtJNUOhR3RvqrWu+tiR5knsO4tUqjWco5kmKe3YgNFHlE9cAyCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:52.481776Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.08511","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30d187bd55d5029e4bf0ea01a3564aae04b0d5a5a342621940540ae9f43c6a29","sha256:bd3b1763803e147bd830c572d7edf2104d8837c5707e535490fde8aba9fc3959"],"state_sha256":"780935ea0dd61f63e6db5dd6267b4e114389616760275ccea745ad3aaebfb5bf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HqcAbBFtqHvh5ezGjgEWkSFAfT8Qo+eo1yoZn0wZSP0Ay7yHMSMl8FOF95XUwnkJTXZjRYQNY34CH5J4DQGKAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T05:41:34.169620Z","bundle_sha256":"23766b6a4a8a8ddd484c8cbb393bcc8a89538c57eede986e4642face8375d082"}}