{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:YQPIZ52YUXVFNMEXSF3IYGTFT2","short_pith_number":"pith:YQPIZ52Y","canonical_record":{"source":{"id":"1904.08894","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-04-18T17:12:37Z","cross_cats_sorted":[],"title_canon_sha256":"132fb07c437154346b2156d159f46dd7a3f0f831ea4679fff39b01309a6ccceb","abstract_canon_sha256":"9dca4fc83957ab20a496c062e12447a6889b810fff259507485e9e7e22ee949b"},"schema_version":"1.0"},"canonical_sha256":"c41e8cf758a5ea56b09791768c1a659e92aa904348343eb492bc3453b4e2c616","source":{"kind":"arxiv","id":"1904.08894","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.08894","created_at":"2026-05-17T23:48:12Z"},{"alias_kind":"arxiv_version","alias_value":"1904.08894v1","created_at":"2026-05-17T23:48:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.08894","created_at":"2026-05-17T23:48:12Z"},{"alias_kind":"pith_short_12","alias_value":"YQPIZ52YUXVF","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"YQPIZ52YUXVFNMEX","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"YQPIZ52Y","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:YQPIZ52YUXVFNMEXSF3IYGTFT2","target":"record","payload":{"canonical_record":{"source":{"id":"1904.08894","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-04-18T17:12:37Z","cross_cats_sorted":[],"title_canon_sha256":"132fb07c437154346b2156d159f46dd7a3f0f831ea4679fff39b01309a6ccceb","abstract_canon_sha256":"9dca4fc83957ab20a496c062e12447a6889b810fff259507485e9e7e22ee949b"},"schema_version":"1.0"},"canonical_sha256":"c41e8cf758a5ea56b09791768c1a659e92aa904348343eb492bc3453b4e2c616","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:12.641437Z","signature_b64":"BFuu3BglMSLfg2QNve0CE0ogN+7zQQQJmr3GUBjk0loN1A0Oh65Q6vsn9tamJixnTfBigdr1iXNZx1ujmNHzDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c41e8cf758a5ea56b09791768c1a659e92aa904348343eb492bc3453b4e2c616","last_reissued_at":"2026-05-17T23:48:12.640814Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:12.640814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.08894","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":"2026-05-17T23:48:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EOJNwa1T1NqxcUzpclmzmVR+yJ5Ba6mT9x9Jr7TiOmz9h/cOUrnIUOqC2uN7B2rtxrUMX7QyDsmK5iMlZ2GpBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:24:24.562052Z"},"content_sha256":"6dfc98c89a473f3dd490a50277cf41d1e90403ce2a6363cc9bfb1ddf03fe9799","schema_version":"1.0","event_id":"sha256:6dfc98c89a473f3dd490a50277cf41d1e90403ce2a6363cc9bfb1ddf03fe9799"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:YQPIZ52YUXVFNMEXSF3IYGTFT2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Julia Module for Polynomial Optimization with Complex Variables applied to Optimal Power Flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Emiliano Traversi, Julie Sliwak, Lucas L\\'etocart, Manuel Ruiz, Miguel F. Anjos","submitted_at":"2019-04-18T17:12:37Z","abstract_excerpt":"Many optimization problems in power transmission networks can be formulated as polynomial problems with complex variables. A polynomial optimization problem with complex variables consists in optimizing a real-valued polynomial whose variables and coefficients are complex numbers subject to some complex polynomial equality or inequality constraints. These problems are usually directly converted to real variables, either using the polar form or the rectangular form. In this work, we propose a Julia module allowing the representation of polynomial problems in their original complex formulation. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.08894","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":"2026-05-17T23:48:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QIhTRhQIYCCLkpLbu4iG6Ujb2ZwMlnz3baPkmumFxWl/PiX9Adu4GqRxh71bsM26emoJJnAUFV/TwM0GidMdBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T20:24:24.562601Z"},"content_sha256":"5ea9ebbfbe928853af3d6b34437f5910c35a17955f7562d595e854adc3739990","schema_version":"1.0","event_id":"sha256:5ea9ebbfbe928853af3d6b34437f5910c35a17955f7562d595e854adc3739990"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YQPIZ52YUXVFNMEXSF3IYGTFT2/bundle.json","state_url":"https://pith.science/pith/YQPIZ52YUXVFNMEXSF3IYGTFT2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YQPIZ52YUXVFNMEXSF3IYGTFT2/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":"2026-06-04T20:24:24Z","links":{"resolver":"https://pith.science/pith/YQPIZ52YUXVFNMEXSF3IYGTFT2","bundle":"https://pith.science/pith/YQPIZ52YUXVFNMEXSF3IYGTFT2/bundle.json","state":"https://pith.science/pith/YQPIZ52YUXVFNMEXSF3IYGTFT2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YQPIZ52YUXVFNMEXSF3IYGTFT2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:YQPIZ52YUXVFNMEXSF3IYGTFT2","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":"9dca4fc83957ab20a496c062e12447a6889b810fff259507485e9e7e22ee949b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-04-18T17:12:37Z","title_canon_sha256":"132fb07c437154346b2156d159f46dd7a3f0f831ea4679fff39b01309a6ccceb"},"schema_version":"1.0","source":{"id":"1904.08894","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.08894","created_at":"2026-05-17T23:48:12Z"},{"alias_kind":"arxiv_version","alias_value":"1904.08894v1","created_at":"2026-05-17T23:48:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.08894","created_at":"2026-05-17T23:48:12Z"},{"alias_kind":"pith_short_12","alias_value":"YQPIZ52YUXVF","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"YQPIZ52YUXVFNMEX","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"YQPIZ52Y","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:5ea9ebbfbe928853af3d6b34437f5910c35a17955f7562d595e854adc3739990","target":"graph","created_at":"2026-05-17T23:48:12Z","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":"Many optimization problems in power transmission networks can be formulated as polynomial problems with complex variables. A polynomial optimization problem with complex variables consists in optimizing a real-valued polynomial whose variables and coefficients are complex numbers subject to some complex polynomial equality or inequality constraints. These problems are usually directly converted to real variables, either using the polar form or the rectangular form. In this work, we propose a Julia module allowing the representation of polynomial problems in their original complex formulation. ","authors_text":"Emiliano Traversi, Julie Sliwak, Lucas L\\'etocart, Manuel Ruiz, Miguel F. Anjos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-04-18T17:12:37Z","title":"A Julia Module for Polynomial Optimization with Complex Variables applied to Optimal Power Flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.08894","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":"sha256:6dfc98c89a473f3dd490a50277cf41d1e90403ce2a6363cc9bfb1ddf03fe9799","target":"record","created_at":"2026-05-17T23:48:12Z","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":"9dca4fc83957ab20a496c062e12447a6889b810fff259507485e9e7e22ee949b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-04-18T17:12:37Z","title_canon_sha256":"132fb07c437154346b2156d159f46dd7a3f0f831ea4679fff39b01309a6ccceb"},"schema_version":"1.0","source":{"id":"1904.08894","kind":"arxiv","version":1}},"canonical_sha256":"c41e8cf758a5ea56b09791768c1a659e92aa904348343eb492bc3453b4e2c616","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c41e8cf758a5ea56b09791768c1a659e92aa904348343eb492bc3453b4e2c616","first_computed_at":"2026-05-17T23:48:12.640814Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:12.640814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BFuu3BglMSLfg2QNve0CE0ogN+7zQQQJmr3GUBjk0loN1A0Oh65Q6vsn9tamJixnTfBigdr1iXNZx1ujmNHzDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:12.641437Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.08894","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6dfc98c89a473f3dd490a50277cf41d1e90403ce2a6363cc9bfb1ddf03fe9799","sha256:5ea9ebbfbe928853af3d6b34437f5910c35a17955f7562d595e854adc3739990"],"state_sha256":"e33adb318e28222fd6090797256e34ee7c7504724ee38edc0bbf0fbd27c6648a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lh9X0Y7Fy6KIwcxVZ1ZMBHkpIdtkJYtsV7WNzlzsow+6U/CtGh6cKtO+uB7LQo0i/8y85oVcmV5Kdt7TklZQAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T20:24:24.565381Z","bundle_sha256":"286726c941e63623324829f85b76aa267de6b9945bf56c7a0a9e99f4e2aef718"}}