{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:BOIYXLDDA3YYCOKHO2JV2VUSO5","short_pith_number":"pith:BOIYXLDD","canonical_record":{"source":{"id":"1807.07227","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-07-19T03:34:55Z","cross_cats_sorted":[],"title_canon_sha256":"ee58b9d2857f119d61b44eef1871622adad1c089f6960861c64d820e9fa0cb39","abstract_canon_sha256":"f0f578d254a92de89a1d18ec211131d9c2670acdf2b591c8c29113c9d1bf486b"},"schema_version":"1.0"},"canonical_sha256":"0b918bac6306f181394776935d569277753a8610afb38eced1483867617f0324","source":{"kind":"arxiv","id":"1807.07227","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.07227","created_at":"2026-05-18T00:10:20Z"},{"alias_kind":"arxiv_version","alias_value":"1807.07227v1","created_at":"2026-05-18T00:10:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.07227","created_at":"2026-05-18T00:10:20Z"},{"alias_kind":"pith_short_12","alias_value":"BOIYXLDDA3YY","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BOIYXLDDA3YYCOKH","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BOIYXLDD","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:BOIYXLDDA3YYCOKHO2JV2VUSO5","target":"record","payload":{"canonical_record":{"source":{"id":"1807.07227","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-07-19T03:34:55Z","cross_cats_sorted":[],"title_canon_sha256":"ee58b9d2857f119d61b44eef1871622adad1c089f6960861c64d820e9fa0cb39","abstract_canon_sha256":"f0f578d254a92de89a1d18ec211131d9c2670acdf2b591c8c29113c9d1bf486b"},"schema_version":"1.0"},"canonical_sha256":"0b918bac6306f181394776935d569277753a8610afb38eced1483867617f0324","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:20.844036Z","signature_b64":"SKiD32x8QiO5f4bIvRvwaxMHgFS5s8cvA66jnHaIC9qj3ijYWzSExC+mQrhlIllQqXhdfdMznhGRI2EVSWMYCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b918bac6306f181394776935d569277753a8610afb38eced1483867617f0324","last_reissued_at":"2026-05-18T00:10:20.843485Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:20.843485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.07227","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":"2026-05-18T00:10:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wr0p/ClqUELKWOvWT+tAPpCl65xDyfHMnyrqahu2pvKNKJYLOVn0X0rIPAZVf03g7GkAa7SFh7TqM12S1MA2Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:41:51.798814Z"},"content_sha256":"0fa5fc7dbceead09d85eb0d031758461dc3966a423c6bf3ca543b9f7d6ee20e8","schema_version":"1.0","event_id":"sha256:0fa5fc7dbceead09d85eb0d031758461dc3966a423c6bf3ca543b9f7d6ee20e8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:BOIYXLDDA3YYCOKHO2JV2VUSO5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convex Relaxations in Power System Optimization: A Brief Introduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Carleton Coffrin, Line Roald","submitted_at":"2018-07-19T03:34:55Z","abstract_excerpt":"Convex relaxations of the AC power flow equations have attracted significant interest in the power systems research community in recent years. The following collection of video lectures provides a brief introduction to the mathematics of AC power systems, continuous nonlinear optimization, and relaxations of the power flow equations. The aim of the videos is to provide the high level ideas of convex relaxations and their applications in power system optimization, and could be used as a starting point for researchers who want to study, use or develop new convex relaxations for use in their own "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07227","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":"2026-05-18T00:10:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YMBwJdWy/ldbaMTaxpd3+R+wjcSsmkM5boVHH3jNWzYisV/RppPO3UFL2UbyWa7OqtCePBXuskRD2B/8g6KuAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:41:51.799159Z"},"content_sha256":"763525105a6c650046325861bafcd2a933c2eb8653200b2cc0bfe5e0b34b5611","schema_version":"1.0","event_id":"sha256:763525105a6c650046325861bafcd2a933c2eb8653200b2cc0bfe5e0b34b5611"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BOIYXLDDA3YYCOKHO2JV2VUSO5/bundle.json","state_url":"https://pith.science/pith/BOIYXLDDA3YYCOKHO2JV2VUSO5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BOIYXLDDA3YYCOKHO2JV2VUSO5/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":"2026-06-03T09:41:51Z","links":{"resolver":"https://pith.science/pith/BOIYXLDDA3YYCOKHO2JV2VUSO5","bundle":"https://pith.science/pith/BOIYXLDDA3YYCOKHO2JV2VUSO5/bundle.json","state":"https://pith.science/pith/BOIYXLDDA3YYCOKHO2JV2VUSO5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BOIYXLDDA3YYCOKHO2JV2VUSO5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BOIYXLDDA3YYCOKHO2JV2VUSO5","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":"f0f578d254a92de89a1d18ec211131d9c2670acdf2b591c8c29113c9d1bf486b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-07-19T03:34:55Z","title_canon_sha256":"ee58b9d2857f119d61b44eef1871622adad1c089f6960861c64d820e9fa0cb39"},"schema_version":"1.0","source":{"id":"1807.07227","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.07227","created_at":"2026-05-18T00:10:20Z"},{"alias_kind":"arxiv_version","alias_value":"1807.07227v1","created_at":"2026-05-18T00:10:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.07227","created_at":"2026-05-18T00:10:20Z"},{"alias_kind":"pith_short_12","alias_value":"BOIYXLDDA3YY","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BOIYXLDDA3YYCOKH","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BOIYXLDD","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:763525105a6c650046325861bafcd2a933c2eb8653200b2cc0bfe5e0b34b5611","target":"graph","created_at":"2026-05-18T00:10:20Z","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":"Convex relaxations of the AC power flow equations have attracted significant interest in the power systems research community in recent years. The following collection of video lectures provides a brief introduction to the mathematics of AC power systems, continuous nonlinear optimization, and relaxations of the power flow equations. The aim of the videos is to provide the high level ideas of convex relaxations and their applications in power system optimization, and could be used as a starting point for researchers who want to study, use or develop new convex relaxations for use in their own ","authors_text":"Carleton Coffrin, Line Roald","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-07-19T03:34:55Z","title":"Convex Relaxations in Power System Optimization: A Brief Introduction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07227","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":"sha256:0fa5fc7dbceead09d85eb0d031758461dc3966a423c6bf3ca543b9f7d6ee20e8","target":"record","created_at":"2026-05-18T00:10:20Z","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":"f0f578d254a92de89a1d18ec211131d9c2670acdf2b591c8c29113c9d1bf486b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-07-19T03:34:55Z","title_canon_sha256":"ee58b9d2857f119d61b44eef1871622adad1c089f6960861c64d820e9fa0cb39"},"schema_version":"1.0","source":{"id":"1807.07227","kind":"arxiv","version":1}},"canonical_sha256":"0b918bac6306f181394776935d569277753a8610afb38eced1483867617f0324","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b918bac6306f181394776935d569277753a8610afb38eced1483867617f0324","first_computed_at":"2026-05-18T00:10:20.843485Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:20.843485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SKiD32x8QiO5f4bIvRvwaxMHgFS5s8cvA66jnHaIC9qj3ijYWzSExC+mQrhlIllQqXhdfdMznhGRI2EVSWMYCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:20.844036Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.07227","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0fa5fc7dbceead09d85eb0d031758461dc3966a423c6bf3ca543b9f7d6ee20e8","sha256:763525105a6c650046325861bafcd2a933c2eb8653200b2cc0bfe5e0b34b5611"],"state_sha256":"078269b2283e2cf45a50fe8c252be3c0a73770acf2d36700b6e66c18b53fa50f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D76e6ZKQQYfZNDSAh2XFkxe6oOWVMq+CMzR8/cl+ySCPlxXJIqC6+ZjG4G0yBCF5T4BCWcM5wBEdu7nTFr0hBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T09:41:51.801156Z","bundle_sha256":"883fef45fd3d311710d9110c922fef60bd53d9f1f5f959aa7658f282faf5358c"}}