{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5CQO2Q3SH7J5HKEUCBM5VDNRZL","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":"f112fbb69b680b7165d058cba7ae2c49d097a964fe93c2465fdea973d14270f0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.DS","submitted_at":"2012-05-10T14:59:58Z","title_canon_sha256":"61ec475c939000acc97477c29b4213bf0782ede3ae82e203c6dd665f5e868d20"},"schema_version":"1.0","source":{"id":"1205.2285","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2285","created_at":"2026-05-18T03:01:11Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2285v2","created_at":"2026-05-18T03:01:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2285","created_at":"2026-05-18T03:01:11Z"},{"alias_kind":"pith_short_12","alias_value":"5CQO2Q3SH7J5","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5CQO2Q3SH7J5HKEU","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5CQO2Q3S","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:851849c46193c9d7513c9ba84d17746975254a975290dd7de5e4dbb33c26143b","target":"graph","created_at":"2026-05-18T03:01:11Z","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":"We consider AC electrical systems where each electrical device has a power demand expressed as a complex number, and there is a limit on the magnitude of total power supply. Motivated by this scenario, we introduce the complex-demand knapsack problem (C-KP), a new variation of the traditional knapsack problem, where each item is associated with a demand as a complex number, rather than a real number often interpreted as weight or size of the item. While keeping the same goal as to maximize the sum of values of the selected items, we put the capacity limit on the magnitude of the sum of satisfi","authors_text":"Chi-Kin Chau, Lan Yu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.DS","submitted_at":"2012-05-10T14:59:58Z","title":"Complex-Demand Knapsack Problems and Incentives in AC Power Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2285","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":"sha256:9972953981b76e3a200c779b09587298574d446f4304dbbb57539895bb440f8b","target":"record","created_at":"2026-05-18T03:01:11Z","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":"f112fbb69b680b7165d058cba7ae2c49d097a964fe93c2465fdea973d14270f0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.DS","submitted_at":"2012-05-10T14:59:58Z","title_canon_sha256":"61ec475c939000acc97477c29b4213bf0782ede3ae82e203c6dd665f5e868d20"},"schema_version":"1.0","source":{"id":"1205.2285","kind":"arxiv","version":2}},"canonical_sha256":"e8a0ed43723fd3d3a8941059da8db1cadfd8b52b90e07b830360f9d76f9869bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8a0ed43723fd3d3a8941059da8db1cadfd8b52b90e07b830360f9d76f9869bd","first_computed_at":"2026-05-18T03:01:11.261471Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:11.261471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ii2uZ6CddbBEamtKOhLdgsnAtHMroproltRIn3ZSYoPZBtKuulCrYmls3eAHrrUN9QukHhJyGeJwHN0zObOSDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:11.262169Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.2285","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9972953981b76e3a200c779b09587298574d446f4304dbbb57539895bb440f8b","sha256:851849c46193c9d7513c9ba84d17746975254a975290dd7de5e4dbb33c26143b"],"state_sha256":"00e263b59cb9158c0c7e1bc248f119d15139df595138f0efdd367ecb54ee3794"}