{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NCIW6IFM6UWT47Q3LRZDLBXFQY","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":"bb0bf7ef0eb562a5e807ffab1527b643ba7f131afca5f4d42c81c157587906ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-05-18T11:58:05Z","title_canon_sha256":"d0b06c0d5e8185a82b9081159cad9cc82337fe862c6ecf9927f59981bdddbc34"},"schema_version":"1.0","source":{"id":"1605.05534","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.05534","created_at":"2026-05-18T01:11:43Z"},{"alias_kind":"arxiv_version","alias_value":"1605.05534v3","created_at":"2026-05-18T01:11:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05534","created_at":"2026-05-18T01:11:43Z"},{"alias_kind":"pith_short_12","alias_value":"NCIW6IFM6UWT","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NCIW6IFM6UWT47Q3","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NCIW6IFM","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:a7e681a6795196b6e588c97a19f5563fb512d6578f0bcb5cac9070750898651f","target":"graph","created_at":"2026-05-18T01:11:43Z","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":"A unified model is addressed for general optimization problems in multi-scale complex systems. Based on necessary conditions and basic principles in physics, the canonical duality-triality theory is presented in a precise way to include traditional duality theories and popular methods as special applications. Two conjectures on NP-hardness are discussed, which should play important roles for correctly understanding and efficiently solving challenging real-world problems. Applications are illustrated for both nonconvex continuous optimization and mixed integer nonlinear programming. Misundersta","authors_text":"David Yang Gao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-05-18T11:58:05Z","title":"On Unified Modeling, Canonical Duality-Triality Theory, Challenges and Breakthrough in Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05534","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":"sha256:97bacb5448f670b6183996cadc18a93df27a4d25a768dbf340cdd15d752e943a","target":"record","created_at":"2026-05-18T01:11:43Z","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":"bb0bf7ef0eb562a5e807ffab1527b643ba7f131afca5f4d42c81c157587906ef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-05-18T11:58:05Z","title_canon_sha256":"d0b06c0d5e8185a82b9081159cad9cc82337fe862c6ecf9927f59981bdddbc34"},"schema_version":"1.0","source":{"id":"1605.05534","kind":"arxiv","version":3}},"canonical_sha256":"68916f20acf52d3e7e1b5c723586e5863af07301ddf23d6bdd66e053e0707834","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68916f20acf52d3e7e1b5c723586e5863af07301ddf23d6bdd66e053e0707834","first_computed_at":"2026-05-18T01:11:43.466569Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:43.466569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3b8E/ZH/NaXxUXSbrUMXZDa/Xw/ZULhiK0Iv2Q1BeBMUaFndAB0Tlls6ZZN0cYZX8eMm/qt+U428deR9oLQRDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:43.466926Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.05534","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97bacb5448f670b6183996cadc18a93df27a4d25a768dbf340cdd15d752e943a","sha256:a7e681a6795196b6e588c97a19f5563fb512d6578f0bcb5cac9070750898651f"],"state_sha256":"b04e39deaa2fea6ba8bf189517a0f705785b1e6eeca013fb9c08795d6d9b339a"}