{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:WFXWAIARC74N2DGGXZQHBJ3TL2","short_pith_number":"pith:WFXWAIAR","canonical_record":{"source":{"id":"1512.08343","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-12-28T08:40:02Z","cross_cats_sorted":[],"title_canon_sha256":"16a6361699fe6c87fb2aef5924942e936c8fe16e983e81b1f2144f536b155edc","abstract_canon_sha256":"418ffb063968de8807c46a54092bce706dafd844283f43c0d036696f550f459e"},"schema_version":"1.0"},"canonical_sha256":"b16f60201117f8dd0cc6be6070a7735e94f25065765f3a8e8c4ed30046b3aef8","source":{"kind":"arxiv","id":"1512.08343","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08343","created_at":"2026-05-18T01:08:18Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08343v1","created_at":"2026-05-18T01:08:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08343","created_at":"2026-05-18T01:08:18Z"},{"alias_kind":"pith_short_12","alias_value":"WFXWAIARC74N","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WFXWAIARC74N2DGG","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WFXWAIAR","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:WFXWAIARC74N2DGGXZQHBJ3TL2","target":"record","payload":{"canonical_record":{"source":{"id":"1512.08343","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-12-28T08:40:02Z","cross_cats_sorted":[],"title_canon_sha256":"16a6361699fe6c87fb2aef5924942e936c8fe16e983e81b1f2144f536b155edc","abstract_canon_sha256":"418ffb063968de8807c46a54092bce706dafd844283f43c0d036696f550f459e"},"schema_version":"1.0"},"canonical_sha256":"b16f60201117f8dd0cc6be6070a7735e94f25065765f3a8e8c4ed30046b3aef8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:18.788555Z","signature_b64":"vyK1+YwETr0ExOmxXHHgMGOmbLWQBQEFATNTZXGBPM6i1SM2ZkJ9PZCkg0oBeYQt8rrelbcQAKEHSuMvTjwOBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b16f60201117f8dd0cc6be6070a7735e94f25065765f3a8e8c4ed30046b3aef8","last_reissued_at":"2026-05-18T01:08:18.787984Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:18.787984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.08343","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":"2026-05-18T01:08:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cOjBDGQwwNTNRNNCTBB/oizRxB+H5rkxMAN7uTLN+AyKgWt4SLpwEZKsb9s187So5MQ7d+1yYkHfzC5pF8c6Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:18:56.019041Z"},"content_sha256":"395bd78136f844d922904e8af11ddefd3e908128d42deee26fde8fb199fc32c5","schema_version":"1.0","event_id":"sha256:395bd78136f844d922904e8af11ddefd3e908128d42deee26fde8fb199fc32c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:WFXWAIARC74N2DGGXZQHBJ3TL2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global Optimal Trajectory in Chaos and NP-Hardness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"David Yang Gao, Vittorio Latorre","submitted_at":"2015-12-28T08:40:02Z","abstract_excerpt":"This paper presents a new canonical duality methodology for solving general nonlinear dynamical systems. Instead of the conventional iterative methods, the discretized nonlinear system is first formulated as a global optimization problem via the least squares method. The canonical duality theory shows that this nonconvex minimization problem can be solved deterministically in polynomial time if a global optimality condition is satisfied. The so-called pseudo-chaos produced by Runge-Kutta type of linear iterations are mainly due to the intrinsic numerical error accumulations. Otherwise, the glo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08343","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":"2026-05-18T01:08:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e6zfXlQlTxt83doiyfbQEtli0noYOqOK79oQMfUO2H7lAUWKJ9GylESK1MPmtZizOEJ3Ap8SPOp99giBbNmKBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:18:56.019390Z"},"content_sha256":"558782550de9cc1c9403bb142a544f4d82737d58b66c1b34686b3ef329e01736","schema_version":"1.0","event_id":"sha256:558782550de9cc1c9403bb142a544f4d82737d58b66c1b34686b3ef329e01736"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WFXWAIARC74N2DGGXZQHBJ3TL2/bundle.json","state_url":"https://pith.science/pith/WFXWAIARC74N2DGGXZQHBJ3TL2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WFXWAIARC74N2DGGXZQHBJ3TL2/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":"2026-06-23T16:18:56Z","links":{"resolver":"https://pith.science/pith/WFXWAIARC74N2DGGXZQHBJ3TL2","bundle":"https://pith.science/pith/WFXWAIARC74N2DGGXZQHBJ3TL2/bundle.json","state":"https://pith.science/pith/WFXWAIARC74N2DGGXZQHBJ3TL2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WFXWAIARC74N2DGGXZQHBJ3TL2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WFXWAIARC74N2DGGXZQHBJ3TL2","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":"418ffb063968de8807c46a54092bce706dafd844283f43c0d036696f550f459e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-12-28T08:40:02Z","title_canon_sha256":"16a6361699fe6c87fb2aef5924942e936c8fe16e983e81b1f2144f536b155edc"},"schema_version":"1.0","source":{"id":"1512.08343","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08343","created_at":"2026-05-18T01:08:18Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08343v1","created_at":"2026-05-18T01:08:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08343","created_at":"2026-05-18T01:08:18Z"},{"alias_kind":"pith_short_12","alias_value":"WFXWAIARC74N","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WFXWAIARC74N2DGG","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WFXWAIAR","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:558782550de9cc1c9403bb142a544f4d82737d58b66c1b34686b3ef329e01736","target":"graph","created_at":"2026-05-18T01:08:18Z","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 presents a new canonical duality methodology for solving general nonlinear dynamical systems. Instead of the conventional iterative methods, the discretized nonlinear system is first formulated as a global optimization problem via the least squares method. The canonical duality theory shows that this nonconvex minimization problem can be solved deterministically in polynomial time if a global optimality condition is satisfied. The so-called pseudo-chaos produced by Runge-Kutta type of linear iterations are mainly due to the intrinsic numerical error accumulations. Otherwise, the glo","authors_text":"David Yang Gao, Vittorio Latorre","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-12-28T08:40:02Z","title":"Global Optimal Trajectory in Chaos and NP-Hardness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08343","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":"sha256:395bd78136f844d922904e8af11ddefd3e908128d42deee26fde8fb199fc32c5","target":"record","created_at":"2026-05-18T01:08:18Z","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":"418ffb063968de8807c46a54092bce706dafd844283f43c0d036696f550f459e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-12-28T08:40:02Z","title_canon_sha256":"16a6361699fe6c87fb2aef5924942e936c8fe16e983e81b1f2144f536b155edc"},"schema_version":"1.0","source":{"id":"1512.08343","kind":"arxiv","version":1}},"canonical_sha256":"b16f60201117f8dd0cc6be6070a7735e94f25065765f3a8e8c4ed30046b3aef8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b16f60201117f8dd0cc6be6070a7735e94f25065765f3a8e8c4ed30046b3aef8","first_computed_at":"2026-05-18T01:08:18.787984Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:18.787984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vyK1+YwETr0ExOmxXHHgMGOmbLWQBQEFATNTZXGBPM6i1SM2ZkJ9PZCkg0oBeYQt8rrelbcQAKEHSuMvTjwOBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:18.788555Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.08343","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:395bd78136f844d922904e8af11ddefd3e908128d42deee26fde8fb199fc32c5","sha256:558782550de9cc1c9403bb142a544f4d82737d58b66c1b34686b3ef329e01736"],"state_sha256":"b164b8fe281dc8642741123dc638c32dba2fcaef07095ff76255fc97965dfd08"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ih5OjhmK5jt9C0V3XE8yVxbm/+Z+OtSZQQxQjqmFGFu1XcEr2dH0yzxGwKdQCbNVJRjj2fLvgMeE8hm/yUrfCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T16:18:56.021264Z","bundle_sha256":"c09faabfdbd6e62b5f59d51322393ef8a3c815b4dd9e91635c7bd202490cf3e9"}}