{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YGPP64O2HKXLCXSNSZOXD2CSDL","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":"56090b5be6397512816de17299029e3ae93f362069339a9ed70cf3736a5667c9","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-10-25T09:43:54Z","title_canon_sha256":"f0c1d440b8fdbeb38233ba3fcbe3eaba96027a1be2bf666dbd3c6af71c251791"},"schema_version":"1.0","source":{"id":"1210.6773","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.6773","created_at":"2026-05-18T03:42:23Z"},{"alias_kind":"arxiv_version","alias_value":"1210.6773v1","created_at":"2026-05-18T03:42:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6773","created_at":"2026-05-18T03:42:23Z"},{"alias_kind":"pith_short_12","alias_value":"YGPP64O2HKXL","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"YGPP64O2HKXLCXSN","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"YGPP64O2","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:ccaa3900f2cbcb06ddb87da5da7abc4eeb40a68ea57dd9f42bb10e6409bb3978","target":"graph","created_at":"2026-05-18T03:42:23Z","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":"Pontryagin's Maximum Principle is an outstanding result for solving optimal control problems by means of optimizing a specific function on some particular variables, the so called controls. However, this is not always enough for solving all these problems. A high order maximum principle (Krener, 1977) must be used in order to obtain more necessary conditions for optimality. These new conditions determine candidates to be optimal controls for a wider range of optimal control problems.\n  Here, we focus on control-affine systems. Krener's high order perturbations are redefined following the notio","authors_text":"M. Barbero-Li\\~n\\'an, M. C. Mu\\~noz-Lecanda","cross_cats":["math-ph","math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-10-25T09:43:54Z","title":"Presymplectic high order maximum principle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6773","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":"sha256:0987cf7df3e71cbcfacdc97ac90faa50997649f497a5d4d4b3d9d5f78132a1cd","target":"record","created_at":"2026-05-18T03:42:23Z","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":"56090b5be6397512816de17299029e3ae93f362069339a9ed70cf3736a5667c9","cross_cats_sorted":["math-ph","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-10-25T09:43:54Z","title_canon_sha256":"f0c1d440b8fdbeb38233ba3fcbe3eaba96027a1be2bf666dbd3c6af71c251791"},"schema_version":"1.0","source":{"id":"1210.6773","kind":"arxiv","version":1}},"canonical_sha256":"c19eff71da3aaeb15e4d965d71e8521af67eba796b06ff7cac080fb0cb3a4d8b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c19eff71da3aaeb15e4d965d71e8521af67eba796b06ff7cac080fb0cb3a4d8b","first_computed_at":"2026-05-18T03:42:23.177749Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:23.177749Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"txkZCuH0Y/A/mDxIHpYceHBAE182+gQIJuwmRo8X3+/K/xFBeSqVOfBSab+PuPxRmjlnAMNfumZ69lh1SQi5DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:23.178568Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.6773","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0987cf7df3e71cbcfacdc97ac90faa50997649f497a5d4d4b3d9d5f78132a1cd","sha256:ccaa3900f2cbcb06ddb87da5da7abc4eeb40a68ea57dd9f42bb10e6409bb3978"],"state_sha256":"d8158ec85ede9bf1b0556aa9f5da94e65bdaa1b048f21d770b1a965f55194f2d"}