{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:MG2DR67MJ2DAX45HDA56ADHCTW","short_pith_number":"pith:MG2DR67M","schema_version":"1.0","canonical_sha256":"61b438fbec4e860bf3a7183be00ce29dabba9981b5758a50f09c9ab2141e76ca","source":{"kind":"arxiv","id":"1506.08580","version":1},"attestation_state":"computed","paper":{"title":"Second-order variational problems on Lie groupoids and optimal control applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.OC","math.SG"],"primary_cat":"math.DS","authors_text":"David Martin de Diego, Leonardo Colombo","submitted_at":"2015-06-29T11:04:24Z","abstract_excerpt":"In this paper we study, from a variational and geometrical point of view, second-order variational problems on Lie groupoids and the construction of variational integrators for optimal control problems. First, we develop variational techniques for second-order variational problems on Lie groupoids and their applications to the construction of variational integrators for optimal control problems of mechanical systems. Next, we show how Lagrangian submanifolds of a symplectic groupoid gives intrinsically the discrete dynamics for second-order systems, both unconstrained and constrained, and we s"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1506.08580","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-06-29T11:04:24Z","cross_cats_sorted":["math-ph","math.MP","math.OC","math.SG"],"title_canon_sha256":"9c090f9cb37738b3262a3129b82348f54c7809abaf1ee66bdedee9f4dc05aa1a","abstract_canon_sha256":"2bd2494df789c5ff31b9befcf8791b91ba8ccb0fc21a7a1481e714ced7e70850"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:43.897119Z","signature_b64":"B9q4S3Atc8Sln15U1PbNsmi+/BdeIZEmWyEAYLJy9DBp+OM8VWL0Pn6wcoXQXZbkfPwI7s2QIyTvILCeY9EiAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61b438fbec4e860bf3a7183be00ce29dabba9981b5758a50f09c9ab2141e76ca","last_reissued_at":"2026-05-18T01:37:43.896630Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:43.896630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Second-order variational problems on Lie groupoids and optimal control applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.OC","math.SG"],"primary_cat":"math.DS","authors_text":"David Martin de Diego, Leonardo Colombo","submitted_at":"2015-06-29T11:04:24Z","abstract_excerpt":"In this paper we study, from a variational and geometrical point of view, second-order variational problems on Lie groupoids and the construction of variational integrators for optimal control problems. First, we develop variational techniques for second-order variational problems on Lie groupoids and their applications to the construction of variational integrators for optimal control problems of mechanical systems. Next, we show how Lagrangian submanifolds of a symplectic groupoid gives intrinsically the discrete dynamics for second-order systems, both unconstrained and constrained, and we s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08580","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1506.08580","created_at":"2026-05-18T01:37:43.896708+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.08580v1","created_at":"2026-05-18T01:37:43.896708+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.08580","created_at":"2026-05-18T01:37:43.896708+00:00"},{"alias_kind":"pith_short_12","alias_value":"MG2DR67MJ2DA","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"MG2DR67MJ2DAX45H","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"MG2DR67M","created_at":"2026-05-18T12:29:32.376354+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MG2DR67MJ2DAX45HDA56ADHCTW","json":"https://pith.science/pith/MG2DR67MJ2DAX45HDA56ADHCTW.json","graph_json":"https://pith.science/api/pith-number/MG2DR67MJ2DAX45HDA56ADHCTW/graph.json","events_json":"https://pith.science/api/pith-number/MG2DR67MJ2DAX45HDA56ADHCTW/events.json","paper":"https://pith.science/paper/MG2DR67M"},"agent_actions":{"view_html":"https://pith.science/pith/MG2DR67MJ2DAX45HDA56ADHCTW","download_json":"https://pith.science/pith/MG2DR67MJ2DAX45HDA56ADHCTW.json","view_paper":"https://pith.science/paper/MG2DR67M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.08580&json=true","fetch_graph":"https://pith.science/api/pith-number/MG2DR67MJ2DAX45HDA56ADHCTW/graph.json","fetch_events":"https://pith.science/api/pith-number/MG2DR67MJ2DAX45HDA56ADHCTW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MG2DR67MJ2DAX45HDA56ADHCTW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MG2DR67MJ2DAX45HDA56ADHCTW/action/storage_attestation","attest_author":"https://pith.science/pith/MG2DR67MJ2DAX45HDA56ADHCTW/action/author_attestation","sign_citation":"https://pith.science/pith/MG2DR67MJ2DAX45HDA56ADHCTW/action/citation_signature","submit_replication":"https://pith.science/pith/MG2DR67MJ2DAX45HDA56ADHCTW/action/replication_record"}},"created_at":"2026-05-18T01:37:43.896708+00:00","updated_at":"2026-05-18T01:37:43.896708+00:00"}