{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:U3N55LLJAGLTHHNPCKMV72RSFE","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":"456df73f82e0cf38e4d71d938c55ab1d5ef6013ade28f84db444af24d7625589","cross_cats_sorted":["math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-10-06T05:53:44Z","title_canon_sha256":"a30d939fade24b56ef8387e8cc23c9b42c72eaf278ef2cf8c4c801704e201137"},"schema_version":"1.0","source":{"id":"1310.2131","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.2131","created_at":"2026-05-18T03:10:59Z"},{"alias_kind":"arxiv_version","alias_value":"1310.2131v1","created_at":"2026-05-18T03:10:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2131","created_at":"2026-05-18T03:10:59Z"},{"alias_kind":"pith_short_12","alias_value":"U3N55LLJAGLT","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U3N55LLJAGLTHHNP","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U3N55LLJ","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:48b1bd508deb28c6118ea1c8672ff05252525a9eab88529e0df2c5eaebcf4c0f","target":"graph","created_at":"2026-05-18T03:10:59Z","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":"\\emph{Mechanical systems} called by use, \\emph{mechanical}$\\left(\\rho ,\\eta\\right) $\\emph{-systems, Lagrange mechanical}$\\left(\\rho ,\\eta \\right) $\\emph{-systems} or \\emph{Finsler mechanical}$\\left(\\rho ,\\eta \\right) $\\emph{-systems} are presented. The canonical $\\left(\\rho ,\\eta \\right) $\\emph{-}semi(spray) associated to a mechanical $\\left(\\rho ,\\eta \\right) $-system is obtained. New and important results are obtained in the particular case of Lie algebroids. The Lagrange mechanical $(\\rho ,\\eta)$% -systems are the spaces necessary to develop a new Lagrangian formalism. We obtain the $(\\rho ","authors_text":"Constantin M. Arcus","cross_cats":["math.DS","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-10-06T05:53:44Z","title":"Mechanical Systems in the Generalized Lie Algebroids Framework"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2131","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:c06f934e5c54f920c008a3c99c66b98d3af94f24794186cab3af26ac4f6a258f","target":"record","created_at":"2026-05-18T03:10:59Z","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":"456df73f82e0cf38e4d71d938c55ab1d5ef6013ade28f84db444af24d7625589","cross_cats_sorted":["math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-10-06T05:53:44Z","title_canon_sha256":"a30d939fade24b56ef8387e8cc23c9b42c72eaf278ef2cf8c4c801704e201137"},"schema_version":"1.0","source":{"id":"1310.2131","kind":"arxiv","version":1}},"canonical_sha256":"a6dbdead690197339daf12995fea32292061d2a70b7fa1ef9939f1d2d64a5013","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6dbdead690197339daf12995fea32292061d2a70b7fa1ef9939f1d2d64a5013","first_computed_at":"2026-05-18T03:10:59.241752Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:59.241752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DRVougVrvitvNljBTWRlR+s/0Ru+u/Zc84WjAnaKcGAosmGxfJ4YyJAf1ygm7xYEIfvuJZ37ihiWo1Efr2VnAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:59.242510Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.2131","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c06f934e5c54f920c008a3c99c66b98d3af94f24794186cab3af26ac4f6a258f","sha256:48b1bd508deb28c6118ea1c8672ff05252525a9eab88529e0df2c5eaebcf4c0f"],"state_sha256":"ced2abb0914a75b5ca6fcfd88bc97c57e3abb25b9ee4ca1d172743a643cd4e89"}