{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:U3N55LLJAGLTHHNPCKMV72RSFE","short_pith_number":"pith:U3N55LLJ","canonical_record":{"source":{"id":"1310.2131","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-10-06T05:53:44Z","cross_cats_sorted":["math.DS","math.MP"],"title_canon_sha256":"a30d939fade24b56ef8387e8cc23c9b42c72eaf278ef2cf8c4c801704e201137","abstract_canon_sha256":"456df73f82e0cf38e4d71d938c55ab1d5ef6013ade28f84db444af24d7625589"},"schema_version":"1.0"},"canonical_sha256":"a6dbdead690197339daf12995fea32292061d2a70b7fa1ef9939f1d2d64a5013","source":{"kind":"arxiv","id":"1310.2131","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:U3N55LLJAGLTHHNPCKMV72RSFE","target":"record","payload":{"canonical_record":{"source":{"id":"1310.2131","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-10-06T05:53:44Z","cross_cats_sorted":["math.DS","math.MP"],"title_canon_sha256":"a30d939fade24b56ef8387e8cc23c9b42c72eaf278ef2cf8c4c801704e201137","abstract_canon_sha256":"456df73f82e0cf38e4d71d938c55ab1d5ef6013ade28f84db444af24d7625589"},"schema_version":"1.0"},"canonical_sha256":"a6dbdead690197339daf12995fea32292061d2a70b7fa1ef9939f1d2d64a5013","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:59.242510Z","signature_b64":"DRVougVrvitvNljBTWRlR+s/0Ru+u/Zc84WjAnaKcGAosmGxfJ4YyJAf1ygm7xYEIfvuJZ37ihiWo1Efr2VnAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6dbdead690197339daf12995fea32292061d2a70b7fa1ef9939f1d2d64a5013","last_reissued_at":"2026-05-18T03:10:59.241752Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:59.241752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.2131","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":"2026-05-18T03:10:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EaSOC9oLULeTeaGNWrI3GOY6MJ8ahUuyZTu88Bowc88m7pY5mnyDjxTpewzOZxwfPnHAIkOLlYePbSvVT8cVBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T18:55:22.070556Z"},"content_sha256":"c06f934e5c54f920c008a3c99c66b98d3af94f24794186cab3af26ac4f6a258f","schema_version":"1.0","event_id":"sha256:c06f934e5c54f920c008a3c99c66b98d3af94f24794186cab3af26ac4f6a258f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:U3N55LLJAGLTHHNPCKMV72RSFE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mechanical Systems in the Generalized Lie Algebroids Framework","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MP"],"primary_cat":"math-ph","authors_text":"Constantin M. Arcus","submitted_at":"2013-10-06T05:53:44Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2131","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":"2026-05-18T03:10:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zC4oTn4EJHqIurKeDM5E/VnpeyZAz4mLhmAHhELyv+7prA3ajZTBztJgWrGXq3EX+tCTM3ideCjh2ogyK+0fBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T18:55:22.070895Z"},"content_sha256":"48b1bd508deb28c6118ea1c8672ff05252525a9eab88529e0df2c5eaebcf4c0f","schema_version":"1.0","event_id":"sha256:48b1bd508deb28c6118ea1c8672ff05252525a9eab88529e0df2c5eaebcf4c0f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U3N55LLJAGLTHHNPCKMV72RSFE/bundle.json","state_url":"https://pith.science/pith/U3N55LLJAGLTHHNPCKMV72RSFE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U3N55LLJAGLTHHNPCKMV72RSFE/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":"2026-06-27T18:55:22Z","links":{"resolver":"https://pith.science/pith/U3N55LLJAGLTHHNPCKMV72RSFE","bundle":"https://pith.science/pith/U3N55LLJAGLTHHNPCKMV72RSFE/bundle.json","state":"https://pith.science/pith/U3N55LLJAGLTHHNPCKMV72RSFE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U3N55LLJAGLTHHNPCKMV72RSFE/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WormoDRxa++q4fhlp7lgnxIkJDVKOS5DWMdyQdMIzSLLKJub8E5Ub1cVr2Tak23dCyWZn3HaFPn3cjoY1K4JCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T18:55:22.072787Z","bundle_sha256":"089c11a001d6294e958421dd90ef62b1693e1d3735e99a3f5c9ed8bb279870cf"}}