{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:7NPBUXT3UAUPIENSO7W2M7AJVQ","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":"9b6b2170d5855d7ba7e04f601e81c18c12257acf59afd578e4d0970557c69cdb","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-12-19T13:02:25Z","title_canon_sha256":"178e014796dbba3c080ffa19e4fe2ed7c64ea43e54da2cea3da124d6c7bda9c4"},"schema_version":"1.0","source":{"id":"2212.09427","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.09427","created_at":"2026-07-05T08:40:51Z"},{"alias_kind":"arxiv_version","alias_value":"2212.09427v1","created_at":"2026-07-05T08:40:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.09427","created_at":"2026-07-05T08:40:51Z"},{"alias_kind":"pith_short_12","alias_value":"7NPBUXT3UAUP","created_at":"2026-07-05T08:40:51Z"},{"alias_kind":"pith_short_16","alias_value":"7NPBUXT3UAUPIENS","created_at":"2026-07-05T08:40:51Z"},{"alias_kind":"pith_short_8","alias_value":"7NPBUXT3","created_at":"2026-07-05T08:40:51Z"}],"graph_snapshots":[{"event_id":"sha256:255c14be75f9a4f00cc6e1d949bde6fb5e626c5553b1c048a6df9936b9ff11a5","target":"graph","created_at":"2026-07-05T08:40:51Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2212.09427/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Motivated by the time-dependent Hamiltonian dynamics, we extend the notion of Arnold-Liouville and noncommutative integrability of Hamiltonian systems on symplectic manifolds to that on cosymplectic manifolds. We prove a variant of the non-commutative integrability for evaluation and Reeb vector fields on cosymplectic manifolds and provide a construction of cosymplectic action-angle variables.","authors_text":"Bozidar Jovanovic, Katarina Lukic","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-12-19T13:02:25Z","title":"Integrable systems in cosymplectic geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.09427","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":"sha256:985175dc4bf183b0094ef7ca6320a309fe005ee7ec8082d2dd3ac2d8acf49090","target":"record","created_at":"2026-07-05T08:40:51Z","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":"9b6b2170d5855d7ba7e04f601e81c18c12257acf59afd578e4d0970557c69cdb","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-12-19T13:02:25Z","title_canon_sha256":"178e014796dbba3c080ffa19e4fe2ed7c64ea43e54da2cea3da124d6c7bda9c4"},"schema_version":"1.0","source":{"id":"2212.09427","kind":"arxiv","version":1}},"canonical_sha256":"fb5e1a5e7ba028f411b277eda67c09ac27993b3dcc3eeeb6a980a9ff48dad4e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb5e1a5e7ba028f411b277eda67c09ac27993b3dcc3eeeb6a980a9ff48dad4e4","first_computed_at":"2026-07-05T08:40:51.919012Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:40:51.919012Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jy7NLr+VzWRD7S/7iNZz+UjqIJCq6wNlC/zmGuz9UXUzwW1Z3bAqzmFPjm251mRFr8UbwN+RW8mtzL1UbzwbAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:40:51.919428Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.09427","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:985175dc4bf183b0094ef7ca6320a309fe005ee7ec8082d2dd3ac2d8acf49090","sha256:255c14be75f9a4f00cc6e1d949bde6fb5e626c5553b1c048a6df9936b9ff11a5"],"state_sha256":"332b668ad5ad128293ff5784a18fc81da1baf5475f74363210e6539f1ff1cd31"}