{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:PDB5NGVCMUVWGODSLTBZSWCCKL","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":"11400f659d4f68f625f44d0906f28667b3db25a6ce631241d156f822b54343b0","cross_cats_sorted":["math.DG","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-11-04T09:47:50Z","title_canon_sha256":"b04780b2845b104983e3ccf0c5d5ec85699c36462cf39fec4e3f94c8a56506d0"},"schema_version":"1.0","source":{"id":"1911.01094","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.01094","created_at":"2026-07-05T00:16:45Z"},{"alias_kind":"arxiv_version","alias_value":"1911.01094v1","created_at":"2026-07-05T00:16:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.01094","created_at":"2026-07-05T00:16:45Z"},{"alias_kind":"pith_short_12","alias_value":"PDB5NGVCMUVW","created_at":"2026-07-05T00:16:45Z"},{"alias_kind":"pith_short_16","alias_value":"PDB5NGVCMUVWGODS","created_at":"2026-07-05T00:16:45Z"},{"alias_kind":"pith_short_8","alias_value":"PDB5NGVC","created_at":"2026-07-05T00:16:45Z"}],"graph_snapshots":[{"event_id":"sha256:e2d8230d60b67d8d1769bc7fddadac07a9066c929748b74373922fd72194caa5","target":"graph","created_at":"2026-07-05T00:16:45Z","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/1911.01094/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper provides a geometric description for Lie--Hamilton systems on $\\mathbb{R}^2$ with locally transitive Vessiot--Guldberg Lie algebras through two types of geometric models. The first one is the restriction of a class of Lie--Hamilton systems on the dual of a Lie algebra to even-dimensional symplectic leaves relative to the Kirillov-Kostant-Souriau bracket. The second is a projection onto a quotient space of an automorphic Lie--Hamilton system relative to a naturally defined Poisson structure or, more generally, an automorphic Lie system with a compatible bivector field. These models g","authors_text":"J. de Lucas, J. Lange","cross_cats":["math.DG","math.MP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-11-04T09:47:50Z","title":"Geometric models for Lie--Hamilton systems on $\\mathbb{R}^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.01094","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":"sha256:5e9643f239fbba16f09282cbf3cc0ad4aea413f142eac3117ebd6993e0236caf","target":"record","created_at":"2026-07-05T00:16:45Z","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":"11400f659d4f68f625f44d0906f28667b3db25a6ce631241d156f822b54343b0","cross_cats_sorted":["math.DG","math.MP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-11-04T09:47:50Z","title_canon_sha256":"b04780b2845b104983e3ccf0c5d5ec85699c36462cf39fec4e3f94c8a56506d0"},"schema_version":"1.0","source":{"id":"1911.01094","kind":"arxiv","version":1}},"canonical_sha256":"78c3d69aa2652b6338725cc399584252ee6358ed7b045960950496dc343167e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78c3d69aa2652b6338725cc399584252ee6358ed7b045960950496dc343167e4","first_computed_at":"2026-07-05T00:16:45.654357Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:16:45.654357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3+wzUNL3nG7esJxthTsHverK8eLg8wsnhhwbr2lU7hVtsOjHf3YDCvZQSyjD+g2/L8U4XOsxpHQ3Z43zDoK/CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:16:45.654744Z","signed_message":"canonical_sha256_bytes"},"source_id":"1911.01094","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e9643f239fbba16f09282cbf3cc0ad4aea413f142eac3117ebd6993e0236caf","sha256:e2d8230d60b67d8d1769bc7fddadac07a9066c929748b74373922fd72194caa5"],"state_sha256":"a34bb917b12f4371019c10633fdb50677154ad4a05682e873752133049f9f8c0"}