{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FNPBSRGFD5BZMT34I44BSGZYTC","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":"db63aff29f887014ab2df29abf142271d519ae7739066edd250e77ab8cb6213c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-04-27T08:04:57Z","title_canon_sha256":"1c9111624885345baa246f0ab574311ab4687d644c079154d8e78d679aeed6b0"},"schema_version":"1.0","source":{"id":"1804.10375","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.10375","created_at":"2026-05-18T00:00:56Z"},{"alias_kind":"arxiv_version","alias_value":"1804.10375v1","created_at":"2026-05-18T00:00:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.10375","created_at":"2026-05-18T00:00:56Z"},{"alias_kind":"pith_short_12","alias_value":"FNPBSRGFD5BZ","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FNPBSRGFD5BZMT34","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FNPBSRGF","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:eb4ff9c5e8aa6b31c186bb7695d0e78fa44ba8b152585c56cbf7a9abc948c4fe","target":"graph","created_at":"2026-05-18T00:00:56Z","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":"A mathematically correct description is presented on the interrelations between the dynamics of divergence free vector fields on an oriented 3-dimensional manifold $M$ and the dynamics of Hamiltonian systems. It is shown that for a given divergence free vector field $X$ with a global cross-section there exist some 4-dimensional symplectic manifold $\\tilde{M}\\supset M$ and a smooth Hamilton function $H: \\tilde{M}\\to \\mathbb R$ such that for some $c\\in \\mathbb R$ one gets $M = \\{H=c\\}$ and the Hamiltonian vector field $X_H$ restricted on this level coincides with $X$. For divergence free vector ","authors_text":"E. Yakovlev, L. Lerman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-04-27T08:04:57Z","title":"On interrelations between divergence-free and Hamiltonian dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.10375","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:bdfeddad9ac64b6f90383994e85a267d861a735dc76ddad885229cf6eb75ee36","target":"record","created_at":"2026-05-18T00:00:56Z","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":"db63aff29f887014ab2df29abf142271d519ae7739066edd250e77ab8cb6213c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-04-27T08:04:57Z","title_canon_sha256":"1c9111624885345baa246f0ab574311ab4687d644c079154d8e78d679aeed6b0"},"schema_version":"1.0","source":{"id":"1804.10375","kind":"arxiv","version":1}},"canonical_sha256":"2b5e1944c51f43964f7c4738191b3898ac9a0c4fb66cbe56fa7cd55df930e3e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b5e1944c51f43964f7c4738191b3898ac9a0c4fb66cbe56fa7cd55df930e3e9","first_computed_at":"2026-05-18T00:00:56.252040Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:56.252040Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nvevv+GJw9d6Gl4/cJOzqHt6akHDggLf1qzh1hTonj9Ilp8IXy1BXpdZWXfNXWcV8TFHBMduArfrmHEvbtEEDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:56.252584Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.10375","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bdfeddad9ac64b6f90383994e85a267d861a735dc76ddad885229cf6eb75ee36","sha256:eb4ff9c5e8aa6b31c186bb7695d0e78fa44ba8b152585c56cbf7a9abc948c4fe"],"state_sha256":"45b3564695608395fa2158dfd7f897658a2503eacd301a4cc1a64b7ecad279ff"}