{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:PCEX5AYWUJSBUWCECR64H3GQT5","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":"a7fb0331fd8a22350b9c721ec116975d8eddc4a1275468230ddbc780b0b3ea4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-11-26T08:56:14Z","title_canon_sha256":"bd63d6f4d5487d451b1318826e6045a7abac91a8c88f763b1d36f025d6b30fac"},"schema_version":"1.0","source":{"id":"1011.5731","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.5731","created_at":"2026-05-18T04:28:19Z"},{"alias_kind":"arxiv_version","alias_value":"1011.5731v2","created_at":"2026-05-18T04:28:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.5731","created_at":"2026-05-18T04:28:19Z"},{"alias_kind":"pith_short_12","alias_value":"PCEX5AYWUJSB","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"PCEX5AYWUJSBUWCE","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"PCEX5AYW","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:61f67c34cda9027474abde49c8d89d732d6899a44062bea48539a92e5b1913c4","target":"graph","created_at":"2026-05-18T04:28:19Z","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":"Let $X$ be a Hamiltonian vector field defined on a symplectic manifold $(M,\\omega)$, $g$ a nowhere vanishing smooth function defined on an open dense subset $M^0$ of $M$. We will say that the vector field $Y = gX$ is conformally Hamiltonian. We prove that when $X$ is complete, when $Y$ is Hamiltonian with respect to another symplectic form $\\omega_2$ defined on $M^0$, and when another technical condition is satisfied, there exists a symplectic diffeomorphism from $(M^0,\\omega_2)$ onto an open subset of $(M,\\omega)$, equivariant with respect to the flows of the vector fields $Y$ on $M^0$ and $X","authors_text":"Charles-Michel Marle","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-11-26T08:56:14Z","title":"A property of conformally Hamiltonian vector fields; application to the Kepler problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5731","kind":"arxiv","version":2},"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":"sha256:9f1557c29e156620239109921e044efa639c101e6f09e931b28d186c14c8a3b5","target":"record","created_at":"2026-05-18T04:28:19Z","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":"a7fb0331fd8a22350b9c721ec116975d8eddc4a1275468230ddbc780b0b3ea4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2010-11-26T08:56:14Z","title_canon_sha256":"bd63d6f4d5487d451b1318826e6045a7abac91a8c88f763b1d36f025d6b30fac"},"schema_version":"1.0","source":{"id":"1011.5731","kind":"arxiv","version":2}},"canonical_sha256":"78897e8316a2641a5844147dc3ecd09f594a25e85a5dbb7aa0655abfbd3d124e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78897e8316a2641a5844147dc3ecd09f594a25e85a5dbb7aa0655abfbd3d124e","first_computed_at":"2026-05-18T04:28:19.823387Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:19.823387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GbkvQN3uhGR2ANi3yLJly+HreavQm/14HmDtIJguLL1a1ulfgYb5x9YkRNgDMwnhcD582p0Pzv81Dg3RPjkACA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:19.824268Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.5731","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f1557c29e156620239109921e044efa639c101e6f09e931b28d186c14c8a3b5","sha256:61f67c34cda9027474abde49c8d89d732d6899a44062bea48539a92e5b1913c4"],"state_sha256":"8a61c8b101492954b78fccc36a456cb59768c0d7298ef601009311030db1b62d"}