{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:HHMPUOE7BCF54RO2CZOXTORZDD","short_pith_number":"pith:HHMPUOE7","schema_version":"1.0","canonical_sha256":"39d8fa389f088bde45da165d79ba3918c333bc5bf5417f3b2e41c01a0601cee1","source":{"kind":"arxiv","id":"0709.2511","version":3},"attestation_state":"computed","paper":{"title":"Hamiltonian vector fields of homogeneous polynomials in two variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Sergiy Maksymenko","submitted_at":"2007-09-16T20:30:00Z","abstract_excerpt":"Let $g:\\mathbb{R}^2\\to\\mathbb{R}$ be a homogeneous polynomial of degree $p>1$, $G=(-g'_{y}, g'_{x})$ be its Hamiltonian vector field, and $G_t$ be the local flow generated by $G$. Denote by $E(G,O)$ the space of germs of $C^{\\infty}$ diffeomorphisms $(\\mathbb{R}^2,O)\\to(\\mathbb{R}^2,O)$ that preserve orbits of $G$. Let also $E_{\\mathrm{id}}(G,O)$ be the identity component of $E(G,O)$ with respect to $C^1$-topology.\n  Suppose that $g$ has no multiple prime factors. Then we prove that for every $h\\in E_{\\mathrm{id}}(G,O)$ there exists a germ of a smooth function $\\alpha:\\mathbb{R}^2\\to\\mathbb{R}"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0709.2511","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2007-09-16T20:30:00Z","cross_cats_sorted":[],"title_canon_sha256":"75b5c437eae0750f52478c28764064591c124a82da488d764a4d69cb44498ad3","abstract_canon_sha256":"607d0793a78eb2fea2d950976172b7101b91a12bbe8530117a962fa8ce4ad685"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:48.605902Z","signature_b64":"9AZJGmQ6Lf4f8MLDvEV6v+eRhCAt1g9p9whdYU7SJUPkXWL0rxvAS0POD6m2aYshmTFQQhg9jb+RiQhk+2EJDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39d8fa389f088bde45da165d79ba3918c333bc5bf5417f3b2e41c01a0601cee1","last_reissued_at":"2026-05-18T01:23:48.605294Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:48.605294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hamiltonian vector fields of homogeneous polynomials in two variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Sergiy Maksymenko","submitted_at":"2007-09-16T20:30:00Z","abstract_excerpt":"Let $g:\\mathbb{R}^2\\to\\mathbb{R}$ be a homogeneous polynomial of degree $p>1$, $G=(-g'_{y}, g'_{x})$ be its Hamiltonian vector field, and $G_t$ be the local flow generated by $G$. Denote by $E(G,O)$ the space of germs of $C^{\\infty}$ diffeomorphisms $(\\mathbb{R}^2,O)\\to(\\mathbb{R}^2,O)$ that preserve orbits of $G$. Let also $E_{\\mathrm{id}}(G,O)$ be the identity component of $E(G,O)$ with respect to $C^1$-topology.\n  Suppose that $g$ has no multiple prime factors. Then we prove that for every $h\\in E_{\\mathrm{id}}(G,O)$ there exists a germ of a smooth function $\\alpha:\\mathbb{R}^2\\to\\mathbb{R}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0709.2511","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0709.2511","created_at":"2026-05-18T01:23:48.605417+00:00"},{"alias_kind":"arxiv_version","alias_value":"0709.2511v3","created_at":"2026-05-18T01:23:48.605417+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0709.2511","created_at":"2026-05-18T01:23:48.605417+00:00"},{"alias_kind":"pith_short_12","alias_value":"HHMPUOE7BCF5","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"HHMPUOE7BCF54RO2","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"HHMPUOE7","created_at":"2026-05-18T12:25:55.427421+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HHMPUOE7BCF54RO2CZOXTORZDD","json":"https://pith.science/pith/HHMPUOE7BCF54RO2CZOXTORZDD.json","graph_json":"https://pith.science/api/pith-number/HHMPUOE7BCF54RO2CZOXTORZDD/graph.json","events_json":"https://pith.science/api/pith-number/HHMPUOE7BCF54RO2CZOXTORZDD/events.json","paper":"https://pith.science/paper/HHMPUOE7"},"agent_actions":{"view_html":"https://pith.science/pith/HHMPUOE7BCF54RO2CZOXTORZDD","download_json":"https://pith.science/pith/HHMPUOE7BCF54RO2CZOXTORZDD.json","view_paper":"https://pith.science/paper/HHMPUOE7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0709.2511&json=true","fetch_graph":"https://pith.science/api/pith-number/HHMPUOE7BCF54RO2CZOXTORZDD/graph.json","fetch_events":"https://pith.science/api/pith-number/HHMPUOE7BCF54RO2CZOXTORZDD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HHMPUOE7BCF54RO2CZOXTORZDD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HHMPUOE7BCF54RO2CZOXTORZDD/action/storage_attestation","attest_author":"https://pith.science/pith/HHMPUOE7BCF54RO2CZOXTORZDD/action/author_attestation","sign_citation":"https://pith.science/pith/HHMPUOE7BCF54RO2CZOXTORZDD/action/citation_signature","submit_replication":"https://pith.science/pith/HHMPUOE7BCF54RO2CZOXTORZDD/action/replication_record"}},"created_at":"2026-05-18T01:23:48.605417+00:00","updated_at":"2026-05-18T01:23:48.605417+00:00"}