{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:NRPDXN6VK5PN4EZ2QHIGPD4HTI","short_pith_number":"pith:NRPDXN6V","schema_version":"1.0","canonical_sha256":"6c5e3bb7d5575ede133a81d0678f879a3d40939d795cfbfb7fbba2a6cd4359cf","source":{"kind":"arxiv","id":"0801.3072","version":1},"attestation_state":"computed","paper":{"title":"Hamiltonian elliptic dynamics on symplectic 4-manifolds","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Joao Lopes Dias, Mario Bessa","submitted_at":"2008-01-21T19:31:49Z","abstract_excerpt":"We consider C2 Hamiltonian functions on compact 4-dimensional symplectic manifolds to study elliptic dynamics of the Hamiltonian flow, namely the so-called Newhouse dichotomy. We show that for any open set U intersecting a far from Anosov regular energy surface, there is a nearby Hamiltonian having an elliptic closed orbit through U. Moreover, this implies that for far from Anosov regular energy surfaces of a C2-generic Hamiltonian the elliptic closed orbits are generic."},"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":"0801.3072","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"2008-01-21T19:31:49Z","cross_cats_sorted":[],"title_canon_sha256":"5e5104335f105d2de3990b466115f7fd232ac942e7c1d12d8117869df9133fb5","abstract_canon_sha256":"13440b988ac1eb3d4c91b2623b24a5a8254e30ccf3ae672992a095f635ae58bd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:59.831092Z","signature_b64":"M5osJ7PCYqyiNvPUl1zQQmr13dcsfh0FJDkOGbEuN+CWgmLRlC+ELXsed5bOBWMWp34RDhCxyHEgqLMyVUJrCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c5e3bb7d5575ede133a81d0678f879a3d40939d795cfbfb7fbba2a6cd4359cf","last_reissued_at":"2026-05-18T04:39:59.830431Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:59.830431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hamiltonian elliptic dynamics on symplectic 4-manifolds","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Joao Lopes Dias, Mario Bessa","submitted_at":"2008-01-21T19:31:49Z","abstract_excerpt":"We consider C2 Hamiltonian functions on compact 4-dimensional symplectic manifolds to study elliptic dynamics of the Hamiltonian flow, namely the so-called Newhouse dichotomy. We show that for any open set U intersecting a far from Anosov regular energy surface, there is a nearby Hamiltonian having an elliptic closed orbit through U. Moreover, this implies that for far from Anosov regular energy surfaces of a C2-generic Hamiltonian the elliptic closed orbits are generic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.3072","kind":"arxiv","version":1},"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":"0801.3072","created_at":"2026-05-18T04:39:59.830520+00:00"},{"alias_kind":"arxiv_version","alias_value":"0801.3072v1","created_at":"2026-05-18T04:39:59.830520+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.3072","created_at":"2026-05-18T04:39:59.830520+00:00"},{"alias_kind":"pith_short_12","alias_value":"NRPDXN6VK5PN","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"NRPDXN6VK5PN4EZ2","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"NRPDXN6V","created_at":"2026-05-18T12:25:57.157939+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/NRPDXN6VK5PN4EZ2QHIGPD4HTI","json":"https://pith.science/pith/NRPDXN6VK5PN4EZ2QHIGPD4HTI.json","graph_json":"https://pith.science/api/pith-number/NRPDXN6VK5PN4EZ2QHIGPD4HTI/graph.json","events_json":"https://pith.science/api/pith-number/NRPDXN6VK5PN4EZ2QHIGPD4HTI/events.json","paper":"https://pith.science/paper/NRPDXN6V"},"agent_actions":{"view_html":"https://pith.science/pith/NRPDXN6VK5PN4EZ2QHIGPD4HTI","download_json":"https://pith.science/pith/NRPDXN6VK5PN4EZ2QHIGPD4HTI.json","view_paper":"https://pith.science/paper/NRPDXN6V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0801.3072&json=true","fetch_graph":"https://pith.science/api/pith-number/NRPDXN6VK5PN4EZ2QHIGPD4HTI/graph.json","fetch_events":"https://pith.science/api/pith-number/NRPDXN6VK5PN4EZ2QHIGPD4HTI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NRPDXN6VK5PN4EZ2QHIGPD4HTI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NRPDXN6VK5PN4EZ2QHIGPD4HTI/action/storage_attestation","attest_author":"https://pith.science/pith/NRPDXN6VK5PN4EZ2QHIGPD4HTI/action/author_attestation","sign_citation":"https://pith.science/pith/NRPDXN6VK5PN4EZ2QHIGPD4HTI/action/citation_signature","submit_replication":"https://pith.science/pith/NRPDXN6VK5PN4EZ2QHIGPD4HTI/action/replication_record"}},"created_at":"2026-05-18T04:39:59.830520+00:00","updated_at":"2026-05-18T04:39:59.830520+00:00"}