{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:DFXLTBP3S2PXZZKBN7EG7IJIJQ","short_pith_number":"pith:DFXLTBP3","schema_version":"1.0","canonical_sha256":"196eb985fb969f7ce5416fc86fa1284c233183037b8884ef1dd794fe41597b87","source":{"kind":"arxiv","id":"1512.06336","version":3},"attestation_state":"computed","paper":{"title":"A $C^\\infty$ closing lemma for Hamiltonian diffeomorphisms of closed surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.SG","authors_text":"Kei Irie, Masayuki Asaoka","submitted_at":"2015-12-20T09:04:08Z","abstract_excerpt":"We prove a $C^\\infty$ closing lemma for Hamiltonian diffeomorphisms of closed surfaces. This is a consequence of a $C^\\infty$ closing lemma for Reeb flows on closed contact three-manifolds, which was recently proved as an application of spectral invariants in embedded contact homology. A key new ingredient of this paper is an analysis of an area-preserving map near its fixed point, which is based on some classical results in Hamiltonian dynamics: existence of KAM invariant circles for elliptic fixed points, and convergence of the Birkhoff normal form for hyperbolic fixed points."},"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":"1512.06336","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-12-20T09:04:08Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"5fd2efe81fac10fec077979e5d1aa9cd8a546f296b6c86bb009f5da9de1d6a8d","abstract_canon_sha256":"232094373a159799f08a25d41e5a63eb7ce115c2f33c226cc17fe5434950583a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:41.544509Z","signature_b64":"7IdGqUv07j47zK80VfiV5YxPIPZcFC4esx2EeGNulzJ4iGSMnao2kXKfWA98atuszJgmbA3Y0r66MMwX5CwADg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"196eb985fb969f7ce5416fc86fa1284c233183037b8884ef1dd794fe41597b87","last_reissued_at":"2026-05-18T01:04:41.543880Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:41.543880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A $C^\\infty$ closing lemma for Hamiltonian diffeomorphisms of closed surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.SG","authors_text":"Kei Irie, Masayuki Asaoka","submitted_at":"2015-12-20T09:04:08Z","abstract_excerpt":"We prove a $C^\\infty$ closing lemma for Hamiltonian diffeomorphisms of closed surfaces. This is a consequence of a $C^\\infty$ closing lemma for Reeb flows on closed contact three-manifolds, which was recently proved as an application of spectral invariants in embedded contact homology. A key new ingredient of this paper is an analysis of an area-preserving map near its fixed point, which is based on some classical results in Hamiltonian dynamics: existence of KAM invariant circles for elliptic fixed points, and convergence of the Birkhoff normal form for hyperbolic fixed points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06336","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":"1512.06336","created_at":"2026-05-18T01:04:41.543975+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.06336v3","created_at":"2026-05-18T01:04:41.543975+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.06336","created_at":"2026-05-18T01:04:41.543975+00:00"},{"alias_kind":"pith_short_12","alias_value":"DFXLTBP3S2PX","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"DFXLTBP3S2PXZZKB","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"DFXLTBP3","created_at":"2026-05-18T12:29:17.054201+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/DFXLTBP3S2PXZZKBN7EG7IJIJQ","json":"https://pith.science/pith/DFXLTBP3S2PXZZKBN7EG7IJIJQ.json","graph_json":"https://pith.science/api/pith-number/DFXLTBP3S2PXZZKBN7EG7IJIJQ/graph.json","events_json":"https://pith.science/api/pith-number/DFXLTBP3S2PXZZKBN7EG7IJIJQ/events.json","paper":"https://pith.science/paper/DFXLTBP3"},"agent_actions":{"view_html":"https://pith.science/pith/DFXLTBP3S2PXZZKBN7EG7IJIJQ","download_json":"https://pith.science/pith/DFXLTBP3S2PXZZKBN7EG7IJIJQ.json","view_paper":"https://pith.science/paper/DFXLTBP3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.06336&json=true","fetch_graph":"https://pith.science/api/pith-number/DFXLTBP3S2PXZZKBN7EG7IJIJQ/graph.json","fetch_events":"https://pith.science/api/pith-number/DFXLTBP3S2PXZZKBN7EG7IJIJQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DFXLTBP3S2PXZZKBN7EG7IJIJQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DFXLTBP3S2PXZZKBN7EG7IJIJQ/action/storage_attestation","attest_author":"https://pith.science/pith/DFXLTBP3S2PXZZKBN7EG7IJIJQ/action/author_attestation","sign_citation":"https://pith.science/pith/DFXLTBP3S2PXZZKBN7EG7IJIJQ/action/citation_signature","submit_replication":"https://pith.science/pith/DFXLTBP3S2PXZZKBN7EG7IJIJQ/action/replication_record"}},"created_at":"2026-05-18T01:04:41.543975+00:00","updated_at":"2026-05-18T01:04:41.543975+00:00"}