{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:Q54DRQWQYNW6FBYNVOHIYHZSBX","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":"af14b508cadefb1686650ef6cd07c7148a13e0cb6bb9c5cd01a49aa023a9409d","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"2003-03-24T20:42:56Z","title_canon_sha256":"2d46379693d962b6dbf4c2228f57fb50e871ab251b322dcd4388a1c033b6d41c"},"schema_version":"1.0","source":{"id":"math/0303296","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0303296","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"arxiv_version","alias_value":"math/0303296v2","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0303296","created_at":"2026-05-18T02:38:00Z"},{"alias_kind":"pith_short_12","alias_value":"Q54DRQWQYNW6","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"Q54DRQWQYNW6FBYN","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"Q54DRQWQ","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:c9b147337270ea6e64474260d728a927ed34c22306ec0c137a6d1d2ef5746d2d","target":"graph","created_at":"2026-05-18T02:38:00Z","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":"The main result of this paper is that every non-trivial Hamiltonian diffeomorphism of a closed oriented surface of genus at least one has periodic points of arbitrarily high period. The same result is true for S^2 provided the diffeomorphism has at least three fixed points. In addition we show that up to isotopy relative to its fixed point set, every orientation preserving diffeomorphism F: S --> S of a closed orientable surface has a normal form. If the fixed point set is finite this is just the Thurston normal form.","authors_text":"John Franks, Michael Handel","cross_cats":[],"headline":"","license":"","primary_cat":"math.DS","submitted_at":"2003-03-24T20:42:56Z","title":"Periodic points of Hamiltonian surface diffeomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0303296","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:ae1552259727a54c851d45713a1ae9442bc85efd32716eec04fcc6d6fd560ec9","target":"record","created_at":"2026-05-18T02:38:00Z","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":"af14b508cadefb1686650ef6cd07c7148a13e0cb6bb9c5cd01a49aa023a9409d","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"2003-03-24T20:42:56Z","title_canon_sha256":"2d46379693d962b6dbf4c2228f57fb50e871ab251b322dcd4388a1c033b6d41c"},"schema_version":"1.0","source":{"id":"math/0303296","kind":"arxiv","version":2}},"canonical_sha256":"877838c2d0c36de2870dab8e8c1f320ddfec6ad57e44c5f90185a0209f8a4c02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"877838c2d0c36de2870dab8e8c1f320ddfec6ad57e44c5f90185a0209f8a4c02","first_computed_at":"2026-05-18T02:38:00.410611Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:00.410611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vD4fTag4IyhD50oHfMx+a5I2wbwNU6i9nq48EEQSmKFBVh3kk/XL0B0J1GyKoz15C4ctEzoV9fqyVMfQCPoBBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:00.411188Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0303296","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae1552259727a54c851d45713a1ae9442bc85efd32716eec04fcc6d6fd560ec9","sha256:c9b147337270ea6e64474260d728a927ed34c22306ec0c137a6d1d2ef5746d2d"],"state_sha256":"0cb4379913e5d0b610f47fe08b4cd70fba1b3a0b2552c453aa046d781e00e2cb"}