{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NUNKGB32Q63CI6T3H3DL3N54EG","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":"2e56d1cfa4df1ebb77c82b139d5eea566c5f42955ed58f573d2ea7d908f39765","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-10-30T10:01:05Z","title_canon_sha256":"a3c7a7d2d7caf97c6bece31d654c86c928a207e9dbc45b4e67cb537c31479c88"},"schema_version":"1.0","source":{"id":"1210.7947","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.7947","created_at":"2026-05-17T23:51:49Z"},{"alias_kind":"arxiv_version","alias_value":"1210.7947v1","created_at":"2026-05-17T23:51:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.7947","created_at":"2026-05-17T23:51:49Z"},{"alias_kind":"pith_short_12","alias_value":"NUNKGB32Q63C","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NUNKGB32Q63CI6T3","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NUNKGB32","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:e1e0f2d02766b24d6498a271a2d0a25788ea5a8cfdff41730a611c017579beed","target":"graph","created_at":"2026-05-17T23:51:49Z","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":"We show the existence of a contractible periodic Reeb orbit for any contact structure supported by an open book whose binding can be realised as a hypersurface of restricted contact type in a subcritical Stein manifold. A key ingredient in the proof is a higher-dimensional version of Eliashberg's theorem about symplectic cobordisms from a contact manifold to a symplectic fibration.","authors_text":"Hansj\\\"org Geiges, Kai Zehmisch, Max D\\\"orner","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-10-30T10:01:05Z","title":"Open books and the Weinstein conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7947","kind":"arxiv","version":1},"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":"sha256:0692b996e957686ba30a7e60c294c6c38500f5a5b247079b681384150d9f4505","target":"record","created_at":"2026-05-17T23:51:49Z","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":"2e56d1cfa4df1ebb77c82b139d5eea566c5f42955ed58f573d2ea7d908f39765","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-10-30T10:01:05Z","title_canon_sha256":"a3c7a7d2d7caf97c6bece31d654c86c928a207e9dbc45b4e67cb537c31479c88"},"schema_version":"1.0","source":{"id":"1210.7947","kind":"arxiv","version":1}},"canonical_sha256":"6d1aa3077a87b6247a7b3ec6bdb7bc21ac031998dfd33571545af82338bf0c8e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d1aa3077a87b6247a7b3ec6bdb7bc21ac031998dfd33571545af82338bf0c8e","first_computed_at":"2026-05-17T23:51:49.892051Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:49.892051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3YinoHvohUdeAbT76pA3BUZHk2q8nh5ULnSN170glyhCGsNAbipgL92i49SJZOfYLkWmfcQNaJNCoSWa872gCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:49.892786Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.7947","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0692b996e957686ba30a7e60c294c6c38500f5a5b247079b681384150d9f4505","sha256:e1e0f2d02766b24d6498a271a2d0a25788ea5a8cfdff41730a611c017579beed"],"state_sha256":"1b734e230a6a2e96c1ede8aa2dd51b42e239acbc8493e7ee0a24a6e46866519d"}