{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZVNOTZIZ6PZZRKUVG3QGSYVKSE","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":"41e1d2927252e936ffca3bd2456addf808e76d400be515f43a23f2ee9d660ef3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-05-05T19:01:48Z","title_canon_sha256":"af950903634608e9d85a27bd96f39374673b3780c46f7d3747a7f9d910ad6216"},"schema_version":"1.0","source":{"id":"1305.1041","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1041","created_at":"2026-05-18T02:40:03Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1041v2","created_at":"2026-05-18T02:40:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1041","created_at":"2026-05-18T02:40:03Z"},{"alias_kind":"pith_short_12","alias_value":"ZVNOTZIZ6PZZ","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZVNOTZIZ6PZZRKUV","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZVNOTZIZ","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:8c65d14acadeebe3c533a917081eb67649b8fba27ffc31cb521606c1e0d77f7d","target":"graph","created_at":"2026-05-18T02:40:03Z","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":"In this note we prove that the symplectic homology of a Liouville domain W displaceable in the symplectic completion vanishes. Nevertheless if the Euler characteristic of (W,\\p W) is odd, the filtered symplectic homologies of W do not vanish and give rise to leafwise intersection points on the symplectic completion of W for a perturbation displacing $W$ from itself. In contrast to the existing results we can find a leafwise intersection point for a given period but its energy varies by period instead.","authors_text":"Jungsoo Kang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-05-05T19:01:48Z","title":"Symplectic homology of displaceable Liouville domains and Leafwise intersection points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1041","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":"sha256:1d89ede9bdbd8a7fd9e6182df17bc4bc7f93a8f9b2920fa8aa72787fe59cea31","target":"record","created_at":"2026-05-18T02:40:03Z","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":"41e1d2927252e936ffca3bd2456addf808e76d400be515f43a23f2ee9d660ef3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2013-05-05T19:01:48Z","title_canon_sha256":"af950903634608e9d85a27bd96f39374673b3780c46f7d3747a7f9d910ad6216"},"schema_version":"1.0","source":{"id":"1305.1041","kind":"arxiv","version":2}},"canonical_sha256":"cd5ae9e519f3f398aa9536e06962aa911172a402a942f4ae623c46717f3c1435","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd5ae9e519f3f398aa9536e06962aa911172a402a942f4ae623c46717f3c1435","first_computed_at":"2026-05-18T02:40:03.476610Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:03.476610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ruGMBLPnK/cheWtgoQsDMxh/0VKPEjzMlkse2fwa3TjKVZEuPkiJcg/VqCjzFrJeSwBkQAWl0UxBStz7GGdUAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:03.477249Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.1041","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d89ede9bdbd8a7fd9e6182df17bc4bc7f93a8f9b2920fa8aa72787fe59cea31","sha256:8c65d14acadeebe3c533a917081eb67649b8fba27ffc31cb521606c1e0d77f7d"],"state_sha256":"7b6b2c2b1bcb40c7e473f160051cec56198c1e4222fe65105b6f08075e37ba89"}