{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:FS2CWCPRIMQTSH3UWFOMBRZTXX","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":"2830949a98c3697517f31c0ead0a5cc6642867d4a01e2ebee2d93d63183b2e2c","cross_cats_sorted":[],"license":"","primary_cat":"math.SG","submitted_at":"2002-01-06T13:19:50Z","title_canon_sha256":"a510ca465ac268e1db443e87aa656a70a6fcf4b517f2e79c5d03a9f0207d1403"},"schema_version":"1.0","source":{"id":"math/0201032","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0201032","created_at":"2026-07-04T14:35:50Z"},{"alias_kind":"arxiv_version","alias_value":"math/0201032v2","created_at":"2026-07-04T14:35:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0201032","created_at":"2026-07-04T14:35:50Z"},{"alias_kind":"pith_short_12","alias_value":"FS2CWCPRIMQT","created_at":"2026-07-04T14:35:50Z"},{"alias_kind":"pith_short_16","alias_value":"FS2CWCPRIMQTSH3U","created_at":"2026-07-04T14:35:50Z"},{"alias_kind":"pith_short_8","alias_value":"FS2CWCPR","created_at":"2026-07-04T14:35:50Z"}],"graph_snapshots":[{"event_id":"sha256:f557d42788a8413c69fbab32f8fffa73c0aca4cf8dbe48daf49030cb3a0435e4","target":"graph","created_at":"2026-07-04T14:35:50Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0201032/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"These notes combine material from short lecture courses given in Paris, France, in July 2001 and in Srni, the Czech Republic, in January 2003. They discuss groups of symplectomorphisms of closed symplectic manifolds (M,\\om) from various points of view. Lectures 1 and 2 provide an overview of our current knowledge of their algebraic, geometric and homotopy theoretic properties. Lecture 3 sketches the arguments used by Gromov, Abreu and Abreu-McDuff to figure out the rational homotopy type of these groups in the cases M= CP^2 and M=S^2\\times S^2. We outline the needed J-holomorphic curve techniq","authors_text":"Dusa McDuff","cross_cats":[],"headline":"","license":"","primary_cat":"math.SG","submitted_at":"2002-01-06T13:19:50Z","title":"Lectures on Groups of Symplectomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0201032","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":"sha256:94fd4dcd73f9e963213209c4b208fef483595addb68752b7a71657548d94a885","target":"record","created_at":"2026-07-04T14:35:50Z","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":"2830949a98c3697517f31c0ead0a5cc6642867d4a01e2ebee2d93d63183b2e2c","cross_cats_sorted":[],"license":"","primary_cat":"math.SG","submitted_at":"2002-01-06T13:19:50Z","title_canon_sha256":"a510ca465ac268e1db443e87aa656a70a6fcf4b517f2e79c5d03a9f0207d1403"},"schema_version":"1.0","source":{"id":"math/0201032","kind":"arxiv","version":2}},"canonical_sha256":"2cb42b09f14321391f74b15cc0c733bdd52ec891ac47378746b05e7fd291e5bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2cb42b09f14321391f74b15cc0c733bdd52ec891ac47378746b05e7fd291e5bf","first_computed_at":"2026-07-04T14:35:50.910510Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:35:50.910510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+7X4MB/r48dsRvHzs6kclv0FaO3b8LQzQ5kCQcHb6OX9gDMAecxYfRoitAZ1msRnvcNlLacgY3XkfKkrKWATDw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:35:50.910871Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0201032","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94fd4dcd73f9e963213209c4b208fef483595addb68752b7a71657548d94a885","sha256:f557d42788a8413c69fbab32f8fffa73c0aca4cf8dbe48daf49030cb3a0435e4"],"state_sha256":"41f5b860bbb35e8d00f5279fc9bcc6fe2fad8c0fd81c9e8a0fd926aef0349f74"}