{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:RWQBU2I2DJGH3QE3BBTQW2MZYO","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":"0e744235688f18d41186f37c6478a1cf763568be02fb5eceb43c09684fa5b210","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-08-01T01:32:48Z","title_canon_sha256":"6bee0f88ee1d182854335eade6a5c9b78bb44d9c5c9cc369666cd0b0d0948f75"},"schema_version":"1.0","source":{"id":"1108.0218","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.0218","created_at":"2026-05-18T04:16:22Z"},{"alias_kind":"arxiv_version","alias_value":"1108.0218v2","created_at":"2026-05-18T04:16:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.0218","created_at":"2026-05-18T04:16:22Z"},{"alias_kind":"pith_short_12","alias_value":"RWQBU2I2DJGH","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"RWQBU2I2DJGH3QE3","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"RWQBU2I2","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:550ae915591ebd1204a4637f62d3d2e899b8ed16fea056fb1e4dadca03888a32","target":"graph","created_at":"2026-05-18T04:16:22Z","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":"Let F be a fibration on a simply-connected base with symplectic fibre (M, \\omega). Assume that the fibre is nilpotent and T^{2k}-separable for some integer k or a nilmanifold. Then our main theorem, Theorem 1.8, gives a necessary and sufficient condition for the cohomology class [\\omega] to extend to a cohomology class of the total space of F. This allows us to describe Thurston's criterion for a symplectic fibration to admit a compatible symplectic form in terms of the classifying map for the underlying fibration. The obstruction due to Lalond and McDuff for a symplectic bundle to be Hamilton","authors_text":"Katsuhiko Kuribayashi","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-08-01T01:32:48Z","title":"On extensions of a symplectic class"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0218","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":"sha256:5780b3e60743d4bae6b8f9d3f0935c904784f28a8331fb3a605c7f4b6d7bd5fe","target":"record","created_at":"2026-05-18T04:16:22Z","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":"0e744235688f18d41186f37c6478a1cf763568be02fb5eceb43c09684fa5b210","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-08-01T01:32:48Z","title_canon_sha256":"6bee0f88ee1d182854335eade6a5c9b78bb44d9c5c9cc369666cd0b0d0948f75"},"schema_version":"1.0","source":{"id":"1108.0218","kind":"arxiv","version":2}},"canonical_sha256":"8da01a691a1a4c7dc09b08670b6999c3b688709e4d64db4df0ea86b32dc8187a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8da01a691a1a4c7dc09b08670b6999c3b688709e4d64db4df0ea86b32dc8187a","first_computed_at":"2026-05-18T04:16:22.232239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:22.232239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D9VRaCE5iB8rK7mYvPn+Ba7OKReuUNHcOOBiWH4DD+9nsFI26kmhrQp9m7FVZFih/Rnzml0wCfC3WfKC83txBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:22.232780Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.0218","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5780b3e60743d4bae6b8f9d3f0935c904784f28a8331fb3a605c7f4b6d7bd5fe","sha256:550ae915591ebd1204a4637f62d3d2e899b8ed16fea056fb1e4dadca03888a32"],"state_sha256":"cdc2c3035268bcb8e934ae7bd6fd1b21b2fa6494a50309f76ca3c34e3d5ba1c2"}