{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:F7IX5XYI234C3VWYKTGKFF2X4I","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":"964e718900fe42cc577082f984861521e006b6866270b7599035f69bee039302","cross_cats_sorted":["math.SG"],"license":"","primary_cat":"math.GT","submitted_at":"2007-01-24T20:31:44Z","title_canon_sha256":"03a95e9da26b4233c808e27875f6d0f6f46336ec1d23634c0893bf9f7e2df112"},"schema_version":"1.0","source":{"id":"math/0701717","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0701717","created_at":"2026-05-17T23:57:44Z"},{"alias_kind":"arxiv_version","alias_value":"math/0701717v2","created_at":"2026-05-17T23:57:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0701717","created_at":"2026-05-17T23:57:44Z"},{"alias_kind":"pith_short_12","alias_value":"F7IX5XYI234C","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"F7IX5XYI234C3VWY","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"F7IX5XYI","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:571ed4958ec2dc62a65ea7e7640c4e9cd43634450fbd133164000fd5f97b9dae","target":"graph","created_at":"2026-05-17T23:57:44Z","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 N be a closed, oriented 3-manifold. A folklore conjecture states that $S^{1} \\times N$ admits a symplectic structure if and only if $N$ admits a fibration over the circle. We will prove this conjecture in the case when N is irreducible and its fundamental group satisfies appropriate subgroup separability conditions. This statement includes 3-manifolds with vanishing Thurston norm, graph manifolds and 3-manifolds with surface subgroup separability (a condition satisfied conjecturally by all hyperbolic 3-manifolds). Our result covers, in particular, the case of 0-framed surgeries along knots","authors_text":"Stefan Friedl, Stefano Vidussi","cross_cats":["math.SG"],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2007-01-24T20:31:44Z","title":"Symplectic S^1 x N^3, subgroup separability, and vanishing Thurston norm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0701717","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":"sha256:2c96cd77cd3a232f096b5eb8bb9518db7b8d63f7d7534c511c680b69a2aa320b","target":"record","created_at":"2026-05-17T23:57:44Z","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":"964e718900fe42cc577082f984861521e006b6866270b7599035f69bee039302","cross_cats_sorted":["math.SG"],"license":"","primary_cat":"math.GT","submitted_at":"2007-01-24T20:31:44Z","title_canon_sha256":"03a95e9da26b4233c808e27875f6d0f6f46336ec1d23634c0893bf9f7e2df112"},"schema_version":"1.0","source":{"id":"math/0701717","kind":"arxiv","version":2}},"canonical_sha256":"2fd17edf08d6f82dd6d854cca29757e215c60d79362af9d80e4538fcbef1c0e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2fd17edf08d6f82dd6d854cca29757e215c60d79362af9d80e4538fcbef1c0e1","first_computed_at":"2026-05-17T23:57:44.752562Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:44.752562Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ffTtTKF4x+wOsasXz0q0vkdJ3s51b0+6NA/ndH94brtLb/1QLuNUoUFy0P69o/NJuAo20+fsJ8uAI/2BRyLXCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:44.753091Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0701717","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c96cd77cd3a232f096b5eb8bb9518db7b8d63f7d7534c511c680b69a2aa320b","sha256:571ed4958ec2dc62a65ea7e7640c4e9cd43634450fbd133164000fd5f97b9dae"],"state_sha256":"5a78656ddf413f3c9d63d0d30d18231a19cbe70a5b74877d8c1bac7cb0fcec18"}