{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XYNZT3SKV5CDVYVXHLNSWUGLYW","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":"b7ec70634bdadd65ac24605c5cfe02a0af4d7c0611ec0bd896760891a2b2cf96","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-16T16:58:46Z","title_canon_sha256":"447196d9f01313e0c97d47b5add01ae3916f9d0149f2a53f6fbf01fbb865851f"},"schema_version":"1.0","source":{"id":"1510.04946","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04946","created_at":"2026-05-18T00:00:22Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04946v3","created_at":"2026-05-18T00:00:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04946","created_at":"2026-05-18T00:00:22Z"},{"alias_kind":"pith_short_12","alias_value":"XYNZT3SKV5CD","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XYNZT3SKV5CDVYVX","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XYNZT3SK","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:31993db1d68fcde2c478432a71ac227ce764f9291c7c0e300433699ad99fb55e","target":"graph","created_at":"2026-05-18T00:00:22Z","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":"We establish a Hard Lefschetz Theorem for the de Rham cohomology of compact Vaisman manifolds. A similar result is proved for the basic cohomology with respect to the Lee vector field. Motivated by these results, we introduce the notions of a Lefschetz and of a basic Lefschetz locally conformal symplectic (l.c.s.) manifold of the first kind. We prove that the two notions are equivalent if there exists a Riemannian metric such that the Lee vector field is unitary and parallel and its metric dual $1$-form coincides with the Lee $1$-form. Finally, we discuss several examples of compact l.c.s. man","authors_text":"Antonio De Nicola, Beniamino Cappelletti-Montano, Ivan Yudin, Juan Carlos Marrero","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-16T16:58:46Z","title":"Hard Lefschetz Theorem for Vaisman manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04946","kind":"arxiv","version":3},"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":"sha256:90f891e93552e179ed4002f88bde6b559b450fd83965493e4d3f2b7d4b131583","target":"record","created_at":"2026-05-18T00:00:22Z","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":"b7ec70634bdadd65ac24605c5cfe02a0af4d7c0611ec0bd896760891a2b2cf96","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-10-16T16:58:46Z","title_canon_sha256":"447196d9f01313e0c97d47b5add01ae3916f9d0149f2a53f6fbf01fbb865851f"},"schema_version":"1.0","source":{"id":"1510.04946","kind":"arxiv","version":3}},"canonical_sha256":"be1b99ee4aaf443ae2b73adb2b50cbc592c4521543e1db9ab4e34fe2ad3313a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be1b99ee4aaf443ae2b73adb2b50cbc592c4521543e1db9ab4e34fe2ad3313a9","first_computed_at":"2026-05-18T00:00:22.891148Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:22.891148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"poFnTNd2m2ocXKte3HCZWecDBa40SEERytWe0AmLEu3yPyUl2ikXRHzmN8GSguLaJKbogNTNHiNBed6WIVOpCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:22.891667Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.04946","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90f891e93552e179ed4002f88bde6b559b450fd83965493e4d3f2b7d4b131583","sha256:31993db1d68fcde2c478432a71ac227ce764f9291c7c0e300433699ad99fb55e"],"state_sha256":"af70764da77c1aeafa0f7acfb289f1c52baa52aa8c627111711329fb661cbac4"}