{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:I5IYDONAB6U3GDH25K7PWIQVKF","short_pith_number":"pith:I5IYDONA","schema_version":"1.0","canonical_sha256":"475181b9a00fa9b30cfaeabefb22155156f52e7013f7664f3cd5eaa29abd508e","source":{"kind":"arxiv","id":"0712.0107","version":4},"attestation_state":"computed","paper":{"title":"Morse-Novikov cohomology of locally conformally K\\\"ahler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CV"],"primary_cat":"math.DG","authors_text":"Liviu Ornea, Misha Verbitsky","submitted_at":"2007-12-01T21:17:30Z","abstract_excerpt":"A locally conformally Kahler (LCK) manifold is a complex manifold admitting a Kahler covering, with the monodromy acting on this covering by homotheties. We define three cohomology invariants, the Lee class, the Morse-Novikov class, and the Bott-Chern class, of an LCK-structure. These invariants together play the same role as the Kahler class in Kahler geometry. If these classes for two LCK-structures coincide, the difference between these structures can be expressed by a smooth potential, similar to the Kahler case. We show that the Morse-Novikov class and the Bott-Chern class of a Vaisman ma"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0712.0107","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2007-12-01T21:17:30Z","cross_cats_sorted":["math.AG","math.CV"],"title_canon_sha256":"2ef19c7fedefb853502a6c775c9df65058a6803c1dc4e4a5ee59e67a378799af","abstract_canon_sha256":"8c344027192805d4f55c072e778ae3ecaaeba24a515a77a5975c277422c54602"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:08.848259Z","signature_b64":"bnshZPDoJwE4wBKQwrxwjA9ideUoDONpF6RZLikHY2rbwBJACksbUc2ZUezNJL2h2RIN8MThREDCVaBvDDw+Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"475181b9a00fa9b30cfaeabefb22155156f52e7013f7664f3cd5eaa29abd508e","last_reissued_at":"2026-05-18T02:16:08.847669Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:08.847669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Morse-Novikov cohomology of locally conformally K\\\"ahler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CV"],"primary_cat":"math.DG","authors_text":"Liviu Ornea, Misha Verbitsky","submitted_at":"2007-12-01T21:17:30Z","abstract_excerpt":"A locally conformally Kahler (LCK) manifold is a complex manifold admitting a Kahler covering, with the monodromy acting on this covering by homotheties. We define three cohomology invariants, the Lee class, the Morse-Novikov class, and the Bott-Chern class, of an LCK-structure. These invariants together play the same role as the Kahler class in Kahler geometry. If these classes for two LCK-structures coincide, the difference between these structures can be expressed by a smooth potential, similar to the Kahler case. We show that the Morse-Novikov class and the Bott-Chern class of a Vaisman ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.0107","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"0712.0107","created_at":"2026-05-18T02:16:08.847767+00:00"},{"alias_kind":"arxiv_version","alias_value":"0712.0107v4","created_at":"2026-05-18T02:16:08.847767+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.0107","created_at":"2026-05-18T02:16:08.847767+00:00"},{"alias_kind":"pith_short_12","alias_value":"I5IYDONAB6U3","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_16","alias_value":"I5IYDONAB6U3GDH2","created_at":"2026-05-18T12:25:55.427421+00:00"},{"alias_kind":"pith_short_8","alias_value":"I5IYDONA","created_at":"2026-05-18T12:25:55.427421+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/I5IYDONAB6U3GDH25K7PWIQVKF","json":"https://pith.science/pith/I5IYDONAB6U3GDH25K7PWIQVKF.json","graph_json":"https://pith.science/api/pith-number/I5IYDONAB6U3GDH25K7PWIQVKF/graph.json","events_json":"https://pith.science/api/pith-number/I5IYDONAB6U3GDH25K7PWIQVKF/events.json","paper":"https://pith.science/paper/I5IYDONA"},"agent_actions":{"view_html":"https://pith.science/pith/I5IYDONAB6U3GDH25K7PWIQVKF","download_json":"https://pith.science/pith/I5IYDONAB6U3GDH25K7PWIQVKF.json","view_paper":"https://pith.science/paper/I5IYDONA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0712.0107&json=true","fetch_graph":"https://pith.science/api/pith-number/I5IYDONAB6U3GDH25K7PWIQVKF/graph.json","fetch_events":"https://pith.science/api/pith-number/I5IYDONAB6U3GDH25K7PWIQVKF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I5IYDONAB6U3GDH25K7PWIQVKF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I5IYDONAB6U3GDH25K7PWIQVKF/action/storage_attestation","attest_author":"https://pith.science/pith/I5IYDONAB6U3GDH25K7PWIQVKF/action/author_attestation","sign_citation":"https://pith.science/pith/I5IYDONAB6U3GDH25K7PWIQVKF/action/citation_signature","submit_replication":"https://pith.science/pith/I5IYDONAB6U3GDH25K7PWIQVKF/action/replication_record"}},"created_at":"2026-05-18T02:16:08.847767+00:00","updated_at":"2026-05-18T02:16:08.847767+00:00"}