{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:TYRU7HYTGK5UFGLGLYCXLD6RZI","short_pith_number":"pith:TYRU7HYT","schema_version":"1.0","canonical_sha256":"9e234f9f1332bb4299665e05758fd1ca3ad4c422f1be229ec1752899712dcf16","source":{"kind":"arxiv","id":"1609.07675","version":2},"attestation_state":"computed","paper":{"title":"Morse-Novikov cohomology of locally conformally K\\\"ahler surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.SG"],"primary_cat":"math.DG","authors_text":"Alexandra Otiman","submitted_at":"2016-09-24T20:59:26Z","abstract_excerpt":"We review the properties of the Morse-Novikov cohomology and compute it for all known compact complex surfaces with locally conformally K\\\"ahler metrics. We present explicit computations for the Inoue surfaces $\\mathcal{S}^0$, $\\mathcal{S}^+$, $\\mathcal{S}^-$ and classify the locally conformally K\\\"ahler (and the tamed locally conformally symplectic) forms on $\\mathcal{S}^0$. We prove the nonexistence of LCK metrics with potential and more generally, of $d_\\theta$-exact LCK metrics on Inoue surfaces and Oeljeklaus-Toma manifolds."},"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":"1609.07675","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-09-24T20:59:26Z","cross_cats_sorted":["math.AT","math.SG"],"title_canon_sha256":"3ee9d899ea6cc28c3e112a8fb8164b9cd869582d45568471e782a11c0e8950eb","abstract_canon_sha256":"f7260290e5c1b1ffbb0d2420f29294be0d41dde65cec20f9cb6ccd304417f9c4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:12.247040Z","signature_b64":"TKnGI9tb8+8M461oFc9hoZKx6h8iE1MHdAzS9DetYAjGmxNbt2HNkDYsYWNjqlrH4y4pYrc92liRYP8UhEUCCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e234f9f1332bb4299665e05758fd1ca3ad4c422f1be229ec1752899712dcf16","last_reissued_at":"2026-05-18T01:02:12.246423Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:12.246423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Morse-Novikov cohomology of locally conformally K\\\"ahler surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.SG"],"primary_cat":"math.DG","authors_text":"Alexandra Otiman","submitted_at":"2016-09-24T20:59:26Z","abstract_excerpt":"We review the properties of the Morse-Novikov cohomology and compute it for all known compact complex surfaces with locally conformally K\\\"ahler metrics. We present explicit computations for the Inoue surfaces $\\mathcal{S}^0$, $\\mathcal{S}^+$, $\\mathcal{S}^-$ and classify the locally conformally K\\\"ahler (and the tamed locally conformally symplectic) forms on $\\mathcal{S}^0$. We prove the nonexistence of LCK metrics with potential and more generally, of $d_\\theta$-exact LCK metrics on Inoue surfaces and Oeljeklaus-Toma manifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07675","kind":"arxiv","version":2},"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":"1609.07675","created_at":"2026-05-18T01:02:12.246528+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.07675v2","created_at":"2026-05-18T01:02:12.246528+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07675","created_at":"2026-05-18T01:02:12.246528+00:00"},{"alias_kind":"pith_short_12","alias_value":"TYRU7HYTGK5U","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"TYRU7HYTGK5UFGLG","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"TYRU7HYT","created_at":"2026-05-18T12:30:46.583412+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/TYRU7HYTGK5UFGLGLYCXLD6RZI","json":"https://pith.science/pith/TYRU7HYTGK5UFGLGLYCXLD6RZI.json","graph_json":"https://pith.science/api/pith-number/TYRU7HYTGK5UFGLGLYCXLD6RZI/graph.json","events_json":"https://pith.science/api/pith-number/TYRU7HYTGK5UFGLGLYCXLD6RZI/events.json","paper":"https://pith.science/paper/TYRU7HYT"},"agent_actions":{"view_html":"https://pith.science/pith/TYRU7HYTGK5UFGLGLYCXLD6RZI","download_json":"https://pith.science/pith/TYRU7HYTGK5UFGLGLYCXLD6RZI.json","view_paper":"https://pith.science/paper/TYRU7HYT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.07675&json=true","fetch_graph":"https://pith.science/api/pith-number/TYRU7HYTGK5UFGLGLYCXLD6RZI/graph.json","fetch_events":"https://pith.science/api/pith-number/TYRU7HYTGK5UFGLGLYCXLD6RZI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TYRU7HYTGK5UFGLGLYCXLD6RZI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TYRU7HYTGK5UFGLGLYCXLD6RZI/action/storage_attestation","attest_author":"https://pith.science/pith/TYRU7HYTGK5UFGLGLYCXLD6RZI/action/author_attestation","sign_citation":"https://pith.science/pith/TYRU7HYTGK5UFGLGLYCXLD6RZI/action/citation_signature","submit_replication":"https://pith.science/pith/TYRU7HYTGK5UFGLGLYCXLD6RZI/action/replication_record"}},"created_at":"2026-05-18T01:02:12.246528+00:00","updated_at":"2026-05-18T01:02:12.246528+00:00"}