{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:N5O4HOKKCBIRTVT7Z7O263AZ4M","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":"5c18115d0ea69e7aaa1ce5a1f03551cc0a2e91518dd976cc0f3cf297a8138d9a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DG","submitted_at":"2015-12-03T07:05:38Z","title_canon_sha256":"16f84abf64ea6759d77c71e4116c766a935858865a19c9f59d7864ac05eaf408"},"schema_version":"1.0","source":{"id":"1512.00968","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.00968","created_at":"2026-05-18T01:21:36Z"},{"alias_kind":"arxiv_version","alias_value":"1512.00968v2","created_at":"2026-05-18T01:21:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.00968","created_at":"2026-05-18T01:21:36Z"},{"alias_kind":"pith_short_12","alias_value":"N5O4HOKKCBIR","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"N5O4HOKKCBIRTVT7","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"N5O4HOKK","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:e0ac9b30baf249ffd1f171c1e315bc047c695bd1ab34f6dde8abedf67d125d05","target":"graph","created_at":"2026-05-18T01:21:36Z","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":"A locally conformally Kahler manifold is a Hermitian manifold $(M,I,\\omega)$ satisfying $d\\omega=\\theta\\wedge \\omega$, where $\\theta$ is a closed 1-form, called the Lee form of $M$. It is called pluricanonical if $\\nabla\\theta$ is of Hodge type $(2,0)+(0,2)$, where $\\nabla$ is the Levi-Civita connection, and Vaisman if $\\nabla\\theta=0$. We show that a compact LCK manifold is pluricanonical if and only if the Lee form has constant length and the Kahler form of its covering admits an automorphic potential. Using a degenerate Monge-Ampere equation and the classification of surfaces of Kahler rank","authors_text":"Liviu Ornea, Misha Verbitsky","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DG","submitted_at":"2015-12-03T07:05:38Z","title":"Compact pluricanonical manifolds are Vaisman"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00968","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":"sha256:92e3a53dc0f52308d11bcc72a191d738f9a6b5a96e4fdce1225fd8864726f8b4","target":"record","created_at":"2026-05-18T01:21:36Z","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":"5c18115d0ea69e7aaa1ce5a1f03551cc0a2e91518dd976cc0f3cf297a8138d9a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.DG","submitted_at":"2015-12-03T07:05:38Z","title_canon_sha256":"16f84abf64ea6759d77c71e4116c766a935858865a19c9f59d7864ac05eaf408"},"schema_version":"1.0","source":{"id":"1512.00968","kind":"arxiv","version":2}},"canonical_sha256":"6f5dc3b94a105119d67fcfddaf6c19e3134e3801e16ccf00c78f9deeea2a703a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f5dc3b94a105119d67fcfddaf6c19e3134e3801e16ccf00c78f9deeea2a703a","first_computed_at":"2026-05-18T01:21:36.731696Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:36.731696Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZxHC1oKTbSwcW2tsUvbG5bVCm+aBJ39H4EAGSUD5kF55aMiYs7rWiyDH4MwF6uc0mPJ5MrQg7S8Fd4dMx0yCAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:36.732142Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.00968","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92e3a53dc0f52308d11bcc72a191d738f9a6b5a96e4fdce1225fd8864726f8b4","sha256:e0ac9b30baf249ffd1f171c1e315bc047c695bd1ab34f6dde8abedf67d125d05"],"state_sha256":"2b8ba0b5b2623127d18934579e3090fdee527c9ee25b4d83c08259717570be66"}