{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TYRU7HYTGK5UFGLGLYCXLD6RZI","short_pith_number":"pith:TYRU7HYT","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"},"canonical_sha256":"9e234f9f1332bb4299665e05758fd1ca3ad4c422f1be229ec1752899712dcf16","source":{"kind":"arxiv","id":"1609.07675","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07675","created_at":"2026-05-18T01:02:12Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07675v2","created_at":"2026-05-18T01:02:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07675","created_at":"2026-05-18T01:02:12Z"},{"alias_kind":"pith_short_12","alias_value":"TYRU7HYTGK5U","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TYRU7HYTGK5UFGLG","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TYRU7HYT","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TYRU7HYTGK5UFGLGLYCXLD6RZI","target":"record","payload":{"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"},"canonical_sha256":"9e234f9f1332bb4299665e05758fd1ca3ad4c422f1be229ec1752899712dcf16","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"},"source_kind":"arxiv","source_id":"1609.07675","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:02:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ePW/4kFt/6s6Xojrag/SvtMQq1669LLfxD1bfadvwWddBSM1FgclPmtKR4coWNBMI/uudIn0vt2OlALvhQorAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T15:35:10.824783Z"},"content_sha256":"2abd5eaff130a6e08323b94f67bdc0f3a4ae984fae1b222f0fab124386036288","schema_version":"1.0","event_id":"sha256:2abd5eaff130a6e08323b94f67bdc0f3a4ae984fae1b222f0fab124386036288"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TYRU7HYTGK5UFGLGLYCXLD6RZI","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:02:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3djpj+xIDVKEjWKOE/ubtZd6tMaV1WPPiXPlC5BkqXiLX/jvoF7v6imYPG1zQJfwbrLeHvupJ0E7OubyMM7IAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T15:35:10.825157Z"},"content_sha256":"0a8c84a75ef9c5cfbbee28a6717e6b405e15056ae335fd9ec70164cf963c1dcf","schema_version":"1.0","event_id":"sha256:0a8c84a75ef9c5cfbbee28a6717e6b405e15056ae335fd9ec70164cf963c1dcf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TYRU7HYTGK5UFGLGLYCXLD6RZI/bundle.json","state_url":"https://pith.science/pith/TYRU7HYTGK5UFGLGLYCXLD6RZI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TYRU7HYTGK5UFGLGLYCXLD6RZI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T15:35:10Z","links":{"resolver":"https://pith.science/pith/TYRU7HYTGK5UFGLGLYCXLD6RZI","bundle":"https://pith.science/pith/TYRU7HYTGK5UFGLGLYCXLD6RZI/bundle.json","state":"https://pith.science/pith/TYRU7HYTGK5UFGLGLYCXLD6RZI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TYRU7HYTGK5UFGLGLYCXLD6RZI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TYRU7HYTGK5UFGLGLYCXLD6RZI","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":"f7260290e5c1b1ffbb0d2420f29294be0d41dde65cec20f9cb6ccd304417f9c4","cross_cats_sorted":["math.AT","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-09-24T20:59:26Z","title_canon_sha256":"3ee9d899ea6cc28c3e112a8fb8164b9cd869582d45568471e782a11c0e8950eb"},"schema_version":"1.0","source":{"id":"1609.07675","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07675","created_at":"2026-05-18T01:02:12Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07675v2","created_at":"2026-05-18T01:02:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07675","created_at":"2026-05-18T01:02:12Z"},{"alias_kind":"pith_short_12","alias_value":"TYRU7HYTGK5U","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TYRU7HYTGK5UFGLG","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TYRU7HYT","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:0a8c84a75ef9c5cfbbee28a6717e6b405e15056ae335fd9ec70164cf963c1dcf","target":"graph","created_at":"2026-05-18T01:02:12Z","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 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.","authors_text":"Alexandra Otiman","cross_cats":["math.AT","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-09-24T20:59:26Z","title":"Morse-Novikov cohomology of locally conformally K\\\"ahler surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07675","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":"sha256:2abd5eaff130a6e08323b94f67bdc0f3a4ae984fae1b222f0fab124386036288","target":"record","created_at":"2026-05-18T01:02:12Z","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":"f7260290e5c1b1ffbb0d2420f29294be0d41dde65cec20f9cb6ccd304417f9c4","cross_cats_sorted":["math.AT","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-09-24T20:59:26Z","title_canon_sha256":"3ee9d899ea6cc28c3e112a8fb8164b9cd869582d45568471e782a11c0e8950eb"},"schema_version":"1.0","source":{"id":"1609.07675","kind":"arxiv","version":2}},"canonical_sha256":"9e234f9f1332bb4299665e05758fd1ca3ad4c422f1be229ec1752899712dcf16","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e234f9f1332bb4299665e05758fd1ca3ad4c422f1be229ec1752899712dcf16","first_computed_at":"2026-05-18T01:02:12.246423Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:12.246423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TKnGI9tb8+8M461oFc9hoZKx6h8iE1MHdAzS9DetYAjGmxNbt2HNkDYsYWNjqlrH4y4pYrc92liRYP8UhEUCCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:12.247040Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.07675","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2abd5eaff130a6e08323b94f67bdc0f3a4ae984fae1b222f0fab124386036288","sha256:0a8c84a75ef9c5cfbbee28a6717e6b405e15056ae335fd9ec70164cf963c1dcf"],"state_sha256":"b9a74f8aac5fdcbc6c506ea206d4d68a83b943f06932a4782808059ef745d6f2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pr9OQO/wB5E4FJgUDq7YWefBEpVHvqaBOmdCAwVq3igR1SGpRyXFS5cip7rWnLWz933IROgjFZneFcNfaiq0Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T15:35:10.827173Z","bundle_sha256":"2f3983adec1bd35e1e26b0498635c849235fcf63109093aae977b0d39911bd13"}}