{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NNTIESNMA6SXDTKU6E7RMS3T7S","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":"be32767dee9a9837a1bbd019209ab77da2d479737fcf13ea9c4c994d2bac9de5","cross_cats_sorted":["math.AG","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-09-08T15:49:49Z","title_canon_sha256":"f0849c30093e4c9afd26b5b1c3f78b98bb3dfeda5ee06bf9efdc9d4c982eb532"},"schema_version":"1.0","source":{"id":"1409.2404","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.2404","created_at":"2026-05-18T02:41:03Z"},{"alias_kind":"arxiv_version","alias_value":"1409.2404v2","created_at":"2026-05-18T02:41:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2404","created_at":"2026-05-18T02:41:03Z"},{"alias_kind":"pith_short_12","alias_value":"NNTIESNMA6SX","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NNTIESNMA6SXDTKU","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NNTIESNM","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:59e31bab0cdd678bc950bdc57cb8153d24b52b7adfcfa909c17bba4349923821","target":"graph","created_at":"2026-05-18T02:41:03Z","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":"By using analytic method, we prove that there exist rational curves on compact Hermitian manifolds with positive holomorphic bisectional curvature. It confirms a question of S.-T. Yau. It is well-known that Mori proved in \\cite{Mori79} that every compact complex manifold $N$ with $c_1(N)>0$ contains at least one rational curve. However, as a borderline example, we show that the standard Hopf surface $S^1\\times S^3$ has a Hermitian metric with non-negative holomorphic bisectional curvature (in particular, $c_1(S^1\\times S^3)\\geq 0$), but it contains no rational curve.","authors_text":"Huitao Feng, Kefeng Liu, Xiaokui Yang, Xueyuan Wan","cross_cats":["math.AG","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-09-08T15:49:49Z","title":"Rational curves on Hermitian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2404","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":"sha256:8be47d7cfeaa708023c3c0d1080fdb90168f047c0bb6a5dbda62da6628257482","target":"record","created_at":"2026-05-18T02:41:03Z","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":"be32767dee9a9837a1bbd019209ab77da2d479737fcf13ea9c4c994d2bac9de5","cross_cats_sorted":["math.AG","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-09-08T15:49:49Z","title_canon_sha256":"f0849c30093e4c9afd26b5b1c3f78b98bb3dfeda5ee06bf9efdc9d4c982eb532"},"schema_version":"1.0","source":{"id":"1409.2404","kind":"arxiv","version":2}},"canonical_sha256":"6b668249ac07a571cd54f13f164b73fc9197674ba1a8724164fa8b9b8368a16b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b668249ac07a571cd54f13f164b73fc9197674ba1a8724164fa8b9b8368a16b","first_computed_at":"2026-05-18T02:41:03.252460Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:03.252460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T4n4BsPOCvjiIYQqSSPbN7vch+MTNDtJiJCv359Q9s17kwDJA6quktRa3e9BRX0g5NRIvwUSUZBwP8ig9JtaBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:03.253095Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.2404","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8be47d7cfeaa708023c3c0d1080fdb90168f047c0bb6a5dbda62da6628257482","sha256:59e31bab0cdd678bc950bdc57cb8153d24b52b7adfcfa909c17bba4349923821"],"state_sha256":"f227d32105aac4197897321a0056b7aa174a36045ef1a83085ffbf0ec721772f"}