{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:DFZ2EMDTIVDWZOSO6YKAG3NHUG","short_pith_number":"pith:DFZ2EMDT","schema_version":"1.0","canonical_sha256":"1973a2307345476cba4ef614036da7a192f99324475bf47df53022f341b9cf2f","source":{"kind":"arxiv","id":"1911.04717","version":3},"attestation_state":"computed","paper":{"title":"Holomorphic vector fields and rationality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Wenchuan Hu","submitted_at":"2019-11-12T07:51:32Z","abstract_excerpt":"We show that a nonsingular complex projective variety admitting a holomorphic vector field with nonempty isolated zeroes, is rational using a key technique by Harvey-Lawson on finite volume flows. This statement was conjectured by J. Carrell. By the same technique, we obtain a uniform upper bound of Betti numbers of nonsingular complex projective variety admitting a holomorphic vector field with exact one zero point. Such an upper bound depends only on the dimension of the variety, which is a stronger version of a result of Akyildiz and Carrell."},"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":"1911.04717","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-11-12T07:51:32Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"c2c984909e8a1b6506d86a78ad56eb36c4af2b5995583103b4aa8efbf95577d8","abstract_canon_sha256":"6829a1a4770fda3957e484f77863cea1ba9d564533a578f7691a542cfe823587"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:44:41.361031Z","signature_b64":"1ZDXthNvq16lRAL05Kb6YXEz6zNwTBMlpJlZAlX+QHsx5fTptYtAXnEwjgPe4uPIZtKha7V82XN5RgvLSFqEAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1973a2307345476cba4ef614036da7a192f99324475bf47df53022f341b9cf2f","last_reissued_at":"2026-07-05T00:44:41.360570Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:44:41.360570Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Holomorphic vector fields and rationality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Wenchuan Hu","submitted_at":"2019-11-12T07:51:32Z","abstract_excerpt":"We show that a nonsingular complex projective variety admitting a holomorphic vector field with nonempty isolated zeroes, is rational using a key technique by Harvey-Lawson on finite volume flows. This statement was conjectured by J. Carrell. By the same technique, we obtain a uniform upper bound of Betti numbers of nonsingular complex projective variety admitting a holomorphic vector field with exact one zero point. Such an upper bound depends only on the dimension of the variety, which is a stronger version of a result of Akyildiz and Carrell."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.04717","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1911.04717/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1911.04717","created_at":"2026-07-05T00:44:41.360627+00:00"},{"alias_kind":"arxiv_version","alias_value":"1911.04717v3","created_at":"2026-07-05T00:44:41.360627+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.04717","created_at":"2026-07-05T00:44:41.360627+00:00"},{"alias_kind":"pith_short_12","alias_value":"DFZ2EMDTIVDW","created_at":"2026-07-05T00:44:41.360627+00:00"},{"alias_kind":"pith_short_16","alias_value":"DFZ2EMDTIVDWZOSO","created_at":"2026-07-05T00:44:41.360627+00:00"},{"alias_kind":"pith_short_8","alias_value":"DFZ2EMDT","created_at":"2026-07-05T00:44:41.360627+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/DFZ2EMDTIVDWZOSO6YKAG3NHUG","json":"https://pith.science/pith/DFZ2EMDTIVDWZOSO6YKAG3NHUG.json","graph_json":"https://pith.science/api/pith-number/DFZ2EMDTIVDWZOSO6YKAG3NHUG/graph.json","events_json":"https://pith.science/api/pith-number/DFZ2EMDTIVDWZOSO6YKAG3NHUG/events.json","paper":"https://pith.science/paper/DFZ2EMDT"},"agent_actions":{"view_html":"https://pith.science/pith/DFZ2EMDTIVDWZOSO6YKAG3NHUG","download_json":"https://pith.science/pith/DFZ2EMDTIVDWZOSO6YKAG3NHUG.json","view_paper":"https://pith.science/paper/DFZ2EMDT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1911.04717&json=true","fetch_graph":"https://pith.science/api/pith-number/DFZ2EMDTIVDWZOSO6YKAG3NHUG/graph.json","fetch_events":"https://pith.science/api/pith-number/DFZ2EMDTIVDWZOSO6YKAG3NHUG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DFZ2EMDTIVDWZOSO6YKAG3NHUG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DFZ2EMDTIVDWZOSO6YKAG3NHUG/action/storage_attestation","attest_author":"https://pith.science/pith/DFZ2EMDTIVDWZOSO6YKAG3NHUG/action/author_attestation","sign_citation":"https://pith.science/pith/DFZ2EMDTIVDWZOSO6YKAG3NHUG/action/citation_signature","submit_replication":"https://pith.science/pith/DFZ2EMDTIVDWZOSO6YKAG3NHUG/action/replication_record"}},"created_at":"2026-07-05T00:44:41.360627+00:00","updated_at":"2026-07-05T00:44:41.360627+00:00"}