{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:TQGSFXCWUPZHM2XWGL7HR6BIZ4","short_pith_number":"pith:TQGSFXCW","schema_version":"1.0","canonical_sha256":"9c0d22dc56a3f2766af632fe78f828cf1bbd22fd14f24dc988194f5053bf5a31","source":{"kind":"arxiv","id":"1206.2576","version":1},"attestation_state":"computed","paper":{"title":"Scalar curvature and uniruledness on projective manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.DG"],"primary_cat":"math.AG","authors_text":"Bun Wong, Gordon Heier","submitted_at":"2012-06-12T16:03:27Z","abstract_excerpt":"It is a basic tenet in complex geometry that {\\it negative} curvature corresponds, in a suitable sense, to the absence of rational curves on, say, a complex projective manifold, while {\\it positive} curvature corresponds to the abundance of rational curves. In this spirit, we prove in this note that a projective manifold $M$ with a K\\\"ahler metric with positive total scalar curvature is uniruled, which is equivalent to every point of $M$ being contained in a rational curve. We also prove that if $M$ possesses a K\\\"ahler metric of total scalar curvature equal to zero, then either $M$ is unirule"},"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":"1206.2576","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-06-12T16:03:27Z","cross_cats_sorted":["math.CV","math.DG"],"title_canon_sha256":"d2240cb6bf9e5c244bf10ba2b110e77eec3e79f52bc7a3bfd984dc1ad88f646e","abstract_canon_sha256":"93bcc5fc9eda57e884060d3d37a8cee20ad98d58a3db0fa9c7e017071049ec7a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:44.134069Z","signature_b64":"rYMhkqVE/Px7WGd/AlEGa99OkHn4IBh8yHsaylINpXStJJYgASeXItTFkol5IpGE1Qc3m8El26WClsuHx8sbAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c0d22dc56a3f2766af632fe78f828cf1bbd22fd14f24dc988194f5053bf5a31","last_reissued_at":"2026-05-18T03:53:44.133554Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:44.133554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scalar curvature and uniruledness on projective manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.DG"],"primary_cat":"math.AG","authors_text":"Bun Wong, Gordon Heier","submitted_at":"2012-06-12T16:03:27Z","abstract_excerpt":"It is a basic tenet in complex geometry that {\\it negative} curvature corresponds, in a suitable sense, to the absence of rational curves on, say, a complex projective manifold, while {\\it positive} curvature corresponds to the abundance of rational curves. In this spirit, we prove in this note that a projective manifold $M$ with a K\\\"ahler metric with positive total scalar curvature is uniruled, which is equivalent to every point of $M$ being contained in a rational curve. We also prove that if $M$ possesses a K\\\"ahler metric of total scalar curvature equal to zero, then either $M$ is unirule"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2576","kind":"arxiv","version":1},"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":"1206.2576","created_at":"2026-05-18T03:53:44.133631+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.2576v1","created_at":"2026-05-18T03:53:44.133631+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.2576","created_at":"2026-05-18T03:53:44.133631+00:00"},{"alias_kind":"pith_short_12","alias_value":"TQGSFXCWUPZH","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"TQGSFXCWUPZHM2XW","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"TQGSFXCW","created_at":"2026-05-18T12:27:23.164592+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/TQGSFXCWUPZHM2XWGL7HR6BIZ4","json":"https://pith.science/pith/TQGSFXCWUPZHM2XWGL7HR6BIZ4.json","graph_json":"https://pith.science/api/pith-number/TQGSFXCWUPZHM2XWGL7HR6BIZ4/graph.json","events_json":"https://pith.science/api/pith-number/TQGSFXCWUPZHM2XWGL7HR6BIZ4/events.json","paper":"https://pith.science/paper/TQGSFXCW"},"agent_actions":{"view_html":"https://pith.science/pith/TQGSFXCWUPZHM2XWGL7HR6BIZ4","download_json":"https://pith.science/pith/TQGSFXCWUPZHM2XWGL7HR6BIZ4.json","view_paper":"https://pith.science/paper/TQGSFXCW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.2576&json=true","fetch_graph":"https://pith.science/api/pith-number/TQGSFXCWUPZHM2XWGL7HR6BIZ4/graph.json","fetch_events":"https://pith.science/api/pith-number/TQGSFXCWUPZHM2XWGL7HR6BIZ4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TQGSFXCWUPZHM2XWGL7HR6BIZ4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TQGSFXCWUPZHM2XWGL7HR6BIZ4/action/storage_attestation","attest_author":"https://pith.science/pith/TQGSFXCWUPZHM2XWGL7HR6BIZ4/action/author_attestation","sign_citation":"https://pith.science/pith/TQGSFXCWUPZHM2XWGL7HR6BIZ4/action/citation_signature","submit_replication":"https://pith.science/pith/TQGSFXCWUPZHM2XWGL7HR6BIZ4/action/replication_record"}},"created_at":"2026-05-18T03:53:44.133631+00:00","updated_at":"2026-05-18T03:53:44.133631+00:00"}