{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:X672ZEIPZILK6NIIUYSOPBHNHZ","short_pith_number":"pith:X672ZEIP","schema_version":"1.0","canonical_sha256":"bfbfac910fca16af3508a624e784ed3e45a8f6bf17da6d78bd16ffce47d086ea","source":{"kind":"arxiv","id":"math/0504422","version":3},"attestation_state":"computed","paper":{"title":"On the complex structure of K\\\"ahler manifolds with nonnegative curvature","license":"","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Albert Chau, Luen-fai Tam","submitted_at":"2005-04-21T03:55:31Z","abstract_excerpt":"We study the asymptotic behavior of the K\\\"ahler-Ricci flow on K\\\"ahler manifolds of nonnegative holomorphic bisectional curvature. Using these results we prove that a complete noncompact K\\\"ahler manifold with nonnegative bounded holomorphic bisectional curvature and maximal volume growth is biholomorphic to complex Euclidean space $\\C^n$. We also show that the volume growth condition can be removed if we assume $(M, g)$ has average quadratic scalar curvature decay (see Theorem 2.1) and positive curvature operator."},"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":"math/0504422","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2005-04-21T03:55:31Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"3007297e274814d799b6d56e9bde4c8e8a31b8142a0612e0e5bd4ff49ad04884","abstract_canon_sha256":"1f891fe3724202845cd56d2dbe68f0fa3a6d16e309f8aac08eac8ad1f336e2b7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:23.497046Z","signature_b64":"0LCDMXdqIUJX16jijuT1G0SNzgWwzr/fTna9RSJWZl6ILqHecyPOYHqMr3ivvy7BtOIWB4lZH7Nc5yKs2ai3CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bfbfac910fca16af3508a624e784ed3e45a8f6bf17da6d78bd16ffce47d086ea","last_reissued_at":"2026-05-18T01:05:23.496563Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:23.496563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the complex structure of K\\\"ahler manifolds with nonnegative curvature","license":"","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Albert Chau, Luen-fai Tam","submitted_at":"2005-04-21T03:55:31Z","abstract_excerpt":"We study the asymptotic behavior of the K\\\"ahler-Ricci flow on K\\\"ahler manifolds of nonnegative holomorphic bisectional curvature. Using these results we prove that a complete noncompact K\\\"ahler manifold with nonnegative bounded holomorphic bisectional curvature and maximal volume growth is biholomorphic to complex Euclidean space $\\C^n$. We also show that the volume growth condition can be removed if we assume $(M, g)$ has average quadratic scalar curvature decay (see Theorem 2.1) and positive curvature operator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0504422","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":""},"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":"math/0504422","created_at":"2026-05-18T01:05:23.496639+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0504422v3","created_at":"2026-05-18T01:05:23.496639+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0504422","created_at":"2026-05-18T01:05:23.496639+00:00"},{"alias_kind":"pith_short_12","alias_value":"X672ZEIPZILK","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_16","alias_value":"X672ZEIPZILK6NII","created_at":"2026-05-18T12:25:53.939244+00:00"},{"alias_kind":"pith_short_8","alias_value":"X672ZEIP","created_at":"2026-05-18T12:25:53.939244+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/X672ZEIPZILK6NIIUYSOPBHNHZ","json":"https://pith.science/pith/X672ZEIPZILK6NIIUYSOPBHNHZ.json","graph_json":"https://pith.science/api/pith-number/X672ZEIPZILK6NIIUYSOPBHNHZ/graph.json","events_json":"https://pith.science/api/pith-number/X672ZEIPZILK6NIIUYSOPBHNHZ/events.json","paper":"https://pith.science/paper/X672ZEIP"},"agent_actions":{"view_html":"https://pith.science/pith/X672ZEIPZILK6NIIUYSOPBHNHZ","download_json":"https://pith.science/pith/X672ZEIPZILK6NIIUYSOPBHNHZ.json","view_paper":"https://pith.science/paper/X672ZEIP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0504422&json=true","fetch_graph":"https://pith.science/api/pith-number/X672ZEIPZILK6NIIUYSOPBHNHZ/graph.json","fetch_events":"https://pith.science/api/pith-number/X672ZEIPZILK6NIIUYSOPBHNHZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X672ZEIPZILK6NIIUYSOPBHNHZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X672ZEIPZILK6NIIUYSOPBHNHZ/action/storage_attestation","attest_author":"https://pith.science/pith/X672ZEIPZILK6NIIUYSOPBHNHZ/action/author_attestation","sign_citation":"https://pith.science/pith/X672ZEIPZILK6NIIUYSOPBHNHZ/action/citation_signature","submit_replication":"https://pith.science/pith/X672ZEIPZILK6NIIUYSOPBHNHZ/action/replication_record"}},"created_at":"2026-05-18T01:05:23.496639+00:00","updated_at":"2026-05-18T01:05:23.496639+00:00"}