{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:Q7HQKQEFYI5ZKWPDUCHTDU7QK6","short_pith_number":"pith:Q7HQKQEF","canonical_record":{"source":{"id":"1109.2504","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-12T15:26:43Z","cross_cats_sorted":[],"title_canon_sha256":"fcec1c6042cfd9ed16bd8e91089e7f59a803d28337ce8f16fdcf15f7f289a9ef","abstract_canon_sha256":"21dda81ddd4181e649a04551ed6d6aa6f8a07e0dcf544bbd2e812838786ad804"},"schema_version":"1.0"},"canonical_sha256":"87cf054085c23b9559e3a08f31d3f057a83ae6853733746f3a19682adfbfb745","source":{"kind":"arxiv","id":"1109.2504","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2504","created_at":"2026-05-18T04:13:37Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2504v1","created_at":"2026-05-18T04:13:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2504","created_at":"2026-05-18T04:13:37Z"},{"alias_kind":"pith_short_12","alias_value":"Q7HQKQEFYI5Z","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q7HQKQEFYI5ZKWPD","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q7HQKQEF","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:Q7HQKQEFYI5ZKWPDUCHTDU7QK6","target":"record","payload":{"canonical_record":{"source":{"id":"1109.2504","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-12T15:26:43Z","cross_cats_sorted":[],"title_canon_sha256":"fcec1c6042cfd9ed16bd8e91089e7f59a803d28337ce8f16fdcf15f7f289a9ef","abstract_canon_sha256":"21dda81ddd4181e649a04551ed6d6aa6f8a07e0dcf544bbd2e812838786ad804"},"schema_version":"1.0"},"canonical_sha256":"87cf054085c23b9559e3a08f31d3f057a83ae6853733746f3a19682adfbfb745","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:13:37.522819Z","signature_b64":"FeMVLyi6JIIaleye3+Jdz9NTi9gxzBFKgEhKlDFy6DCGPk9hP+v6FrERzeJvPYBxjYTCk60Fn4S2l8klvs0cAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87cf054085c23b9559e3a08f31d3f057a83ae6853733746f3a19682adfbfb745","last_reissued_at":"2026-05-18T04:13:37.521959Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:13:37.521959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.2504","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:13:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+MafOSUtL9sl4dTIvwRlXXqyN6EtVwwOYcqLPwvMj1B+4jxDDsvMu3Ug1rML9HYA5voBCmthL+fr61JhoZe1BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:42:01.700721Z"},"content_sha256":"fefd4441d257b9c39d0bca5fc9815dca88412abafed326bedab77703ce5fd1a6","schema_version":"1.0","event_id":"sha256:fefd4441d257b9c39d0bca5fc9815dca88412abafed326bedab77703ce5fd1a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:Q7HQKQEFYI5ZKWPDUCHTDU7QK6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Note on Wu-Zheng's Splitting Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Chengjie Yu","submitted_at":"2011-09-12T15:26:43Z","abstract_excerpt":"Cao's splitting theorem says that for any complete K\\\"ahler-Ricci flow $(M,g(t))$ with $t\\in [0,T)$, $M$ simply connected and nonnegative bounded holomorphic bisectional curvature, $(M,g(t))$ is holomorphically isometric to $\\C^k\\times (N,h(t))$ where $(N,h(t))$ is a Kahler-Ricci flow with positive Ricci curvature for $t>0$. In this article, we show that $k=n-r$ where $r$ is the Ricci rank of the initial metric. As a corollary, we also confirm a splitting conjecture of Wu-Zheng when curvature is assumed to be bounded."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2504","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:13:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q/8Kag9Pw9OEsigMqu8bcd50KvGwP8MGni/CChYbVlBiZaCx48iI27Vq+bn+PWbwYMFA8n+y5ZuFY/iDh9LRDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:42:01.701444Z"},"content_sha256":"e34a01f8881ab22d8b945e1cca77fa4f534f3c4655ec8a31156374f54abeae9f","schema_version":"1.0","event_id":"sha256:e34a01f8881ab22d8b945e1cca77fa4f534f3c4655ec8a31156374f54abeae9f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q7HQKQEFYI5ZKWPDUCHTDU7QK6/bundle.json","state_url":"https://pith.science/pith/Q7HQKQEFYI5ZKWPDUCHTDU7QK6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q7HQKQEFYI5ZKWPDUCHTDU7QK6/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":"2026-06-07T17:42:01Z","links":{"resolver":"https://pith.science/pith/Q7HQKQEFYI5ZKWPDUCHTDU7QK6","bundle":"https://pith.science/pith/Q7HQKQEFYI5ZKWPDUCHTDU7QK6/bundle.json","state":"https://pith.science/pith/Q7HQKQEFYI5ZKWPDUCHTDU7QK6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q7HQKQEFYI5ZKWPDUCHTDU7QK6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Q7HQKQEFYI5ZKWPDUCHTDU7QK6","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":"21dda81ddd4181e649a04551ed6d6aa6f8a07e0dcf544bbd2e812838786ad804","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-12T15:26:43Z","title_canon_sha256":"fcec1c6042cfd9ed16bd8e91089e7f59a803d28337ce8f16fdcf15f7f289a9ef"},"schema_version":"1.0","source":{"id":"1109.2504","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2504","created_at":"2026-05-18T04:13:37Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2504v1","created_at":"2026-05-18T04:13:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2504","created_at":"2026-05-18T04:13:37Z"},{"alias_kind":"pith_short_12","alias_value":"Q7HQKQEFYI5Z","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q7HQKQEFYI5ZKWPD","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q7HQKQEF","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:e34a01f8881ab22d8b945e1cca77fa4f534f3c4655ec8a31156374f54abeae9f","target":"graph","created_at":"2026-05-18T04:13:37Z","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":"Cao's splitting theorem says that for any complete K\\\"ahler-Ricci flow $(M,g(t))$ with $t\\in [0,T)$, $M$ simply connected and nonnegative bounded holomorphic bisectional curvature, $(M,g(t))$ is holomorphically isometric to $\\C^k\\times (N,h(t))$ where $(N,h(t))$ is a Kahler-Ricci flow with positive Ricci curvature for $t>0$. In this article, we show that $k=n-r$ where $r$ is the Ricci rank of the initial metric. As a corollary, we also confirm a splitting conjecture of Wu-Zheng when curvature is assumed to be bounded.","authors_text":"Chengjie Yu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-12T15:26:43Z","title":"A Note on Wu-Zheng's Splitting Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2504","kind":"arxiv","version":1},"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:fefd4441d257b9c39d0bca5fc9815dca88412abafed326bedab77703ce5fd1a6","target":"record","created_at":"2026-05-18T04:13:37Z","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":"21dda81ddd4181e649a04551ed6d6aa6f8a07e0dcf544bbd2e812838786ad804","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-12T15:26:43Z","title_canon_sha256":"fcec1c6042cfd9ed16bd8e91089e7f59a803d28337ce8f16fdcf15f7f289a9ef"},"schema_version":"1.0","source":{"id":"1109.2504","kind":"arxiv","version":1}},"canonical_sha256":"87cf054085c23b9559e3a08f31d3f057a83ae6853733746f3a19682adfbfb745","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87cf054085c23b9559e3a08f31d3f057a83ae6853733746f3a19682adfbfb745","first_computed_at":"2026-05-18T04:13:37.521959Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:13:37.521959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FeMVLyi6JIIaleye3+Jdz9NTi9gxzBFKgEhKlDFy6DCGPk9hP+v6FrERzeJvPYBxjYTCk60Fn4S2l8klvs0cAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:13:37.522819Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.2504","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fefd4441d257b9c39d0bca5fc9815dca88412abafed326bedab77703ce5fd1a6","sha256:e34a01f8881ab22d8b945e1cca77fa4f534f3c4655ec8a31156374f54abeae9f"],"state_sha256":"d814cd763f0d7949234c084c3466961adf0d7cba98282a83d2da711312fa9397"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fH4YOrzIw1Vcs67lrD5PVZbPUaKAzJm9dREno7tYR4op44aE1XltmMo4uXVI1bZr3jkoqak2rq0uWET1qJyTBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T17:42:01.705266Z","bundle_sha256":"173449a571521742e355d5af3350d4a7d0db3e3fc7390678349dfc267c226495"}}