{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZU5BJNEB2HLUACMYDSQ7C6QJTD","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":"a8f5e6409697012fa5e40d841f8981f03269c6d0a67fecbf9bf5763dde38e8c0","cross_cats_sorted":["math.AG","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-20T02:21:21Z","title_canon_sha256":"3b6cce5593ac06a3264f11db546c684cdaa22b312ac851f88666f6344b14a265"},"schema_version":"1.0","source":{"id":"1104.3924","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.3924","created_at":"2026-05-18T03:01:54Z"},{"alias_kind":"arxiv_version","alias_value":"1104.3924v2","created_at":"2026-05-18T03:01:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3924","created_at":"2026-05-18T03:01:54Z"},{"alias_kind":"pith_short_12","alias_value":"ZU5BJNEB2HLU","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"ZU5BJNEB2HLUACMY","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"ZU5BJNEB","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:43adac46263a3b2276d0ecc2c85139a430e857e6448590144b8f16af57878036","target":"graph","created_at":"2026-05-18T03:01:54Z","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":"We study the K\\\"ahler-Ricci flow on a class of projective bundles $\\mathbb{P}(\\mathcal{O}_\\Sigma \\oplus L)$ over compact K\\\"ahler-Einstein manifold $\\Sigma^n$. Assuming the initial K\\\"ahler metric $\\omega_0$ admits a U(1)-invariant momentum profile, we give a criterion, characterized by the triple $(\\Sigma, L, [\\omega_0])$, under which the $\\mathbb{P}^1$-fiber collapses along the K\\\"ahler-Ricci flow and the projective bundle converges to $\\Sigma$ in Gromov-Hausdorff sense. Furthermore, the K\\\"ahler-Ricci flow must have Type I singularity and is of $(\\C^n \\times \\mathbb{P}^1)$-type. This genera","authors_text":"Frederick Tsz-Ho Fong","cross_cats":["math.AG","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-20T02:21:21Z","title":"K\\\"ahler-Ricci Flow on Projective Bundles over K\\\"ahler-Einstein Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3924","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":"sha256:57ebb3dc0d9e5dee311af110fa164a26d1ebe5fd5df27e9ec180c727206e3ec6","target":"record","created_at":"2026-05-18T03:01:54Z","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":"a8f5e6409697012fa5e40d841f8981f03269c6d0a67fecbf9bf5763dde38e8c0","cross_cats_sorted":["math.AG","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-20T02:21:21Z","title_canon_sha256":"3b6cce5593ac06a3264f11db546c684cdaa22b312ac851f88666f6344b14a265"},"schema_version":"1.0","source":{"id":"1104.3924","kind":"arxiv","version":2}},"canonical_sha256":"cd3a14b481d1d74009981ca1f17a0998dbf9ad412d10a22e9644f559204f74c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd3a14b481d1d74009981ca1f17a0998dbf9ad412d10a22e9644f559204f74c5","first_computed_at":"2026-05-18T03:01:54.751429Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:54.751429Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IqmxzibU/uU0oBEjMrnG/Lcu3BE2sJS9w8Imh2y0pLLE/imgHloLf4LKjzdSyqtuyYeSv1a2MndagiVko1UtAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:54.752044Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.3924","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57ebb3dc0d9e5dee311af110fa164a26d1ebe5fd5df27e9ec180c727206e3ec6","sha256:43adac46263a3b2276d0ecc2c85139a430e857e6448590144b8f16af57878036"],"state_sha256":"9639b5fb0fa31862e2e6d6bca14ab6b633396628b8ab86b0b77779bff20ab499"}