{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:YT3JDO5POQX2MQAPUV623K32AV","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":"63957fb4929b4d6ab64463de250dc90b52c3a7c5b648ef52410e5fbe5c640177","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.CV","submitted_at":"2005-11-09T12:00:30Z","title_canon_sha256":"ae781404a01ce0291888a2d9051d3c44b66da580f7177525dff1a70b505c4a85"},"schema_version":"1.0","source":{"id":"math/0511225","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0511225","created_at":"2026-05-18T03:41:59Z"},{"alias_kind":"arxiv_version","alias_value":"math/0511225v2","created_at":"2026-05-18T03:41:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0511225","created_at":"2026-05-18T03:41:59Z"},{"alias_kind":"pith_short_12","alias_value":"YT3JDO5POQX2","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"YT3JDO5POQX2MQAP","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"YT3JDO5P","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:8fd750b5603494c7a133983a4805f5ed44d1c51f0c8cf4eda0d0d88928782122","target":"graph","created_at":"2026-05-18T03:41:59Z","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":"Let $L$ be a (semi)-positive line bundle over a Kahler manifold, $X$, fibered over a complex manifold $Y$. Assuming the fibers are compact and non-singular we prove that the hermitian vector bundle $E$ over $Y$ whose fibers over points $y$ are the spaces of global sections over $X_y$ to $L\\gr K_{X/Y}$ endowed with the $L^2$-metric is (semi)-positive in the sense of Nakano. We also discuss various applications, among them a partial result on a conjecture of Griffiths on the positivity of ample bundles. This is a revised and much expanded version of a previous preprint with the title `` Bergman ","authors_text":"Bo Berndtsson","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"math.CV","submitted_at":"2005-11-09T12:00:30Z","title":"Curvature of vector bundles associated to holomorphic fibrations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0511225","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":"sha256:7cd254b06b21a1470ad764b8178f64bdde2ab1fe9eccb5f0487411f470d90d39","target":"record","created_at":"2026-05-18T03:41:59Z","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":"63957fb4929b4d6ab64463de250dc90b52c3a7c5b648ef52410e5fbe5c640177","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.CV","submitted_at":"2005-11-09T12:00:30Z","title_canon_sha256":"ae781404a01ce0291888a2d9051d3c44b66da580f7177525dff1a70b505c4a85"},"schema_version":"1.0","source":{"id":"math/0511225","kind":"arxiv","version":2}},"canonical_sha256":"c4f691bbaf742fa6400fa57dadab7a055e51d0a2a7148cb6672c30005cd7a36b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4f691bbaf742fa6400fa57dadab7a055e51d0a2a7148cb6672c30005cd7a36b","first_computed_at":"2026-05-18T03:41:59.208327Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:59.208327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fApIuPomFVSDatr0sBJebJ4go1RL322lWYXecP1w1ctpNpMJtbJu6ceGiE2FUeH1L4vFj2cuMDO8fjxaeCwJCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:59.209047Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0511225","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7cd254b06b21a1470ad764b8178f64bdde2ab1fe9eccb5f0487411f470d90d39","sha256:8fd750b5603494c7a133983a4805f5ed44d1c51f0c8cf4eda0d0d88928782122"],"state_sha256":"bbbff9faaf155f26c13c466718b98329d87cf4763ce6e02548817c8fe0db8d2c"}