{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:YT3JDO5POQX2MQAPUV623K32AV","short_pith_number":"pith:YT3JDO5P","canonical_record":{"source":{"id":"math/0511225","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.CV","submitted_at":"2005-11-09T12:00:30Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"ae781404a01ce0291888a2d9051d3c44b66da580f7177525dff1a70b505c4a85","abstract_canon_sha256":"63957fb4929b4d6ab64463de250dc90b52c3a7c5b648ef52410e5fbe5c640177"},"schema_version":"1.0"},"canonical_sha256":"c4f691bbaf742fa6400fa57dadab7a055e51d0a2a7148cb6672c30005cd7a36b","source":{"kind":"arxiv","id":"math/0511225","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:YT3JDO5POQX2MQAPUV623K32AV","target":"record","payload":{"canonical_record":{"source":{"id":"math/0511225","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.CV","submitted_at":"2005-11-09T12:00:30Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"ae781404a01ce0291888a2d9051d3c44b66da580f7177525dff1a70b505c4a85","abstract_canon_sha256":"63957fb4929b4d6ab64463de250dc90b52c3a7c5b648ef52410e5fbe5c640177"},"schema_version":"1.0"},"canonical_sha256":"c4f691bbaf742fa6400fa57dadab7a055e51d0a2a7148cb6672c30005cd7a36b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:59.209047Z","signature_b64":"fApIuPomFVSDatr0sBJebJ4go1RL322lWYXecP1w1ctpNpMJtbJu6ceGiE2FUeH1L4vFj2cuMDO8fjxaeCwJCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4f691bbaf742fa6400fa57dadab7a055e51d0a2a7148cb6672c30005cd7a36b","last_reissued_at":"2026-05-18T03:41:59.208327Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:59.208327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0511225","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:41:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a7fv5qCCKWtPZM2voMsD4dSutjLYDK+hwwBvjYTCXS9GgjuFmU8fa399qdjMMFvM65C5ySTSdRARyvbEIqMBBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:23:02.774619Z"},"content_sha256":"7cd254b06b21a1470ad764b8178f64bdde2ab1fe9eccb5f0487411f470d90d39","schema_version":"1.0","event_id":"sha256:7cd254b06b21a1470ad764b8178f64bdde2ab1fe9eccb5f0487411f470d90d39"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:YT3JDO5POQX2MQAPUV623K32AV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Curvature of vector bundles associated to holomorphic fibrations","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"Bo Berndtsson","submitted_at":"2005-11-09T12:00:30Z","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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0511225","kind":"arxiv","version":2},"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":"2026-05-18T03:41:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vFJiP5n0+GN7CRLIwMhOIzgc7dJqP2aGmAoAFAIHJL5UkPnEFxg4NCoPP5wpIlr5WzyOll/beYzrWfOIFPbPAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:23:02.775009Z"},"content_sha256":"8fd750b5603494c7a133983a4805f5ed44d1c51f0c8cf4eda0d0d88928782122","schema_version":"1.0","event_id":"sha256:8fd750b5603494c7a133983a4805f5ed44d1c51f0c8cf4eda0d0d88928782122"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YT3JDO5POQX2MQAPUV623K32AV/bundle.json","state_url":"https://pith.science/pith/YT3JDO5POQX2MQAPUV623K32AV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YT3JDO5POQX2MQAPUV623K32AV/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":"2026-05-27T23:23:02Z","links":{"resolver":"https://pith.science/pith/YT3JDO5POQX2MQAPUV623K32AV","bundle":"https://pith.science/pith/YT3JDO5POQX2MQAPUV623K32AV/bundle.json","state":"https://pith.science/pith/YT3JDO5POQX2MQAPUV623K32AV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YT3JDO5POQX2MQAPUV623K32AV/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mQCJucHgI7rgTc5nUSGpqG5Itbgm3pfaX4tsiJn+HBJX/Fa+ym/V5MBQQhb7rO8w4hko1f7lGuzFm5/hF0+gAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T23:23:02.777337Z","bundle_sha256":"615f280e0609af429fe24c317fcc7b4024027408a1ec7f14bcc3ceddf2bc21fa"}}