{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:QVO5F7QEZQAYUIFVYL2TBY7JCJ","short_pith_number":"pith:QVO5F7QE","canonical_record":{"source":{"id":"1002.3717","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-02-19T11:31:43Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"af84b8967a792f040e5de5730c621103c3654fbc22bee99e638e9fddcd962bd7","abstract_canon_sha256":"29643d6b1a851a45fdc9e6f0fcd1344deff1507d2d813bb54b4835781f7fa166"},"schema_version":"1.0"},"canonical_sha256":"855dd2fe04cc018a20b5c2f530e3e9125a5a905916197007ba1c14863dc5d9c6","source":{"kind":"arxiv","id":"1002.3717","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.3717","created_at":"2026-05-18T04:30:14Z"},{"alias_kind":"arxiv_version","alias_value":"1002.3717v3","created_at":"2026-05-18T04:30:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.3717","created_at":"2026-05-18T04:30:14Z"},{"alias_kind":"pith_short_12","alias_value":"QVO5F7QEZQAY","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"QVO5F7QEZQAYUIFV","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"QVO5F7QE","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:QVO5F7QEZQAYUIFVYL2TBY7JCJ","target":"record","payload":{"canonical_record":{"source":{"id":"1002.3717","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-02-19T11:31:43Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"af84b8967a792f040e5de5730c621103c3654fbc22bee99e638e9fddcd962bd7","abstract_canon_sha256":"29643d6b1a851a45fdc9e6f0fcd1344deff1507d2d813bb54b4835781f7fa166"},"schema_version":"1.0"},"canonical_sha256":"855dd2fe04cc018a20b5c2f530e3e9125a5a905916197007ba1c14863dc5d9c6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:14.544311Z","signature_b64":"74V6zuPlSoyxXOSY2hjOtcquijCWnN4zVI3ad2bMCsJTkSPMxpK6x/7snhtJWCZ3BWBix2LOl4GZvq9EKrcDDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"855dd2fe04cc018a20b5c2f530e3e9125a5a905916197007ba1c14863dc5d9c6","last_reissued_at":"2026-05-18T04:30:14.543601Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:14.543601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1002.3717","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:30:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nW2JMRLgk+tMrNYgGmuW8I8+1jpRaMtmEjYH3vEfv3/YIQVovFxF13uCGGw5VqM5ph2dWy4bSZNeRMdo2FKiBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T09:20:47.982220Z"},"content_sha256":"7d19a972c95422942fe2a6506d743fae5441d902f5ea710a39981f72d285280f","schema_version":"1.0","event_id":"sha256:7d19a972c95422942fe2a6506d743fae5441d902f5ea710a39981f72d285280f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:QVO5F7QEZQAYUIFVYL2TBY7JCJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Relative Kahler-Ricci flows and their quantization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Robert J. Berman","submitted_at":"2010-02-19T11:31:43Z","abstract_excerpt":"Let X be a complex manifold fibered over the base S and let L be a relatively ample line bundle over X. We define relative Kahler-Ricci flows on the space of all Hermitian metrics on L with relatively positive curvature. Mainly three different settings are investigated: the case when the fibers are Calabi-Yau manifolds and the case when L is the relative (anti-) canonical line bundle. The main theme studied is whether posivity in families is preserved under the flows and its relation to the variation of the moduli of the complex structures of the fibres. The quantization of this setting is als"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.3717","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:30:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jMk7svzlHt6ir7In8vtcqF3pZT7fSFlpmQ0hQx8flNMh1CPYqe8ZCAAllVYq8C5lpnzHA7pBZZyaCa3/Cho6AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T09:20:47.982582Z"},"content_sha256":"4226da41d4aee9f3ba3f7c6c550bdd715fcf87d031a00077ed1dce3e5515b0a8","schema_version":"1.0","event_id":"sha256:4226da41d4aee9f3ba3f7c6c550bdd715fcf87d031a00077ed1dce3e5515b0a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QVO5F7QEZQAYUIFVYL2TBY7JCJ/bundle.json","state_url":"https://pith.science/pith/QVO5F7QEZQAYUIFVYL2TBY7JCJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QVO5F7QEZQAYUIFVYL2TBY7JCJ/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":"2026-06-04T09:20:47Z","links":{"resolver":"https://pith.science/pith/QVO5F7QEZQAYUIFVYL2TBY7JCJ","bundle":"https://pith.science/pith/QVO5F7QEZQAYUIFVYL2TBY7JCJ/bundle.json","state":"https://pith.science/pith/QVO5F7QEZQAYUIFVYL2TBY7JCJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QVO5F7QEZQAYUIFVYL2TBY7JCJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:QVO5F7QEZQAYUIFVYL2TBY7JCJ","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":"29643d6b1a851a45fdc9e6f0fcd1344deff1507d2d813bb54b4835781f7fa166","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-02-19T11:31:43Z","title_canon_sha256":"af84b8967a792f040e5de5730c621103c3654fbc22bee99e638e9fddcd962bd7"},"schema_version":"1.0","source":{"id":"1002.3717","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1002.3717","created_at":"2026-05-18T04:30:14Z"},{"alias_kind":"arxiv_version","alias_value":"1002.3717v3","created_at":"2026-05-18T04:30:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1002.3717","created_at":"2026-05-18T04:30:14Z"},{"alias_kind":"pith_short_12","alias_value":"QVO5F7QEZQAY","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"QVO5F7QEZQAYUIFV","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"QVO5F7QE","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:4226da41d4aee9f3ba3f7c6c550bdd715fcf87d031a00077ed1dce3e5515b0a8","target":"graph","created_at":"2026-05-18T04:30:14Z","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 X be a complex manifold fibered over the base S and let L be a relatively ample line bundle over X. We define relative Kahler-Ricci flows on the space of all Hermitian metrics on L with relatively positive curvature. Mainly three different settings are investigated: the case when the fibers are Calabi-Yau manifolds and the case when L is the relative (anti-) canonical line bundle. The main theme studied is whether posivity in families is preserved under the flows and its relation to the variation of the moduli of the complex structures of the fibres. The quantization of this setting is als","authors_text":"Robert J. Berman","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-02-19T11:31:43Z","title":"Relative Kahler-Ricci flows and their quantization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1002.3717","kind":"arxiv","version":3},"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":"sha256:7d19a972c95422942fe2a6506d743fae5441d902f5ea710a39981f72d285280f","target":"record","created_at":"2026-05-18T04:30:14Z","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":"29643d6b1a851a45fdc9e6f0fcd1344deff1507d2d813bb54b4835781f7fa166","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-02-19T11:31:43Z","title_canon_sha256":"af84b8967a792f040e5de5730c621103c3654fbc22bee99e638e9fddcd962bd7"},"schema_version":"1.0","source":{"id":"1002.3717","kind":"arxiv","version":3}},"canonical_sha256":"855dd2fe04cc018a20b5c2f530e3e9125a5a905916197007ba1c14863dc5d9c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"855dd2fe04cc018a20b5c2f530e3e9125a5a905916197007ba1c14863dc5d9c6","first_computed_at":"2026-05-18T04:30:14.543601Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:14.543601Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"74V6zuPlSoyxXOSY2hjOtcquijCWnN4zVI3ad2bMCsJTkSPMxpK6x/7snhtJWCZ3BWBix2LOl4GZvq9EKrcDDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:14.544311Z","signed_message":"canonical_sha256_bytes"},"source_id":"1002.3717","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d19a972c95422942fe2a6506d743fae5441d902f5ea710a39981f72d285280f","sha256:4226da41d4aee9f3ba3f7c6c550bdd715fcf87d031a00077ed1dce3e5515b0a8"],"state_sha256":"04775be688b9546c26a9997ee891bbf2b09be1b0860de60f10aa7e20d527d5f2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WoDdyN76HjmtQLEnKi9P6Q8bwu140hi/+WsjmjvMzCb/but5eCrjNCu8DaY+tuGiXao3NEd6oxJrzzkyuZgsDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T09:20:47.984506Z","bundle_sha256":"c182f3440f8808e6a91463f36707533bf9d4ed643e67597b1b68bcd78924123a"}}