{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YCOW77PVX2AXN5BHY6QHDJ7SSM","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":"93164aec7a46df10a0daa82e06a42b791de923abbbc2be96c17b87d022df1609","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-07-17T17:28:57Z","title_canon_sha256":"a2417869afaf10069b4086fe8249968041c92562160022ea6422e9c8cf961770"},"schema_version":"1.0","source":{"id":"1207.4070","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.4070","created_at":"2026-05-18T03:50:49Z"},{"alias_kind":"arxiv_version","alias_value":"1207.4070v1","created_at":"2026-05-18T03:50:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.4070","created_at":"2026-05-18T03:50:49Z"},{"alias_kind":"pith_short_12","alias_value":"YCOW77PVX2AX","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"YCOW77PVX2AXN5BH","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"YCOW77PV","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:5c9a99462eed31cfa63535f8d8292438f6323ce002dc3b75ab18f276a61800b2","target":"graph","created_at":"2026-05-18T03:50:49Z","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":"It is conjectured that the moduli b-divisor of the Kawamata-Kodaira canonical bundle formula associated to a klt-trivial fibration $(X,B)\\to Z$ is semi-ample. In this paper, we show the semi-ampleness of an arbitrarily small perturbation of the moduli b-divisor by a fixed appropriate divisor which roughly speaking comes from a section of $K_X+B$.\n  We apply the above result to settle a conjecture of Fujino and Gongyo: if $f\\colon X\\to Z$ is a smooth surjective morphism of smooth projective varieties with $-K_X$ semi-ample, then $-K_Z$ is also semi-ample. We list several counter-examples to sho","authors_text":"Caucher Birkar, Yifei Chen","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-07-17T17:28:57Z","title":"On the moduli part of the Kawamata-Kodaira canonical bundle formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4070","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:b10738da655135f9beeaa28ef410b8f06e4d237bd35a21c059756f9cc6ff72ed","target":"record","created_at":"2026-05-18T03:50:49Z","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":"93164aec7a46df10a0daa82e06a42b791de923abbbc2be96c17b87d022df1609","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-07-17T17:28:57Z","title_canon_sha256":"a2417869afaf10069b4086fe8249968041c92562160022ea6422e9c8cf961770"},"schema_version":"1.0","source":{"id":"1207.4070","kind":"arxiv","version":1}},"canonical_sha256":"c09d6ffdf5be8176f427c7a071a7f2930d7fd95d66b9dfbf62db3cfa21c061f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c09d6ffdf5be8176f427c7a071a7f2930d7fd95d66b9dfbf62db3cfa21c061f9","first_computed_at":"2026-05-18T03:50:49.095765Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:49.095765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QXXeqJT93mrH7ASt9Zc914GS4vaJOURgGiMc94kw8JdrSTc1If+tLwcLfrP2aiR5+2TBmUVr4nBsQOqgKwA2DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:49.096559Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.4070","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b10738da655135f9beeaa28ef410b8f06e4d237bd35a21c059756f9cc6ff72ed","sha256:5c9a99462eed31cfa63535f8d8292438f6323ce002dc3b75ab18f276a61800b2"],"state_sha256":"2f94a533896739ac55df0495bf5fd76b7130b3e04b94a230b8f9950f05913fa4"}