{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TYCH3BZ4LPQJHTOCRCHCXDQRN5","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":"2b1ee69eec253c8c67aafe02c8b25f637990df1cbc17063fec5e7bffda999a12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-01-23T09:16:49Z","title_canon_sha256":"d2b1269861473b3d06b9cab1f8ae0b098aa4f74adaa98a5572568116fe4e43ff"},"schema_version":"1.0","source":{"id":"1501.05745","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05745","created_at":"2026-05-18T01:14:59Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05745v2","created_at":"2026-05-18T01:14:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05745","created_at":"2026-05-18T01:14:59Z"},{"alias_kind":"pith_short_12","alias_value":"TYCH3BZ4LPQJ","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"TYCH3BZ4LPQJHTOC","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"TYCH3BZ4","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:0999c5ecd809ca67b118b089c2a8853bb312f61a763bc6584c81a3978af70b18","target":"graph","created_at":"2026-05-18T01:14:59Z","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":"For a minimal $3$-fold $X$ with $K_X\\equiv 0$ and a nef and big Weil divisor $L$ on $X$, we investigate the birational geometry inspired by $L$. We prove that $|mL|$ and $|K_X+mL|$ give birational maps for all $m\\geq 17$. The result remains true under weaker assumption that $L$ is big and has no stable base components.","authors_text":"Chen Jiang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-01-23T09:16:49Z","title":"On birational geometry of minimal threefolds with numerically trivial canonical divisors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05745","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":"sha256:83d25f447e6be6dbf58e77b1d42f0eb940400227efbc15c47f0d5fec0b0df0f8","target":"record","created_at":"2026-05-18T01:14:59Z","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":"2b1ee69eec253c8c67aafe02c8b25f637990df1cbc17063fec5e7bffda999a12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-01-23T09:16:49Z","title_canon_sha256":"d2b1269861473b3d06b9cab1f8ae0b098aa4f74adaa98a5572568116fe4e43ff"},"schema_version":"1.0","source":{"id":"1501.05745","kind":"arxiv","version":2}},"canonical_sha256":"9e047d873c5be093cdc2888e2b8e116f41a8a30557eec591a2830718548e2577","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e047d873c5be093cdc2888e2b8e116f41a8a30557eec591a2830718548e2577","first_computed_at":"2026-05-18T01:14:59.019976Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:59.019976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sp5fmUqh0fYodeKYIN6q1jJNHJSgzbHCnY/iWNZRN8ztX+vl4hqzagFy/uulo/sMTVdAOYyA3y3CjNqfM4gRBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:59.020417Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.05745","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83d25f447e6be6dbf58e77b1d42f0eb940400227efbc15c47f0d5fec0b0df0f8","sha256:0999c5ecd809ca67b118b089c2a8853bb312f61a763bc6584c81a3978af70b18"],"state_sha256":"bb38b74e4d41969ced8fad0e023daaadb1ed41de74fbd91249a0e3e4c059bdc2"}