{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:WMTZ73LBW2YLYTSWUPCIJ2D7WK","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":"ca8ccd6032af00e93f4681d9200727d0fa2ab64d9f3f49a2f3b423ba8a141ecb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-09-22T21:41:03Z","title_canon_sha256":"50869cf3f9923e0b79774c814cf2825a23571892abca00e4384aca0b265d3412"},"schema_version":"1.0","source":{"id":"1909.10098","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.10098","created_at":"2026-07-05T03:46:12Z"},{"alias_kind":"arxiv_version","alias_value":"1909.10098v2","created_at":"2026-07-05T03:46:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.10098","created_at":"2026-07-05T03:46:12Z"},{"alias_kind":"pith_short_12","alias_value":"WMTZ73LBW2YL","created_at":"2026-07-05T03:46:12Z"},{"alias_kind":"pith_short_16","alias_value":"WMTZ73LBW2YLYTSW","created_at":"2026-07-05T03:46:12Z"},{"alias_kind":"pith_short_8","alias_value":"WMTZ73LB","created_at":"2026-07-05T03:46:12Z"}],"graph_snapshots":[{"event_id":"sha256:1e8a27e101f7643aaddfcfda4eba413f534baead752847370d18b946ab3722c5","target":"graph","created_at":"2026-07-05T03:46:12Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1909.10098/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We expand the theory of log canonical $3$-fold complements. We prove that if $X\\rightarrow T$ is a $3$-dimensional contraction of log Calabi-Yau type, then we can find $B\\geq 0$ on $X$ for which $(X,B)$ is log canonical and $n(K_X+B)\\sim_T 0$, where $n$ is an uniform natural number. This means that every $3$-fold of log Calabi-Yau type can be turned into a log Calabi-Yau pair in an effective way.","authors_text":"Joaqu\\'in Moraga, Stefano Filipazzi, Yanning Xu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-09-22T21:41:03Z","title":"Log canonical $3$-fold complements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.10098","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:bdc05bdcbc32e062ec4bcd42ffd94fdcbc985aeb91f0d8342976a4c173046039","target":"record","created_at":"2026-07-05T03:46:12Z","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":"ca8ccd6032af00e93f4681d9200727d0fa2ab64d9f3f49a2f3b423ba8a141ecb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-09-22T21:41:03Z","title_canon_sha256":"50869cf3f9923e0b79774c814cf2825a23571892abca00e4384aca0b265d3412"},"schema_version":"1.0","source":{"id":"1909.10098","kind":"arxiv","version":2}},"canonical_sha256":"b3279fed61b6b0bc4e56a3c484e87fb282d1e0fcf62b30dbdfc2ed4031c0e1f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3279fed61b6b0bc4e56a3c484e87fb282d1e0fcf62b30dbdfc2ed4031c0e1f3","first_computed_at":"2026-07-05T03:46:12.114526Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:46:12.114526Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q4NO1QHGTGujRGgxaEXOuLknN/RZbCWR6O6vx7GkJ7ve7KhYhwE6vkJ8Dozo+Q5Eig8LSJQDl9LF31O/b5SRBA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:46:12.114929Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.10098","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bdc05bdcbc32e062ec4bcd42ffd94fdcbc985aeb91f0d8342976a4c173046039","sha256:1e8a27e101f7643aaddfcfda4eba413f534baead752847370d18b946ab3722c5"],"state_sha256":"e10a4bd0b3d4e3e577621a718e1abf7d97c81bf402ce3c1428dbe2c0e653f709"}