{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:2SKWDRRPRWW2OCDZU3TELILVYY","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":"36aecbdf34c1076ddc98d8932246f3329aedab35e4f4de749606f5b3a2895634","cross_cats_sorted":["math.CV","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-05-29T14:25:13Z","title_canon_sha256":"b9c95b2beab3e93aaaf42f66e54b7c2199b3acf4659d84f0a6760d83226ddf7c"},"schema_version":"1.0","source":{"id":"2105.14308","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.14308","created_at":"2026-07-05T06:45:56Z"},{"alias_kind":"arxiv_version","alias_value":"2105.14308v3","created_at":"2026-07-05T06:45:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.14308","created_at":"2026-07-05T06:45:56Z"},{"alias_kind":"pith_short_12","alias_value":"2SKWDRRPRWW2","created_at":"2026-07-05T06:45:56Z"},{"alias_kind":"pith_short_16","alias_value":"2SKWDRRPRWW2OCDZ","created_at":"2026-07-05T06:45:56Z"},{"alias_kind":"pith_short_8","alias_value":"2SKWDRRP","created_at":"2026-07-05T06:45:56Z"}],"graph_snapshots":[{"event_id":"sha256:7adb8c52a4ed8e7b471fbb42dd80506809eb1797fcb89dedc66ddea50be56ecf","target":"graph","created_at":"2026-07-05T06:45:56Z","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/2105.14308/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we establish a structure theorem for projective klt pairs $(X,\\Delta)$ with nef anti-log canonical divisor; specifically, we prove that, up to replacing $X$ with a finite quasi-\\'etale cover, $X$ admits a locally trivial rationally connected fibration onto a projective klt variety with numerically trivial canonical divisor. This structure theorem generalizes previous works for smooth projective varieties and reduces several structure problems to the singular Beauville-Bogomolov decomposition for Calabi-Yau varieties. As an application, projective varieties of klt Calabi-Yau type","authors_text":"Juanyong Wang, Shin-ichi Matsumura","cross_cats":["math.CV","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-05-29T14:25:13Z","title":"Structure theorem for projective klt pairs with nef anti-canonical divisor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.14308","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":"sha256:937e482ed03de1293bfe60d0660de2350925aff7c6ef73f294e446c398c26dae","target":"record","created_at":"2026-07-05T06:45:56Z","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":"36aecbdf34c1076ddc98d8932246f3329aedab35e4f4de749606f5b3a2895634","cross_cats_sorted":["math.CV","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2021-05-29T14:25:13Z","title_canon_sha256":"b9c95b2beab3e93aaaf42f66e54b7c2199b3acf4659d84f0a6760d83226ddf7c"},"schema_version":"1.0","source":{"id":"2105.14308","kind":"arxiv","version":3}},"canonical_sha256":"d49561c62f8dada70879a6e645a175c6171f5510583eb1b3edaa21f6e28701ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d49561c62f8dada70879a6e645a175c6171f5510583eb1b3edaa21f6e28701ca","first_computed_at":"2026-07-05T06:45:56.239381Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:45:56.239381Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"arUXhMEDjj/gA3adV2QKAHQqAMjFgXle9DfiyfVhm1YkCDb5wIkiAgaZGMsPsS87zeTP3OmOxhsEvdLHaBvKCg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:45:56.239874Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.14308","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:937e482ed03de1293bfe60d0660de2350925aff7c6ef73f294e446c398c26dae","sha256:7adb8c52a4ed8e7b471fbb42dd80506809eb1797fcb89dedc66ddea50be56ecf"],"state_sha256":"ce3b2ad9f4ce27ffa1f35b87237b3ed80926bb8a3a24838d50b70aedc0283220"}