{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:4CA2H7N6TTHCS6E2VPFDMYIDAQ","short_pith_number":"pith:4CA2H7N6","schema_version":"1.0","canonical_sha256":"e081a3fdbe9cce29789aabca366103042168c507d5d133491f950dc008ea3180","source":{"kind":"arxiv","id":"2003.14379","version":3},"attestation_state":"computed","paper":{"title":"Log abundance of the moduli b-divisors of lc-trivial fibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Zhengyu Hu","submitted_at":"2020-03-31T17:24:56Z","abstract_excerpt":"We prove that the moduli b-divisor of an lc-trivial fibration from a log canonical pair is log abundant. The result follows from a theorem on the restriction of the moduli b-divisor, based on a theory of lc-trivial morphisms, which allows us to treat $\\mathbb{R}$-divisors and proper morphisms possibly with disconnected fibres. We also prove a theorem on extending a finite cover over a closed subvariety to that over a variety in arbitrary characteristic."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2003.14379","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2020-03-31T17:24:56Z","cross_cats_sorted":[],"title_canon_sha256":"79e153aaac94ca48c4cd0e44107b985bdbf58e184dccb0dd242fa52ea2ccbcda","abstract_canon_sha256":"7fb588c598320fe9d0b2367a6640f2789e150e76caf961a04982910e4896bc9a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:15:09.905115Z","signature_b64":"dPIb2hUXfzPJjJO7j874zDxb2AxSL0UmweqMRvGJLJlxHkxcTmo4qLy7ASbGRDdU0SFUhYorKNMGvWaIU3SCDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e081a3fdbe9cce29789aabca366103042168c507d5d133491f950dc008ea3180","last_reissued_at":"2026-07-05T02:15:09.904651Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:15:09.904651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Log abundance of the moduli b-divisors of lc-trivial fibrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Zhengyu Hu","submitted_at":"2020-03-31T17:24:56Z","abstract_excerpt":"We prove that the moduli b-divisor of an lc-trivial fibration from a log canonical pair is log abundant. The result follows from a theorem on the restriction of the moduli b-divisor, based on a theory of lc-trivial morphisms, which allows us to treat $\\mathbb{R}$-divisors and proper morphisms possibly with disconnected fibres. We also prove a theorem on extending a finite cover over a closed subvariety to that over a variety in arbitrary characteristic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.14379","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2003.14379/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2003.14379","created_at":"2026-07-05T02:15:09.904708+00:00"},{"alias_kind":"arxiv_version","alias_value":"2003.14379v3","created_at":"2026-07-05T02:15:09.904708+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.14379","created_at":"2026-07-05T02:15:09.904708+00:00"},{"alias_kind":"pith_short_12","alias_value":"4CA2H7N6TTHC","created_at":"2026-07-05T02:15:09.904708+00:00"},{"alias_kind":"pith_short_16","alias_value":"4CA2H7N6TTHCS6E2","created_at":"2026-07-05T02:15:09.904708+00:00"},{"alias_kind":"pith_short_8","alias_value":"4CA2H7N6","created_at":"2026-07-05T02:15:09.904708+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.09087","citing_title":"On the minimal model theory for generalized pairs of relative log numerical dimension zero","ref_index":22,"is_internal_anchor":false},{"citing_arxiv_id":"2606.30983","citing_title":"Addendum: On generalized canonical bundle formula and boundedness of complements in complex analytic setting","ref_index":108,"is_internal_anchor":false},{"citing_arxiv_id":"2305.01752","citing_title":"Nakayama-Zariski decomposition and the termination of flips","ref_index":14,"is_internal_anchor":false},{"citing_arxiv_id":"2605.09898","citing_title":"Quasi-Projective Moduli for Polarized klt Good Minimal Models","ref_index":154,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4CA2H7N6TTHCS6E2VPFDMYIDAQ","json":"https://pith.science/pith/4CA2H7N6TTHCS6E2VPFDMYIDAQ.json","graph_json":"https://pith.science/api/pith-number/4CA2H7N6TTHCS6E2VPFDMYIDAQ/graph.json","events_json":"https://pith.science/api/pith-number/4CA2H7N6TTHCS6E2VPFDMYIDAQ/events.json","paper":"https://pith.science/paper/4CA2H7N6"},"agent_actions":{"view_html":"https://pith.science/pith/4CA2H7N6TTHCS6E2VPFDMYIDAQ","download_json":"https://pith.science/pith/4CA2H7N6TTHCS6E2VPFDMYIDAQ.json","view_paper":"https://pith.science/paper/4CA2H7N6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2003.14379&json=true","fetch_graph":"https://pith.science/api/pith-number/4CA2H7N6TTHCS6E2VPFDMYIDAQ/graph.json","fetch_events":"https://pith.science/api/pith-number/4CA2H7N6TTHCS6E2VPFDMYIDAQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4CA2H7N6TTHCS6E2VPFDMYIDAQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4CA2H7N6TTHCS6E2VPFDMYIDAQ/action/storage_attestation","attest_author":"https://pith.science/pith/4CA2H7N6TTHCS6E2VPFDMYIDAQ/action/author_attestation","sign_citation":"https://pith.science/pith/4CA2H7N6TTHCS6E2VPFDMYIDAQ/action/citation_signature","submit_replication":"https://pith.science/pith/4CA2H7N6TTHCS6E2VPFDMYIDAQ/action/replication_record"}},"created_at":"2026-07-05T02:15:09.904708+00:00","updated_at":"2026-07-05T02:15:09.904708+00:00"}