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semi-ampleness holds for a nef and big $\\Q$-divisor $D$ if $D-(K_X+B)$ is nef and big and $(X,B)$ is projective klt; $\\Q$-factorial dlt models exist for lc pairs $(X,B)$; terminal models exist for klt pair"},"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":"1311.3098","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-11-13T12:05:09Z","cross_cats_sorted":[],"title_canon_sha256":"0a7e760c78154db000dcbe41b835df057c5e560fb9b8175dab3cf31f9d4ce6c3","abstract_canon_sha256":"96f6b82c2599c25643a83512f4c5f51a67bc2e4fb5034fa2294dfe829f2c82d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:02.147878Z","signature_b64":"nxrSSW/Y/rC5BDym2yfa2RqLLMippZ9DoYWRRVh2hTDAS8aBjpmdpo9UnbR3JV4AJOafHbkBjMkaYzLAsvNqDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22149ac11a5f85942ebb028f03e0dfc59ca2e0996855dd1030ebe98baa6335d7","last_reissued_at":"2026-05-18T02:40:02.147255Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:02.147255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of flips and minimal models for 3-folds in char p","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Caucher Birkar","submitted_at":"2013-11-13T12:05:09Z","abstract_excerpt":"We will prove the following results for $3$-fold pairs $(X,B)$ over an algebraically closed field $k$ of characteristic $p>5$: log flips exist for $\\Q$-factorial dlt pairs $(X,B)$; log minimal models exist for projective klt pairs $(X,B)$ with pseudo-effective $K_X+B$; the log canonical ring $R(K_X+B)$ is finitely generated for projective klt pairs $(X,B)$ when $K_X+B$ is a big $\\Q$-divisor; semi-ampleness holds for a nef and big $\\Q$-divisor $D$ if $D-(K_X+B)$ is nef and big and $(X,B)$ is projective klt; $\\Q$-factorial dlt models exist for lc pairs $(X,B)$; terminal models exist for klt pair"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3098","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1311.3098","created_at":"2026-05-18T02:40:02.147336+00:00"},{"alias_kind":"arxiv_version","alias_value":"1311.3098v2","created_at":"2026-05-18T02:40:02.147336+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.3098","created_at":"2026-05-18T02:40:02.147336+00:00"},{"alias_kind":"pith_short_12","alias_value":"EIKJVQI2L6CZ","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"EIKJVQI2L6CZILV3","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"EIKJVQI2","created_at":"2026-05-18T12:27:43.054852+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2307.03938","citing_title":"Abundance for threefolds in positive characteristic when $\\nu=2$","ref_index":4,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EIKJVQI2L6CZILV3AKHQHYG7YW","json":"https://pith.science/pith/EIKJVQI2L6CZILV3AKHQHYG7YW.json","graph_json":"https://pith.science/api/pith-number/EIKJVQI2L6CZILV3AKHQHYG7YW/graph.json","events_json":"https://pith.science/api/pith-number/EIKJVQI2L6CZILV3AKHQHYG7YW/events.json","paper":"https://pith.science/paper/EIKJVQI2"},"agent_actions":{"view_html":"https://pith.science/pith/EIKJVQI2L6CZILV3AKHQHYG7YW","download_json":"https://pith.science/pith/EIKJVQI2L6CZILV3AKHQHYG7YW.json","view_paper":"https://pith.science/paper/EIKJVQI2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1311.3098&json=true","fetch_graph":"https://pith.science/api/pith-number/EIKJVQI2L6CZILV3AKHQHYG7YW/graph.json","fetch_events":"https://pith.science/api/pith-number/EIKJVQI2L6CZILV3AKHQHYG7YW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EIKJVQI2L6CZILV3AKHQHYG7YW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EIKJVQI2L6CZILV3AKHQHYG7YW/action/storage_attestation","attest_author":"https://pith.science/pith/EIKJVQI2L6CZILV3AKHQHYG7YW/action/author_attestation","sign_citation":"https://pith.science/pith/EIKJVQI2L6CZILV3AKHQHYG7YW/action/citation_signature","submit_replication":"https://pith.science/pith/EIKJVQI2L6CZILV3AKHQHYG7YW/action/replication_record"}},"created_at":"2026-05-18T02:40:02.147336+00:00","updated_at":"2026-05-18T02:40:02.147336+00:00"}