{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:HXTLJAYZEDVMVVCRUBBIRQ5GGB","short_pith_number":"pith:HXTLJAYZ","schema_version":"1.0","canonical_sha256":"3de6b4831920eacad451a04288c3a6305952eb6ae9fbd644f67913d6add4d610","source":{"kind":"arxiv","id":"1206.2475","version":1},"attestation_state":"computed","paper":{"title":"The Mukai conjecture for log Fano manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Kento Fujita","submitted_at":"2012-06-12T09:51:10Z","abstract_excerpt":"For a log Fano manifold (X, D) with D\\neq 0 and with the log Fano pseudoindex \\geq 2, we prove that the restriction homomorphism Pic(X)\\to Pic(D_1) of Picard groups is injective for any irreducible component D_1\\subset D.The strategy of our proof is to run a certain minimal model program and is similar to the argument of Casagrande's one. As a corollary, we prove that the Mukai conjecture (resp. the generalized Mukai conjecture) implies the log Mukai conjecture (resp. the log generalized Mukai conjecture)."},"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":"1206.2475","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-06-12T09:51:10Z","cross_cats_sorted":[],"title_canon_sha256":"22d644c271a8e1ca01f38e13fe7e40bc6a4b921a3f3b147a07bd9144a2e6ae34","abstract_canon_sha256":"df7e52b6c360a2e626968eaae00772da19fb27d32f4d8846d46b58d9a05f550a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:44.334022Z","signature_b64":"gsIQvhm0a25QRDIGtrYZuLpbRx90GS4dO7EHuTE5hvM9j5nGSTRwFuISCXqi9rRKj65iayhL5nlPfsGAOwXYDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3de6b4831920eacad451a04288c3a6305952eb6ae9fbd644f67913d6add4d610","last_reissued_at":"2026-05-18T03:53:44.333515Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:44.333515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Mukai conjecture for log Fano manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Kento Fujita","submitted_at":"2012-06-12T09:51:10Z","abstract_excerpt":"For a log Fano manifold (X, D) with D\\neq 0 and with the log Fano pseudoindex \\geq 2, we prove that the restriction homomorphism Pic(X)\\to Pic(D_1) of Picard groups is injective for any irreducible component D_1\\subset D.The strategy of our proof is to run a certain minimal model program and is similar to the argument of Casagrande's one. As a corollary, we prove that the Mukai conjecture (resp. the generalized Mukai conjecture) implies the log Mukai conjecture (resp. the log generalized Mukai conjecture)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2475","kind":"arxiv","version":1},"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":"1206.2475","created_at":"2026-05-18T03:53:44.333599+00:00"},{"alias_kind":"arxiv_version","alias_value":"1206.2475v1","created_at":"2026-05-18T03:53:44.333599+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.2475","created_at":"2026-05-18T03:53:44.333599+00:00"},{"alias_kind":"pith_short_12","alias_value":"HXTLJAYZEDVM","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_16","alias_value":"HXTLJAYZEDVMVVCR","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_8","alias_value":"HXTLJAYZ","created_at":"2026-05-18T12:27:09.501522+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HXTLJAYZEDVMVVCRUBBIRQ5GGB","json":"https://pith.science/pith/HXTLJAYZEDVMVVCRUBBIRQ5GGB.json","graph_json":"https://pith.science/api/pith-number/HXTLJAYZEDVMVVCRUBBIRQ5GGB/graph.json","events_json":"https://pith.science/api/pith-number/HXTLJAYZEDVMVVCRUBBIRQ5GGB/events.json","paper":"https://pith.science/paper/HXTLJAYZ"},"agent_actions":{"view_html":"https://pith.science/pith/HXTLJAYZEDVMVVCRUBBIRQ5GGB","download_json":"https://pith.science/pith/HXTLJAYZEDVMVVCRUBBIRQ5GGB.json","view_paper":"https://pith.science/paper/HXTLJAYZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1206.2475&json=true","fetch_graph":"https://pith.science/api/pith-number/HXTLJAYZEDVMVVCRUBBIRQ5GGB/graph.json","fetch_events":"https://pith.science/api/pith-number/HXTLJAYZEDVMVVCRUBBIRQ5GGB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HXTLJAYZEDVMVVCRUBBIRQ5GGB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HXTLJAYZEDVMVVCRUBBIRQ5GGB/action/storage_attestation","attest_author":"https://pith.science/pith/HXTLJAYZEDVMVVCRUBBIRQ5GGB/action/author_attestation","sign_citation":"https://pith.science/pith/HXTLJAYZEDVMVVCRUBBIRQ5GGB/action/citation_signature","submit_replication":"https://pith.science/pith/HXTLJAYZEDVMVVCRUBBIRQ5GGB/action/replication_record"}},"created_at":"2026-05-18T03:53:44.333599+00:00","updated_at":"2026-05-18T03:53:44.333599+00:00"}