{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2003:VRVDYEC6ET2QQ33F6M6JVPS3Z3","short_pith_number":"pith:VRVDYEC6","schema_version":"1.0","canonical_sha256":"ac6a3c105e24f5086f65f33c9abe5bcecfbb37a570bd7ca0fa1bddce01d0a365","source":{"kind":"arxiv","id":"math/0307180","version":2},"attestation_state":"computed","paper":{"title":"Introduction to the toric Mori theory","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hiroshi Sato, Osamu Fujino","submitted_at":"2003-07-12T12:22:00Z","abstract_excerpt":"The main purpose of this paper is to give a simple and non-combinatorial proof of the toric Mori theory. Here, the toric Mori theory means the (log) Minimal Model Program (MMP, for short) for toric varieties. We minimize the arguments on fans and their decompositions. We recommend this paper to the following people:\n (A) those who are uncomfortable with manipulating fans and their decompositions,\n (B) those who are familiar with toric geometry but not with the MMP. People in the category (A) will be relieved from tedious combinatorial arguments in several problems. Those in the category (B) wi"},"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":"math/0307180","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2003-07-12T12:22:00Z","cross_cats_sorted":[],"title_canon_sha256":"da4718c14d1387623d1635b45957a8d6e1ac8d129b97aacd881c3e15d808e5f8","abstract_canon_sha256":"39500f76966763d4cfa686e4f6a5081874a935eb579d71669524ce89038bf8b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:28.754449Z","signature_b64":"kOCeNlH4TsTyjcxFrCAyDMQJ7WkbHSJamBsNKyLKmy9DaATIOsEr/t5ZaU3A8rxjD4LANg5tkbCnEyM2g+nqDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac6a3c105e24f5086f65f33c9abe5bcecfbb37a570bd7ca0fa1bddce01d0a365","last_reissued_at":"2026-05-18T01:05:28.753966Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:28.753966Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Introduction to the toric Mori theory","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hiroshi Sato, Osamu Fujino","submitted_at":"2003-07-12T12:22:00Z","abstract_excerpt":"The main purpose of this paper is to give a simple and non-combinatorial proof of the toric Mori theory. Here, the toric Mori theory means the (log) Minimal Model Program (MMP, for short) for toric varieties. We minimize the arguments on fans and their decompositions. We recommend this paper to the following people:\n (A) those who are uncomfortable with manipulating fans and their decompositions,\n (B) those who are familiar with toric geometry but not with the MMP. People in the category (A) will be relieved from tedious combinatorial arguments in several problems. Those in the category (B) wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0307180","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":"math/0307180","created_at":"2026-05-18T01:05:28.754046+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0307180v2","created_at":"2026-05-18T01:05:28.754046+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0307180","created_at":"2026-05-18T01:05:28.754046+00:00"},{"alias_kind":"pith_short_12","alias_value":"VRVDYEC6ET2Q","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_16","alias_value":"VRVDYEC6ET2QQ33F","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_8","alias_value":"VRVDYEC6","created_at":"2026-05-18T12:25:52.051335+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/VRVDYEC6ET2QQ33F6M6JVPS3Z3","json":"https://pith.science/pith/VRVDYEC6ET2QQ33F6M6JVPS3Z3.json","graph_json":"https://pith.science/api/pith-number/VRVDYEC6ET2QQ33F6M6JVPS3Z3/graph.json","events_json":"https://pith.science/api/pith-number/VRVDYEC6ET2QQ33F6M6JVPS3Z3/events.json","paper":"https://pith.science/paper/VRVDYEC6"},"agent_actions":{"view_html":"https://pith.science/pith/VRVDYEC6ET2QQ33F6M6JVPS3Z3","download_json":"https://pith.science/pith/VRVDYEC6ET2QQ33F6M6JVPS3Z3.json","view_paper":"https://pith.science/paper/VRVDYEC6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0307180&json=true","fetch_graph":"https://pith.science/api/pith-number/VRVDYEC6ET2QQ33F6M6JVPS3Z3/graph.json","fetch_events":"https://pith.science/api/pith-number/VRVDYEC6ET2QQ33F6M6JVPS3Z3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VRVDYEC6ET2QQ33F6M6JVPS3Z3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VRVDYEC6ET2QQ33F6M6JVPS3Z3/action/storage_attestation","attest_author":"https://pith.science/pith/VRVDYEC6ET2QQ33F6M6JVPS3Z3/action/author_attestation","sign_citation":"https://pith.science/pith/VRVDYEC6ET2QQ33F6M6JVPS3Z3/action/citation_signature","submit_replication":"https://pith.science/pith/VRVDYEC6ET2QQ33F6M6JVPS3Z3/action/replication_record"}},"created_at":"2026-05-18T01:05:28.754046+00:00","updated_at":"2026-05-18T01:05:28.754046+00:00"}