{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:2VGIIZBFBYVZPXH5WYN2CDSWIT","short_pith_number":"pith:2VGIIZBF","canonical_record":{"source":{"id":"1302.0298","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-02-01T21:28:59Z","cross_cats_sorted":[],"title_canon_sha256":"53f0e839590f9da40f3dcd4da845faa2f9483f236722ec36e2816f1a7b744788","abstract_canon_sha256":"9c650509fc27288d0b29fedb01ab92c167902edd2282e20ec7b86ec29b112b22"},"schema_version":"1.0"},"canonical_sha256":"d54c8464250e2b97dcfdb61ba10e5644e6ed9da247a2f5e4d453fa19aac10c81","source":{"kind":"arxiv","id":"1302.0298","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0298","created_at":"2026-05-18T03:19:45Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0298v2","created_at":"2026-05-18T03:19:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0298","created_at":"2026-05-18T03:19:45Z"},{"alias_kind":"pith_short_12","alias_value":"2VGIIZBFBYVZ","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"2VGIIZBFBYVZPXH5","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"2VGIIZBF","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:2VGIIZBFBYVZPXH5WYN2CDSWIT","target":"record","payload":{"canonical_record":{"source":{"id":"1302.0298","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-02-01T21:28:59Z","cross_cats_sorted":[],"title_canon_sha256":"53f0e839590f9da40f3dcd4da845faa2f9483f236722ec36e2816f1a7b744788","abstract_canon_sha256":"9c650509fc27288d0b29fedb01ab92c167902edd2282e20ec7b86ec29b112b22"},"schema_version":"1.0"},"canonical_sha256":"d54c8464250e2b97dcfdb61ba10e5644e6ed9da247a2f5e4d453fa19aac10c81","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:45.698363Z","signature_b64":"dcEcoKrgpf6r0W7dw8imQytNvMWtg8c2KTkdMc/IM/edLsQFPT8aK0dfTildmbuxMZsj94cZMvfDcODWobyvAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d54c8464250e2b97dcfdb61ba10e5644e6ed9da247a2f5e4d453fa19aac10c81","last_reissued_at":"2026-05-18T03:19:45.697540Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:45.697540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.0298","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:19:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RiXkAxriL9iDZlmEEkqkbxtTpyg+c/IXgxQFMp3gpvibVvgsUoVO1txPdrlqiSAGB6ysQk29Tnzg8Js3WPZuBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:51:27.378058Z"},"content_sha256":"cbe381b64f38eaf6d3a580c490d7eb0d36b75daf882d69c941c84b35d7560441","schema_version":"1.0","event_id":"sha256:cbe381b64f38eaf6d3a580c490d7eb0d36b75daf882d69c941c84b35d7560441"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:2VGIIZBFBYVZPXH5WYN2CDSWIT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the three dimensional minimal model program in positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Chenyang Xu, Christopher D. Hacon","submitted_at":"2013-02-01T21:28:59Z","abstract_excerpt":"Let $f:(X,B)\\to Z$ be a 3-fold extremal dlt flipping contraction defined over an algebraically closed field of characteristic $p>5$, such that the coefficients of $\\{B\\}$ are in the standard set $\\{1-\\frac 1n|n\\in \\mathbb N\\}$, then the flip of $f$ exists. As a consequence, we prove the existence of minimal models for any projective $\\Q$-factorial terminal variety $X$ with pseudo-effective canonical divisor $K_X$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0298","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:19:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AkytEq9I9iNGqRgU1kxAPfe5N+emDLL6s479G02jJ+THEatb0/dtK1U+Pn0IOZEg+bhyX5rDJ6M+4z3XU6HNDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:51:27.378811Z"},"content_sha256":"9b35e56683f7117d222aea0d9410c4aab08cee205c472b136acd87a615f164e2","schema_version":"1.0","event_id":"sha256:9b35e56683f7117d222aea0d9410c4aab08cee205c472b136acd87a615f164e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2VGIIZBFBYVZPXH5WYN2CDSWIT/bundle.json","state_url":"https://pith.science/pith/2VGIIZBFBYVZPXH5WYN2CDSWIT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2VGIIZBFBYVZPXH5WYN2CDSWIT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T03:51:27Z","links":{"resolver":"https://pith.science/pith/2VGIIZBFBYVZPXH5WYN2CDSWIT","bundle":"https://pith.science/pith/2VGIIZBFBYVZPXH5WYN2CDSWIT/bundle.json","state":"https://pith.science/pith/2VGIIZBFBYVZPXH5WYN2CDSWIT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2VGIIZBFBYVZPXH5WYN2CDSWIT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2VGIIZBFBYVZPXH5WYN2CDSWIT","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":"9c650509fc27288d0b29fedb01ab92c167902edd2282e20ec7b86ec29b112b22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-02-01T21:28:59Z","title_canon_sha256":"53f0e839590f9da40f3dcd4da845faa2f9483f236722ec36e2816f1a7b744788"},"schema_version":"1.0","source":{"id":"1302.0298","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.0298","created_at":"2026-05-18T03:19:45Z"},{"alias_kind":"arxiv_version","alias_value":"1302.0298v2","created_at":"2026-05-18T03:19:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.0298","created_at":"2026-05-18T03:19:45Z"},{"alias_kind":"pith_short_12","alias_value":"2VGIIZBFBYVZ","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"2VGIIZBFBYVZPXH5","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"2VGIIZBF","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:9b35e56683f7117d222aea0d9410c4aab08cee205c472b136acd87a615f164e2","target":"graph","created_at":"2026-05-18T03:19:45Z","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"},"paper":{"abstract_excerpt":"Let $f:(X,B)\\to Z$ be a 3-fold extremal dlt flipping contraction defined over an algebraically closed field of characteristic $p>5$, such that the coefficients of $\\{B\\}$ are in the standard set $\\{1-\\frac 1n|n\\in \\mathbb N\\}$, then the flip of $f$ exists. As a consequence, we prove the existence of minimal models for any projective $\\Q$-factorial terminal variety $X$ with pseudo-effective canonical divisor $K_X$.","authors_text":"Chenyang Xu, Christopher D. Hacon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-02-01T21:28:59Z","title":"On the three dimensional minimal model program in positive characteristic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0298","kind":"arxiv","version":2},"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:cbe381b64f38eaf6d3a580c490d7eb0d36b75daf882d69c941c84b35d7560441","target":"record","created_at":"2026-05-18T03:19:45Z","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":"9c650509fc27288d0b29fedb01ab92c167902edd2282e20ec7b86ec29b112b22","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-02-01T21:28:59Z","title_canon_sha256":"53f0e839590f9da40f3dcd4da845faa2f9483f236722ec36e2816f1a7b744788"},"schema_version":"1.0","source":{"id":"1302.0298","kind":"arxiv","version":2}},"canonical_sha256":"d54c8464250e2b97dcfdb61ba10e5644e6ed9da247a2f5e4d453fa19aac10c81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d54c8464250e2b97dcfdb61ba10e5644e6ed9da247a2f5e4d453fa19aac10c81","first_computed_at":"2026-05-18T03:19:45.697540Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:45.697540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dcEcoKrgpf6r0W7dw8imQytNvMWtg8c2KTkdMc/IM/edLsQFPT8aK0dfTildmbuxMZsj94cZMvfDcODWobyvAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:45.698363Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.0298","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cbe381b64f38eaf6d3a580c490d7eb0d36b75daf882d69c941c84b35d7560441","sha256:9b35e56683f7117d222aea0d9410c4aab08cee205c472b136acd87a615f164e2"],"state_sha256":"d85c403dcbd4d436f664ab8609f92bfb20097e4a7271563424f3a0fe2ceedc3f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5VC+78Ur8NjgsMAR9iUEdY3Hl5VXUwQNQuVOS1DLLma/SyxRV6qx4KZ45jy99ddFfCF+/LOmOLMStjlRvaGBAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T03:51:27.382148Z","bundle_sha256":"6c23bfb3d1c9e1d51c6245bad8bcda6cf8ba62db4538807064c937f433c6a91f"}}