{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:A64OVQPTBT34RRJ6LRBMTNVPFD","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":"45a8f421b675e41378d301026f8b1bb3fc89d3f52d00c2603b460e0b31d3ffa3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-07T19:55:07Z","title_canon_sha256":"4c56aef79cbcec3bd81ef711144495ba1a8feeee6a96b50259938d212aa2ff4f"},"schema_version":"1.0","source":{"id":"1508.01792","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01792","created_at":"2026-05-18T01:09:46Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01792v1","created_at":"2026-05-18T01:09:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01792","created_at":"2026-05-18T01:09:46Z"},{"alias_kind":"pith_short_12","alias_value":"A64OVQPTBT34","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"A64OVQPTBT34RRJ6","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"A64OVQPT","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:bc64683b6097e61b3df7d8eb883745f06abfe9d4c57ef5576dcb5a17c015eddb","target":"graph","created_at":"2026-05-18T01:09:46Z","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":"We study certain pencils of del Pezzo surfaces generated by a smooth del Pezzo surface S of degree less or equal to 3 anti-canonically embedded into a weighted projective space P and an appropriate multiple of a hyperplane H. Our main observation is that every minimal model program relative to the morphism lifting such pencil on a suitable resolution of its indeterminacies preserves the open subset P H \\^a A^3. As an application, we obtain projective completions of A^3 into del Pezzo fibrations over P^1 of every degree less or equal to 4. We also obtain completions of A^3 into Mori conic bundl","authors_text":"Adrien Dubouloz (IMB), Takashi Kishimoto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-07T19:55:07Z","title":"Explicit biregular/birational geometry of affine threefolds: completions of A^3 into del Pezzo fibrations and Mori conic bundles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01792","kind":"arxiv","version":1},"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":"sha256:01ff5424c4215b441b99c7133cbbbb51db54cd0b0ea6ca0de15969aabb55ac8e","target":"record","created_at":"2026-05-18T01:09:46Z","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":"45a8f421b675e41378d301026f8b1bb3fc89d3f52d00c2603b460e0b31d3ffa3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-08-07T19:55:07Z","title_canon_sha256":"4c56aef79cbcec3bd81ef711144495ba1a8feeee6a96b50259938d212aa2ff4f"},"schema_version":"1.0","source":{"id":"1508.01792","kind":"arxiv","version":1}},"canonical_sha256":"07b8eac1f30cf7c8c53e5c42c9b6af28f731add7aa5ea4e83582c745cde8f8f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07b8eac1f30cf7c8c53e5c42c9b6af28f731add7aa5ea4e83582c745cde8f8f6","first_computed_at":"2026-05-18T01:09:46.125781Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:46.125781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y8vQDzlXnnu1uqYv6bJoLnDeAghCdRERDZ1hltYKG5KtT/Sg209y8Fer2sPAFqtL8nulBDJW8F70+AssJNhEAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:46.126491Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.01792","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:01ff5424c4215b441b99c7133cbbbb51db54cd0b0ea6ca0de15969aabb55ac8e","sha256:bc64683b6097e61b3df7d8eb883745f06abfe9d4c57ef5576dcb5a17c015eddb"],"state_sha256":"19fbd2f30351a431463568eb09047b0f07359ae8aab0351488611801e22bf282"}