{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:C4T53OHFI7RRX4734I2Z66MUZG","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":"9b0a8764282927afa6986133c779bf5a43877926be05d1e32007bc0f06cb2b88","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-29T10:09:29Z","title_canon_sha256":"2483b275bf373ea52188d3d8bdc14784c297c5b056336ef49a36efb0b7fdb440"},"schema_version":"1.0","source":{"id":"1403.7614","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.7614","created_at":"2026-05-18T01:03:06Z"},{"alias_kind":"arxiv_version","alias_value":"1403.7614v1","created_at":"2026-05-18T01:03:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7614","created_at":"2026-05-18T01:03:06Z"},{"alias_kind":"pith_short_12","alias_value":"C4T53OHFI7RR","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"C4T53OHFI7RRX473","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"C4T53OHF","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:2fae4d09054be9c903782ee5a1ef97f77a75b7808b8b88c79c6c11843ab5bb89","target":"graph","created_at":"2026-05-18T01:03:06Z","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":"Consider a singular curve $\\Gamma$ contained in a smooth 3-fold $X$. Assuming the general elephant conjecture, the general hypersurface section $\\Gamma\\subset S\\subset X$ is Du Val. Under that assumption, this paper describes the construction of a divisorial extraction from $\\Gamma$ by Kustin--Miller unprojection. Terminal extractions from $\\Gamma\\subset X$ are proved not to exist if $S$ is of type $D_{2k}, E_7$ or $E_8$ and are classified if $S$ is of type $A_1,A_2$ or $E_6$. The $A_n$ and $D_{2k+1}$ cases shall be considered in a further paper.","authors_text":"Tom Ducat","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-29T10:09:29Z","title":"Divisorial Extractions from Singular Curves in Smooth 3-Folds, I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7614","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":"sha256:6cea0531e9533c625f939cd0763da5c4dd9a63c791a45600290781de4f567020","target":"record","created_at":"2026-05-18T01:03:06Z","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":"9b0a8764282927afa6986133c779bf5a43877926be05d1e32007bc0f06cb2b88","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-03-29T10:09:29Z","title_canon_sha256":"2483b275bf373ea52188d3d8bdc14784c297c5b056336ef49a36efb0b7fdb440"},"schema_version":"1.0","source":{"id":"1403.7614","kind":"arxiv","version":1}},"canonical_sha256":"1727ddb8e547e31bf3fbe2359f7994c9b721d64f53f88080500496ca6a707a6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1727ddb8e547e31bf3fbe2359f7994c9b721d64f53f88080500496ca6a707a6c","first_computed_at":"2026-05-18T01:03:06.722053Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:06.722053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q2A4glcYftQwnOl7YtQvyyK0hLdNEsY/OM/AiFYC2k7i0ceKNYpG6UPU4ZttNS5F3KZ8ICx+7Hr0QvGVZPz2Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:06.722658Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.7614","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6cea0531e9533c625f939cd0763da5c4dd9a63c791a45600290781de4f567020","sha256:2fae4d09054be9c903782ee5a1ef97f77a75b7808b8b88c79c6c11843ab5bb89"],"state_sha256":"0c5add38fd3b72f6d0193d67fdfa8c54d01bb2fbbb8f4240f6426b98c4674620"}