{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:UR2FLXJ6Y3RIET442A6DVJSTBY","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":"2c5f787f41e7a5eb92bc09367477270e3ded3649b5aa2ff79cdf5978a16d2a2e","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-22T09:55:49Z","title_canon_sha256":"261a68561385792b062fe3c663ade90413da722d2ad31058f7505a14d9a31eb2"},"schema_version":"1.0","source":{"id":"1009.4313","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.4313","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"1009.4313v2","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4313","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"UR2FLXJ6Y3RI","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"UR2FLXJ6Y3RIET44","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"UR2FLXJ6","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:78a0845db6d58aabd725a04e2842d60170a71728b45b363339dbc5e5f734d12f","target":"graph","created_at":"2026-05-17T23:53:36Z","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":"This work is part of the Graded Ring Database project [GRDB], and is a sequel to [Altinok's 1998 PhD thesis] and [Altinok, Brown and Reid, Fano 3-folds, K3 surfaces and graded rings, in SISTAG (Singapore, 2001), Contemp. Math. 314, 2002, pp. 25-53]. We introduce a strategy based on Kustin-Miller unprojection that constructs many hundreds of Gorenstein codimension 4 ideals with 9x16 resolutions (that is, 9 equations and 16 first syzygies). Our two basic games are called Tom and Jerry; the main application is the biregular construction of most of the anticanonically polarised Mori Fano 3-folds o","authors_text":"Gavin Brown, Michael Kerber, Miles Reid","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-22T09:55:49Z","title":"Fano 3-folds in codimension 4, Tom and Jerry, Part I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4313","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:ecd22ac2f6435f7237a0ed28e7f9203a7e7698ba77abb0acd6ac5a2a52d9e3c1","target":"record","created_at":"2026-05-17T23:53:36Z","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":"2c5f787f41e7a5eb92bc09367477270e3ded3649b5aa2ff79cdf5978a16d2a2e","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-22T09:55:49Z","title_canon_sha256":"261a68561385792b062fe3c663ade90413da722d2ad31058f7505a14d9a31eb2"},"schema_version":"1.0","source":{"id":"1009.4313","kind":"arxiv","version":2}},"canonical_sha256":"a47455dd3ec6e2824f9cd03c3aa6530e2dcffb7be09828183cd7b20b815195fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a47455dd3ec6e2824f9cd03c3aa6530e2dcffb7be09828183cd7b20b815195fd","first_computed_at":"2026-05-17T23:53:36.868736Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:36.868736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"alI/zaE8xFQWltuJrYGFphC0f2e1C5vDzosTIrHSDiPDgNyhSKwSa+1YL09TaAZU/wQcaAmFyO4I2Fyo9p4NBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:36.869488Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.4313","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ecd22ac2f6435f7237a0ed28e7f9203a7e7698ba77abb0acd6ac5a2a52d9e3c1","sha256:78a0845db6d58aabd725a04e2842d60170a71728b45b363339dbc5e5f734d12f"],"state_sha256":"bc98ed89a487f37af597475788d6d973a84ff3c5902fc9b08c9620c5c4203573"}