{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2OTMNKWL23L4HKBMYTJ7OD2223","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":"f196adeffd3f89bec74cec1d6fad63bfb32c13e8c80f8ddc6f79132bd1c87ad5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-31T17:44:25Z","title_canon_sha256":"e6f4ed97227bc8f5c7065994d06007e0b9083452fd678dd69b1df0c0ce6fc5ea"},"schema_version":"1.0","source":{"id":"1701.09149","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.09149","created_at":"2026-05-18T00:51:38Z"},{"alias_kind":"arxiv_version","alias_value":"1701.09149v1","created_at":"2026-05-18T00:51:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.09149","created_at":"2026-05-18T00:51:38Z"},{"alias_kind":"pith_short_12","alias_value":"2OTMNKWL23L4","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2OTMNKWL23L4HKBM","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2OTMNKWL","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:e3ab59423fd7e43b5edd387b317430acb866bf46d9234de1eaac83b44c90705a","target":"graph","created_at":"2026-05-18T00:51:38Z","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 Cox rings of crepant resolutions of quotient singularities $\\mathbb{C}^3/G$ where $G$ is a finite subgroup of $SL(3,\\mathbb{C})$. We use them to obtain information on the geometric structure of these resolutions, number of different resolutions and relations between them. In particular, we treat explicitly several examples where $G$ contains elements of age 2.","authors_text":"Maksymilian Grab, Maria Donten-Bury","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-31T17:44:25Z","title":"Crepant resolutions of 3-dimensional quotient singularities via Cox rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.09149","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":"sha256:84d61bae5f68d8b373263474a8f61b7039214441ba355ff58878d0843695b2f4","target":"record","created_at":"2026-05-18T00:51:38Z","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":"f196adeffd3f89bec74cec1d6fad63bfb32c13e8c80f8ddc6f79132bd1c87ad5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-31T17:44:25Z","title_canon_sha256":"e6f4ed97227bc8f5c7065994d06007e0b9083452fd678dd69b1df0c0ce6fc5ea"},"schema_version":"1.0","source":{"id":"1701.09149","kind":"arxiv","version":1}},"canonical_sha256":"d3a6c6aacbd6d7c3a82cc4d3f70f5ad6d1720a2275442f8c105ba89ed73be029","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3a6c6aacbd6d7c3a82cc4d3f70f5ad6d1720a2275442f8c105ba89ed73be029","first_computed_at":"2026-05-18T00:51:38.359459Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:38.359459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TzFw58LQGF8GQuE12KKF/RRVe6bMq8WSbeJWhoVh1Lc/mvexof1VD7+ch2Nntb9MZwgoLmV7CWsTDpm2/OsxAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:38.359852Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.09149","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:84d61bae5f68d8b373263474a8f61b7039214441ba355ff58878d0843695b2f4","sha256:e3ab59423fd7e43b5edd387b317430acb866bf46d9234de1eaac83b44c90705a"],"state_sha256":"ee25314ca3a08f29f20b0afb44c68177c9f64200b13d867593f72f1176116deb"}