{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QGSXNXM4W5NI64VFNPHKRWJPRV","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":"9312e2ad83fa254c0bc1062778c6d2aed36c386f76da213ff15142ec876ce786","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-06-14T06:04:34Z","title_canon_sha256":"e51827a6be239e4cb158ad37cdb68d5a5cd7ea0a215f8a6d73a0aeda4ac354ea"},"schema_version":"1.0","source":{"id":"1106.2616","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.2616","created_at":"2026-05-18T03:12:33Z"},{"alias_kind":"arxiv_version","alias_value":"1106.2616v1","created_at":"2026-05-18T03:12:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.2616","created_at":"2026-05-18T03:12:33Z"},{"alias_kind":"pith_short_12","alias_value":"QGSXNXM4W5NI","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QGSXNXM4W5NI64VF","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QGSXNXM4","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:04e2cd5e8eb0a85c7995436351821825070cac09fda51fda42bd0236eb1dc11b","target":"graph","created_at":"2026-05-18T03:12:33Z","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":"In algebraic geometry, one often encounters the following problem: given a scheme X, find a proper birational morphism from Y to X where the geometry of Y is \"nicer\" than that of X. One version of this problem, first studied by Faltings, requires Y to be Cohen-Macaulay; in this case Y is called a Macaulayfication of X. In another variant, one requires Y to satisfy the Serre condition S_r. In this paper, the authors introduce generalized Serre conditions--these are local cohomology conditions which include S_r and the Cohen-Macaulay condition as special cases. To any generalized Serre condition","authors_text":"Christopher L. Bremer, Daniel S. Sage","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-06-14T06:04:34Z","title":"Generalized Serre conditions and perverse coherent sheaves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2616","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:b5f07dd63c7d130a1729baef1edd0069550f042c7d3a581393b48afeeefba87e","target":"record","created_at":"2026-05-18T03:12:33Z","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":"9312e2ad83fa254c0bc1062778c6d2aed36c386f76da213ff15142ec876ce786","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-06-14T06:04:34Z","title_canon_sha256":"e51827a6be239e4cb158ad37cdb68d5a5cd7ea0a215f8a6d73a0aeda4ac354ea"},"schema_version":"1.0","source":{"id":"1106.2616","kind":"arxiv","version":1}},"canonical_sha256":"81a576dd9cb75a8f72a56bcea8d92f8d7afaa4f25c5884e09a4e642daa248994","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81a576dd9cb75a8f72a56bcea8d92f8d7afaa4f25c5884e09a4e642daa248994","first_computed_at":"2026-05-18T03:12:33.531228Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:33.531228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D2cRpu1AURr4uSyjC0jj9kOY+4cc5ONKmnClTjY7Yvsj3iQarLdoSLZyY1SSAjDWxfhbcBdP5xcuVUHCXVxACg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:33.531980Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.2616","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5f07dd63c7d130a1729baef1edd0069550f042c7d3a581393b48afeeefba87e","sha256:04e2cd5e8eb0a85c7995436351821825070cac09fda51fda42bd0236eb1dc11b"],"state_sha256":"d1d1654e23d28e33f21ede303f11bb75693fd094ef9f2724f79321fd671d4412"}