{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:QGSXNXM4W5NI64VFNPHKRWJPRV","short_pith_number":"pith:QGSXNXM4","canonical_record":{"source":{"id":"1106.2616","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-06-14T06:04:34Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"e51827a6be239e4cb158ad37cdb68d5a5cd7ea0a215f8a6d73a0aeda4ac354ea","abstract_canon_sha256":"9312e2ad83fa254c0bc1062778c6d2aed36c386f76da213ff15142ec876ce786"},"schema_version":"1.0"},"canonical_sha256":"81a576dd9cb75a8f72a56bcea8d92f8d7afaa4f25c5884e09a4e642daa248994","source":{"kind":"arxiv","id":"1106.2616","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:QGSXNXM4W5NI64VFNPHKRWJPRV","target":"record","payload":{"canonical_record":{"source":{"id":"1106.2616","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-06-14T06:04:34Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"e51827a6be239e4cb158ad37cdb68d5a5cd7ea0a215f8a6d73a0aeda4ac354ea","abstract_canon_sha256":"9312e2ad83fa254c0bc1062778c6d2aed36c386f76da213ff15142ec876ce786"},"schema_version":"1.0"},"canonical_sha256":"81a576dd9cb75a8f72a56bcea8d92f8d7afaa4f25c5884e09a4e642daa248994","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:33.531980Z","signature_b64":"D2cRpu1AURr4uSyjC0jj9kOY+4cc5ONKmnClTjY7Yvsj3iQarLdoSLZyY1SSAjDWxfhbcBdP5xcuVUHCXVxACg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81a576dd9cb75a8f72a56bcea8d92f8d7afaa4f25c5884e09a4e642daa248994","last_reissued_at":"2026-05-18T03:12:33.531228Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:33.531228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.2616","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:12:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8Kq/4nngdrIMSW1qLNy4DarRadgR3Xyk4UjQCKOmNA6bcb+L2h84kOjJZqF5bhvLcFe+A1CV1RAaFDMcKGR+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T16:20:05.354661Z"},"content_sha256":"b5f07dd63c7d130a1729baef1edd0069550f042c7d3a581393b48afeeefba87e","schema_version":"1.0","event_id":"sha256:b5f07dd63c7d130a1729baef1edd0069550f042c7d3a581393b48afeeefba87e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:QGSXNXM4W5NI64VFNPHKRWJPRV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Serre conditions and perverse coherent sheaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Christopher L. Bremer, Daniel S. Sage","submitted_at":"2011-06-14T06:04:34Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.2616","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:12:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HmxqSTBhlei/qpcd4iCzYiy9GLA6X872Th5Q7LHbQVk8W1KSsjFVkH2KT9K+AZ8NUrxIzH49HiNPcTxqhGHmBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T16:20:05.355089Z"},"content_sha256":"04e2cd5e8eb0a85c7995436351821825070cac09fda51fda42bd0236eb1dc11b","schema_version":"1.0","event_id":"sha256:04e2cd5e8eb0a85c7995436351821825070cac09fda51fda42bd0236eb1dc11b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QGSXNXM4W5NI64VFNPHKRWJPRV/bundle.json","state_url":"https://pith.science/pith/QGSXNXM4W5NI64VFNPHKRWJPRV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QGSXNXM4W5NI64VFNPHKRWJPRV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T16:20:05Z","links":{"resolver":"https://pith.science/pith/QGSXNXM4W5NI64VFNPHKRWJPRV","bundle":"https://pith.science/pith/QGSXNXM4W5NI64VFNPHKRWJPRV/bundle.json","state":"https://pith.science/pith/QGSXNXM4W5NI64VFNPHKRWJPRV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QGSXNXM4W5NI64VFNPHKRWJPRV/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w2srO0f9uL24Gd2Aq2S4eJVhZ5arCrtpn0Mlj/QVCvW5m8cw2AzOmjt+WFSu54SxtRYAPK8sKwq5x6Uvy4dPAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T16:20:05.357123Z","bundle_sha256":"cc3c4999a017a00fd1fef14a051c0eeef737091c9e1dbc995788501c48953b24"}}