{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:SHJZCZDGEUUDJLLF7Q4O3IICZM","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":"a78897f219efb23163b3d093699ae9f18b802a7dc42ef68880da937d15891de4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-09-08T06:10:30Z","title_canon_sha256":"70d134118a2d464734bc895944b5bc65693e53b18ce96b837b54e494ac99a981"},"schema_version":"1.0","source":{"id":"1009.1454","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.1454","created_at":"2026-05-18T03:47:09Z"},{"alias_kind":"arxiv_version","alias_value":"1009.1454v2","created_at":"2026-05-18T03:47:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.1454","created_at":"2026-05-18T03:47:09Z"},{"alias_kind":"pith_short_12","alias_value":"SHJZCZDGEUUD","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SHJZCZDGEUUDJLLF","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SHJZCZDG","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:019ce745c3aaf46c847818068487501da9ff04547e38933827004688df7e8372","target":"graph","created_at":"2026-05-18T03:47:09Z","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 this note we present some remarks on big Cohen-Macaulay algebras. Our methods for doing this are inspired by the notion of dagger closure and by ideas of Northcott on dropping of the Noetherian assumption of certain homological properties.","authors_text":"Mohsen Asgharzadeh, Rajsekhar Bhattacharyya","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-09-08T06:10:30Z","title":"Applications of closure operations on big CohenMacaulay algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.1454","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:a90e3b014b40f39db2e241ffbc5aee4fc341b3268034780cc139e7a4567a4e4d","target":"record","created_at":"2026-05-18T03:47:09Z","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":"a78897f219efb23163b3d093699ae9f18b802a7dc42ef68880da937d15891de4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-09-08T06:10:30Z","title_canon_sha256":"70d134118a2d464734bc895944b5bc65693e53b18ce96b837b54e494ac99a981"},"schema_version":"1.0","source":{"id":"1009.1454","kind":"arxiv","version":2}},"canonical_sha256":"91d3916466252834ad65fc38eda102cb26e93cde7e00ed56599f8f81fc8c703e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91d3916466252834ad65fc38eda102cb26e93cde7e00ed56599f8f81fc8c703e","first_computed_at":"2026-05-18T03:47:09.002143Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:47:09.002143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MqZgBKAtJxDQh2XEA1iWZmuDhz2cqs2p/wZNzN+eiU2GJFVwQy1bPrFmqru46wW6F8QfIubnV4sSzTDkn+dTBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:47:09.002643Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.1454","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a90e3b014b40f39db2e241ffbc5aee4fc341b3268034780cc139e7a4567a4e4d","sha256:019ce745c3aaf46c847818068487501da9ff04547e38933827004688df7e8372"],"state_sha256":"cd007f50f0b164e645832bcdfade50df1cacc0e936453a6eb3c45984bf1de95e"}