{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2LE3JAP2CYZDUUYQDVQMCYFNNP","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":"91c3bfdbb95fafc2a5f9a98e07248fd65937131a82f2de219d463e5d0b57eea5","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-05-01T11:28:08Z","title_canon_sha256":"211478a8d4b63b44eb2c8951ec4835011fb10133d9033b487f43da3da024e284"},"schema_version":"1.0","source":{"id":"1805.00274","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00274","created_at":"2026-05-17T23:56:10Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00274v2","created_at":"2026-05-17T23:56:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00274","created_at":"2026-05-17T23:56:10Z"},{"alias_kind":"pith_short_12","alias_value":"2LE3JAP2CYZD","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2LE3JAP2CYZDUUYQ","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2LE3JAP2","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:163b27cc69734c70124ab8ff98e6d9296c49374f91c5f725e8b8ce38655bd8b3","target":"graph","created_at":"2026-05-17T23:56:10Z","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 review the theory of Co-Gorenstein algebras, which was introduced by Beligiannis in the article \"The Homological Theory of Contravariantly Finite Subcategories: Gorenstein Categories, Auslander-Buchweitz Contexts and (Co-)Stabilization\". We show a connection between Co-Gorenstein algebras and the Nakayama and Generalized Nakayama conjecture.","authors_text":"Rene Marczinzik, Sondre Kvamme","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-05-01T11:28:08Z","title":"Co-Gorenstein algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00274","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":"sha256:40c34c3fe752c5f478e41686ea30be271b87a29530f5d570eb81cf74bcf65493","target":"record","created_at":"2026-05-17T23:56:10Z","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":"91c3bfdbb95fafc2a5f9a98e07248fd65937131a82f2de219d463e5d0b57eea5","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-05-01T11:28:08Z","title_canon_sha256":"211478a8d4b63b44eb2c8951ec4835011fb10133d9033b487f43da3da024e284"},"schema_version":"1.0","source":{"id":"1805.00274","kind":"arxiv","version":2}},"canonical_sha256":"d2c9b481fa16323a53101d60c160ad6bd82fdf2bd3e3f8fa430e51a4b3104224","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2c9b481fa16323a53101d60c160ad6bd82fdf2bd3e3f8fa430e51a4b3104224","first_computed_at":"2026-05-17T23:56:10.147476Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:10.147476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6Ok/9B+/pwlC7cI96wIYP4Yq68FZrYdHk2yC3RQzeq200euNMX9dQBtOxicTddJwuNdAF23/ED44pKKmCV2KCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:10.148123Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.00274","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40c34c3fe752c5f478e41686ea30be271b87a29530f5d570eb81cf74bcf65493","sha256:163b27cc69734c70124ab8ff98e6d9296c49374f91c5f725e8b8ce38655bd8b3"],"state_sha256":"1ee05134c423e4b61226f5d8ab679d89bee0c159843736d31aa9afece2a15446"}