{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:AY2LSM7RPRLSMK76IZWW3BGKDQ","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":"f0165de3dc4020b47a22656e343c50d5c77970015ae14bf124a5d91623d7e21b","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-08-06T10:13:55Z","title_canon_sha256":"0914f6aa4ed07e5c88dc62b114f15bb43689e08621baff74657edda9a8acc597"},"schema_version":"1.0","source":{"id":"1808.01809","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.01809","created_at":"2026-07-05T00:48:36Z"},{"alias_kind":"arxiv_version","alias_value":"1808.01809v4","created_at":"2026-07-05T00:48:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.01809","created_at":"2026-07-05T00:48:36Z"},{"alias_kind":"pith_short_12","alias_value":"AY2LSM7RPRLS","created_at":"2026-07-05T00:48:36Z"},{"alias_kind":"pith_short_16","alias_value":"AY2LSM7RPRLSMK76","created_at":"2026-07-05T00:48:36Z"},{"alias_kind":"pith_short_8","alias_value":"AY2LSM7R","created_at":"2026-07-05T00:48:36Z"}],"graph_snapshots":[{"event_id":"sha256:4720313abe61063508db2bd705d768a6e1b89e655aa7d5dc4951f2b8e1056a4a","target":"graph","created_at":"2026-07-05T00:48:36Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1808.01809/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"An A-module M will be said to be semi-Gorenstein-projective provided that Ext^i(M,A) = 0 for all i > 0. All Gorenstein-projective modules are semi-Gorenstein-projective and only few and quite complicated examples of semi-Gorenstein-projective modules which are not Gorenstein-projective have been known. The aim of the paper is to provide conditions on A such that all semi-Gorenstein-projective modules are Gorenstein-projective (we call such an algebra left weakly Gorenstein). In particular, we show that in case there are only finitely many isomorphism classes of indecomposable left modules whic","authors_text":"Claus Michael Ringel, Pu Zhang","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-08-06T10:13:55Z","title":"Gorenstein-projective and semi-Gorenstein-projective modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01809","kind":"arxiv","version":4},"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":"sha256:2e61e6c1aca1cfb33bcb77fc33afb564f1a598c87f48065e64c31bb7a5b99fff","target":"record","created_at":"2026-07-05T00:48:36Z","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":"f0165de3dc4020b47a22656e343c50d5c77970015ae14bf124a5d91623d7e21b","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2018-08-06T10:13:55Z","title_canon_sha256":"0914f6aa4ed07e5c88dc62b114f15bb43689e08621baff74657edda9a8acc597"},"schema_version":"1.0","source":{"id":"1808.01809","kind":"arxiv","version":4}},"canonical_sha256":"0634b933f17c57262bfe466d6d84ca1c28900737e00490eb18c5d64db019073b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0634b933f17c57262bfe466d6d84ca1c28900737e00490eb18c5d64db019073b","first_computed_at":"2026-07-05T00:48:36.146689Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:48:36.146689Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wGIXqm5lxsjK4oViD5RbfiWEq7jQYMIIejmDkko3iNGuS2npKE6KhWlyndpZYcgVPS3Q5ipVcTb2Mw+RCcPeCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:48:36.147052Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.01809","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e61e6c1aca1cfb33bcb77fc33afb564f1a598c87f48065e64c31bb7a5b99fff","sha256:4720313abe61063508db2bd705d768a6e1b89e655aa7d5dc4951f2b8e1056a4a"],"state_sha256":"12e3aad4f41eb72eb183a41ebc606561040f7eb10a63c87c21df7e82883e0c96"}