{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OSRBD4AOSV4DNQFCRCGQWWUZNP","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":"f6212f66ac5826de0b2b09455183d7f828f923d510ff51c5891c4caf62cec894","cross_cats_sorted":["math.AC","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-04-19T07:25:33Z","title_canon_sha256":"4ebccce59dfd5419730ca320d31757e44adb19926dea92e6367263be93cdd23a"},"schema_version":"1.0","source":{"id":"1104.3658","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.3658","created_at":"2026-05-18T02:30:01Z"},{"alias_kind":"arxiv_version","alias_value":"1104.3658v3","created_at":"2026-05-18T02:30:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3658","created_at":"2026-05-18T02:30:01Z"},{"alias_kind":"pith_short_12","alias_value":"OSRBD4AOSV4D","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OSRBD4AOSV4DNQFC","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OSRBD4AO","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:03d54d25a5b77a654f7abde4e09e7b694d63ebaa782432fefd0dc87e0aa850cc","target":"graph","created_at":"2026-05-18T02:30:01Z","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":"By Auslander's algebraic McKay correspondence, the stable category of Cohen-Macaulay modules over a simple singularity is equivalent to the $1$-cluster category of the path algebra of a Dynkin quiver (i.e. the orbit category of the derived category by the action of the Auslander-Reiten translation). In this paper we give a systematic method to construct a similar type of triangle equivalence between the stable category of Cohen-Macaulay modules over a Gorenstein isolated singularity $R$ and the generalized (higher) cluster category of a finite dimensional algebra $\\Lambda$. The key role is pla","authors_text":"Claire Amiot (IF), Idun Reiten (IMF), Osamu Iyama","cross_cats":["math.AC","math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-04-19T07:25:33Z","title":"Stable categories of Cohen-Macaulay modules and cluster categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3658","kind":"arxiv","version":3},"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":"sha256:2271eb6ac249c46d7661ed8ca358f23f2601437b586e639bc401b9b2c7e1ff89","target":"record","created_at":"2026-05-18T02:30:01Z","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":"f6212f66ac5826de0b2b09455183d7f828f923d510ff51c5891c4caf62cec894","cross_cats_sorted":["math.AC","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-04-19T07:25:33Z","title_canon_sha256":"4ebccce59dfd5419730ca320d31757e44adb19926dea92e6367263be93cdd23a"},"schema_version":"1.0","source":{"id":"1104.3658","kind":"arxiv","version":3}},"canonical_sha256":"74a211f00e957836c0a2888d0b5a996be34220829d692aeab40f0dc8074cee22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74a211f00e957836c0a2888d0b5a996be34220829d692aeab40f0dc8074cee22","first_computed_at":"2026-05-18T02:30:01.522556Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:01.522556Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yMbA3lJ+lVGhXv9jrI/vQZuc9H7UhZJXMrjnUvMNWiCh+8eNvmGS5JVa+ZLObV0X+aeGY+Q++saiHuXjQZ0xDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:01.522962Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.3658","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2271eb6ac249c46d7661ed8ca358f23f2601437b586e639bc401b9b2c7e1ff89","sha256:03d54d25a5b77a654f7abde4e09e7b694d63ebaa782432fefd0dc87e0aa850cc"],"state_sha256":"881df1fd8fb52468aedda3eea7d2c09d4bdd9801620edb0f5910058918bcdde7"}