{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MKGVWEUZ42C4O4PKFGSQ56UUVH","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":"27ac81f6bcd9ddbd065c3f5085030afff6663d113b563f4a91a7fde966e58ac0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-07-23T19:49:47Z","title_canon_sha256":"12713a46833718674bdef0151b733f573144f8e746799b2c089369a264de2114"},"schema_version":"1.0","source":{"id":"1307.6206","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.6206","created_at":"2026-05-18T03:17:45Z"},{"alias_kind":"arxiv_version","alias_value":"1307.6206v1","created_at":"2026-05-18T03:17:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.6206","created_at":"2026-05-18T03:17:45Z"},{"alias_kind":"pith_short_12","alias_value":"MKGVWEUZ42C4","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MKGVWEUZ42C4O4PK","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MKGVWEUZ","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:36590009319db8787aa21c83f5a6de1ccf62ecd51260e9277747deb92a009a48","target":"graph","created_at":"2026-05-18T03:17:45Z","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 paper we show a partial answer the a question of C. Huneke and G. Leuschke (2003): Let R be a standard graded Cohen-Macaulay ring of graded countable Cohen-Macaulay representation type, and assume that R has an isolated singularity. Is R then necessarily of graded finite Cohen-Macaulay representation type? In particular, this question has an affirmative answer for standard graded non-Gorenstein rings as well as for standard graded Gorenstein rings of minimal multiplicity. Along the way, we obtain a partial classification of graded Cohen-Macaulay rings of graded countable Cohen-Macaulay","authors_text":"Branden Stone","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-07-23T19:49:47Z","title":"Non-Gorenstein isolated singularities of graded countable Cohen-Macaulay type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6206","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":"sha256:48acf5657ef5f9d687766a1595d5acb66e890cad17ed828b16374e95547609fc","target":"record","created_at":"2026-05-18T03:17:45Z","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":"27ac81f6bcd9ddbd065c3f5085030afff6663d113b563f4a91a7fde966e58ac0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-07-23T19:49:47Z","title_canon_sha256":"12713a46833718674bdef0151b733f573144f8e746799b2c089369a264de2114"},"schema_version":"1.0","source":{"id":"1307.6206","kind":"arxiv","version":1}},"canonical_sha256":"628d5b1299e685c771ea29a50efa94a9de93c7f799f65c8f32d5b48d026c5710","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"628d5b1299e685c771ea29a50efa94a9de93c7f799f65c8f32d5b48d026c5710","first_computed_at":"2026-05-18T03:17:45.049584Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:45.049584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nVzVIExkWA9S4jJzaCcYZXMBqyAEY9xDrS6SE25APIohSbQqjTK74Aj7i19EEqE0e+347Wm8AJDtSuUdt8S+AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:45.050187Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.6206","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48acf5657ef5f9d687766a1595d5acb66e890cad17ed828b16374e95547609fc","sha256:36590009319db8787aa21c83f5a6de1ccf62ecd51260e9277747deb92a009a48"],"state_sha256":"b0567c1077a6201ca9b05e71e53c94e2ba6da291af43a5bf040aa36b6f4ef7bd"}