{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:OC7BOKVVADH74K7C4PYCVTB3TE","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":"f2f87367aa65365e15809a26b4b0bf01b0a409011662eb3e9fa263fb712fdfcb","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.RA","submitted_at":"2019-06-17T03:10:25Z","title_canon_sha256":"399a59ab1a2ccc47c30edde3e296c850c66c149f86dea968faedaed4cab152cc"},"schema_version":"1.0","source":{"id":"1906.06824","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.06824","created_at":"2026-05-17T23:43:12Z"},{"alias_kind":"arxiv_version","alias_value":"1906.06824v1","created_at":"2026-05-17T23:43:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.06824","created_at":"2026-05-17T23:43:12Z"},{"alias_kind":"pith_short_12","alias_value":"OC7BOKVVADH7","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"OC7BOKVVADH74K7C","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"OC7BOKVV","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:586422ace64edd72637248691d18ad49d3999b7f42b62c4fc434068cd2ba4d48","target":"graph","created_at":"2026-05-17T23:43:12Z","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 study properties of graded maximal Cohen-Macaulay modules over an N-graded locally finite, Auslander Gorenstein, and Cohen-Macaulay algebra of dimension two. As a consequence, we extend a part of McKay correspondence in dimension two to a more general setting.","authors_text":"James Zhang, Xiaoshan Qin, Yanhua Wang","cross_cats":["math.AG"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.RA","submitted_at":"2019-06-17T03:10:25Z","title":"Maximal Cohen-Macaulay modules over a noncommutative 2-dimensional singularity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.06824","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:b3b87966bcd8b7863b68406ab838c5fdbdba2d6ca1279dcfd91c8067ceb47670","target":"record","created_at":"2026-05-17T23:43:12Z","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":"f2f87367aa65365e15809a26b4b0bf01b0a409011662eb3e9fa263fb712fdfcb","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.RA","submitted_at":"2019-06-17T03:10:25Z","title_canon_sha256":"399a59ab1a2ccc47c30edde3e296c850c66c149f86dea968faedaed4cab152cc"},"schema_version":"1.0","source":{"id":"1906.06824","kind":"arxiv","version":1}},"canonical_sha256":"70be172ab500cffe2be2e3f02acc3b993a3b97f6192c7153c57ca6ca03c0959d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70be172ab500cffe2be2e3f02acc3b993a3b97f6192c7153c57ca6ca03c0959d","first_computed_at":"2026-05-17T23:43:12.556338Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:12.556338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0hRO0UEjDE+WgGG0gPD+JY9z3tBChzZwe0LNrJZobHnwnoHpH7LJ+bqIVAWaPST44sc905Ctaz/C/nZqKXebDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:12.556866Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.06824","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3b87966bcd8b7863b68406ab838c5fdbdba2d6ca1279dcfd91c8067ceb47670","sha256:586422ace64edd72637248691d18ad49d3999b7f42b62c4fc434068cd2ba4d48"],"state_sha256":"55bda414d527d4982536acf988f8d0a5a45d1b6a783e779febfbdc4d2dbf1ec9"}