{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VSE4NU4EKT6SRELRHZUEJUHWSK","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":"20c5c77aa1ff51755ec102331573bb5b9da71d28b92524f0413860b1463513dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-01-04T15:18:58Z","title_canon_sha256":"b5abae34ac2ad46928fdae35832b9b4f1a40e4abdc62e879d93f74a889190aee"},"schema_version":"1.0","source":{"id":"1101.0737","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.0737","created_at":"2026-05-18T02:23:05Z"},{"alias_kind":"arxiv_version","alias_value":"1101.0737v2","created_at":"2026-05-18T02:23:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.0737","created_at":"2026-05-18T02:23:05Z"},{"alias_kind":"pith_short_12","alias_value":"VSE4NU4EKT6S","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VSE4NU4EKT6SRELR","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VSE4NU4E","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:bca22f016fff2ada08d78ec8684c12107ed8cd27db445aa183d2f35e3eac37fc","target":"graph","created_at":"2026-05-18T02:23:05Z","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 construct a family of connected graded domains of GK-dimension 4 that are birational to P2, and show that the general member of this family is noetherian. This disproves a conjecture of the first author and Stafford.\n  The algebras we construct are Koszul and have global dimension 4. They fail to be Artin-Schelter Gorenstein, however, showing that a theorem of Zhang and Stephenson for dimension 3 algebras does not extend to dimension 4. The Auslander-Buchsbaum formula also fails to hold for our family.\n  The algebras can be obtained as global sections of a certain quasicoherent graded sheaf","authors_text":"D. Rogalski, S. J. Sierra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-01-04T15:18:58Z","title":"Some noncommutative projective surfaces of GK-dimension 4"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0737","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:fd48a0cb91ad2f65cf2ca985e0bc02d78f0f56902e64f562e07c604190b02baf","target":"record","created_at":"2026-05-18T02:23:05Z","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":"20c5c77aa1ff51755ec102331573bb5b9da71d28b92524f0413860b1463513dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-01-04T15:18:58Z","title_canon_sha256":"b5abae34ac2ad46928fdae35832b9b4f1a40e4abdc62e879d93f74a889190aee"},"schema_version":"1.0","source":{"id":"1101.0737","kind":"arxiv","version":2}},"canonical_sha256":"ac89c6d38454fd2891713e6844d0f69291c49f061b94dbce9973ef5bf558df9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac89c6d38454fd2891713e6844d0f69291c49f061b94dbce9973ef5bf558df9a","first_computed_at":"2026-05-18T02:23:05.603086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:05.603086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DLhlv/+vKpuJWZ2Ao5UGBkgx9ZYVmefBpKDY3+JgfnPX3v/X/PotJDcxriBWsjlPmJPMQI5YPVclkv4vig7mBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:05.603616Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.0737","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd48a0cb91ad2f65cf2ca985e0bc02d78f0f56902e64f562e07c604190b02baf","sha256:bca22f016fff2ada08d78ec8684c12107ed8cd27db445aa183d2f35e3eac37fc"],"state_sha256":"f8c8fbf39c0618a21db3099a1b33240724ab9fcab889808fe282a94b86de35fd"}