{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:WQFPLT56MM2GBCAKUDAHBVPJH5","short_pith_number":"pith:WQFPLT56","schema_version":"1.0","canonical_sha256":"b40af5cfbe633460880aa0c070d5e93f7823749e236d6ee10c55995487dcbccd","source":{"kind":"arxiv","id":"1905.04327","version":2},"attestation_state":"computed","paper":{"title":"Simple $\\mathbb{Z}$-graded domains of Gelfand-Kirillov dimension two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Jason Gaddis, Luigi Ferraro, Robert Won","submitted_at":"2019-05-10T18:17:14Z","abstract_excerpt":"Let $k$ be an algebraically closed field and $A$ a $\\mathbb{Z}$-graded finitely generated simple $k$-algebra which is a domain of Gelfand-Kirillov dimension 2. We show that the category of $\\mathbb{Z}$-graded right $A$-modules is equivalent to the category of quasicoherent sheaves on a certain quotient stack. The theory of these simple algebras is closely related to that of a class of generalized Weyl algebras (GWAs). We prove a translation principle for the noncommutative schemes of these GWAs, shedding new light on the classical translation principle for the infinite-dimensional primitive qu"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1905.04327","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-05-10T18:17:14Z","cross_cats_sorted":[],"title_canon_sha256":"2b6f994f5333069fc7803c55d35e0a82aa87fe7c3881a936ed9184d577f14888","abstract_canon_sha256":"cb3245981f643d25294953bd3643c202a1d96d87624d79bd90dbccad74a3d3cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:57:47.551891Z","signature_b64":"VSdji7COcOKE0/8gl/9xSOetqR2JqwgEOfZ/9gR/CTNvfpNp7GrTZj1CS4NHannRbx+wqBR66PF6tvEQC9YvBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b40af5cfbe633460880aa0c070d5e93f7823749e236d6ee10c55995487dcbccd","last_reissued_at":"2026-07-05T01:57:47.551478Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:57:47.551478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Simple $\\mathbb{Z}$-graded domains of Gelfand-Kirillov dimension two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Jason Gaddis, Luigi Ferraro, Robert Won","submitted_at":"2019-05-10T18:17:14Z","abstract_excerpt":"Let $k$ be an algebraically closed field and $A$ a $\\mathbb{Z}$-graded finitely generated simple $k$-algebra which is a domain of Gelfand-Kirillov dimension 2. We show that the category of $\\mathbb{Z}$-graded right $A$-modules is equivalent to the category of quasicoherent sheaves on a certain quotient stack. The theory of these simple algebras is closely related to that of a class of generalized Weyl algebras (GWAs). We prove a translation principle for the noncommutative schemes of these GWAs, shedding new light on the classical translation principle for the infinite-dimensional primitive qu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04327","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1905.04327/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1905.04327","created_at":"2026-07-05T01:57:47.551537+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.04327v2","created_at":"2026-07-05T01:57:47.551537+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.04327","created_at":"2026-07-05T01:57:47.551537+00:00"},{"alias_kind":"pith_short_12","alias_value":"WQFPLT56MM2G","created_at":"2026-07-05T01:57:47.551537+00:00"},{"alias_kind":"pith_short_16","alias_value":"WQFPLT56MM2GBCAK","created_at":"2026-07-05T01:57:47.551537+00:00"},{"alias_kind":"pith_short_8","alias_value":"WQFPLT56","created_at":"2026-07-05T01:57:47.551537+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WQFPLT56MM2GBCAKUDAHBVPJH5","json":"https://pith.science/pith/WQFPLT56MM2GBCAKUDAHBVPJH5.json","graph_json":"https://pith.science/api/pith-number/WQFPLT56MM2GBCAKUDAHBVPJH5/graph.json","events_json":"https://pith.science/api/pith-number/WQFPLT56MM2GBCAKUDAHBVPJH5/events.json","paper":"https://pith.science/paper/WQFPLT56"},"agent_actions":{"view_html":"https://pith.science/pith/WQFPLT56MM2GBCAKUDAHBVPJH5","download_json":"https://pith.science/pith/WQFPLT56MM2GBCAKUDAHBVPJH5.json","view_paper":"https://pith.science/paper/WQFPLT56","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.04327&json=true","fetch_graph":"https://pith.science/api/pith-number/WQFPLT56MM2GBCAKUDAHBVPJH5/graph.json","fetch_events":"https://pith.science/api/pith-number/WQFPLT56MM2GBCAKUDAHBVPJH5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WQFPLT56MM2GBCAKUDAHBVPJH5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WQFPLT56MM2GBCAKUDAHBVPJH5/action/storage_attestation","attest_author":"https://pith.science/pith/WQFPLT56MM2GBCAKUDAHBVPJH5/action/author_attestation","sign_citation":"https://pith.science/pith/WQFPLT56MM2GBCAKUDAHBVPJH5/action/citation_signature","submit_replication":"https://pith.science/pith/WQFPLT56MM2GBCAKUDAHBVPJH5/action/replication_record"}},"created_at":"2026-07-05T01:57:47.551537+00:00","updated_at":"2026-07-05T01:57:47.551537+00:00"}