{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:W565L4BSDJDSRDNMMKA6UZVLLB","short_pith_number":"pith:W565L4BS","schema_version":"1.0","canonical_sha256":"b77dd5f0321a47288dac6281ea66ab5870e858d42b973d1aeb52a450225f06dc","source":{"kind":"arxiv","id":"1808.01207","version":1},"attestation_state":"computed","paper":{"title":"Fixed rings of generalized Weyl algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Jason Gaddis, Robert Won","submitted_at":"2018-08-03T14:31:19Z","abstract_excerpt":"We study actions by filtered automorphisms on classical generalized Weyl algebras (GWAs). In the case of a defining polynomial of degree two, we prove that the fixed ring under the action of a finite cyclic group of filtered automorphisms is again a classical GWA, extending a result of Jordan and Wells. Partial results are provided for the case of higher degree polynomials. In addition, we establish a version of Auslander's theorem for finite cyclic groups of filtered automorphisms acting on classical GWAs."},"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":"1808.01207","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-08-03T14:31:19Z","cross_cats_sorted":[],"title_canon_sha256":"6e1019bb357f967c2522e1c59bde6dcd359d4b423ba2948069c4d5c2f32c338d","abstract_canon_sha256":"943a4c13ac6543a79b8df892c491bdbab15b7da89dc4566804061c3c85d5a79e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:00:12.448866Z","signature_b64":"4ffnyD8c/B1783jI8oghPKd0jeAxxvvBBPK2Tm+id/ocmlQKjViRWi5pe6tVTQ5XC8BQG6taqUncdCbEvbXABw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b77dd5f0321a47288dac6281ea66ab5870e858d42b973d1aeb52a450225f06dc","last_reissued_at":"2026-07-05T00:00:12.448438Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:00:12.448438Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fixed rings of generalized Weyl algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Jason Gaddis, Robert Won","submitted_at":"2018-08-03T14:31:19Z","abstract_excerpt":"We study actions by filtered automorphisms on classical generalized Weyl algebras (GWAs). In the case of a defining polynomial of degree two, we prove that the fixed ring under the action of a finite cyclic group of filtered automorphisms is again a classical GWA, extending a result of Jordan and Wells. Partial results are provided for the case of higher degree polynomials. In addition, we establish a version of Auslander's theorem for finite cyclic groups of filtered automorphisms acting on classical GWAs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01207","kind":"arxiv","version":1},"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/1808.01207/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":"1808.01207","created_at":"2026-07-05T00:00:12.448488+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.01207v1","created_at":"2026-07-05T00:00:12.448488+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.01207","created_at":"2026-07-05T00:00:12.448488+00:00"},{"alias_kind":"pith_short_12","alias_value":"W565L4BSDJDS","created_at":"2026-07-05T00:00:12.448488+00:00"},{"alias_kind":"pith_short_16","alias_value":"W565L4BSDJDSRDNM","created_at":"2026-07-05T00:00:12.448488+00:00"},{"alias_kind":"pith_short_8","alias_value":"W565L4BS","created_at":"2026-07-05T00:00:12.448488+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/W565L4BSDJDSRDNMMKA6UZVLLB","json":"https://pith.science/pith/W565L4BSDJDSRDNMMKA6UZVLLB.json","graph_json":"https://pith.science/api/pith-number/W565L4BSDJDSRDNMMKA6UZVLLB/graph.json","events_json":"https://pith.science/api/pith-number/W565L4BSDJDSRDNMMKA6UZVLLB/events.json","paper":"https://pith.science/paper/W565L4BS"},"agent_actions":{"view_html":"https://pith.science/pith/W565L4BSDJDSRDNMMKA6UZVLLB","download_json":"https://pith.science/pith/W565L4BSDJDSRDNMMKA6UZVLLB.json","view_paper":"https://pith.science/paper/W565L4BS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.01207&json=true","fetch_graph":"https://pith.science/api/pith-number/W565L4BSDJDSRDNMMKA6UZVLLB/graph.json","fetch_events":"https://pith.science/api/pith-number/W565L4BSDJDSRDNMMKA6UZVLLB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W565L4BSDJDSRDNMMKA6UZVLLB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W565L4BSDJDSRDNMMKA6UZVLLB/action/storage_attestation","attest_author":"https://pith.science/pith/W565L4BSDJDSRDNMMKA6UZVLLB/action/author_attestation","sign_citation":"https://pith.science/pith/W565L4BSDJDSRDNMMKA6UZVLLB/action/citation_signature","submit_replication":"https://pith.science/pith/W565L4BSDJDSRDNMMKA6UZVLLB/action/replication_record"}},"created_at":"2026-07-05T00:00:12.448488+00:00","updated_at":"2026-07-05T00:00:12.448488+00:00"}