{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:RZNFXIAEDD4YPGQ2SBUYO36A2F","short_pith_number":"pith:RZNFXIAE","schema_version":"1.0","canonical_sha256":"8e5a5ba00418f9879a1a9069876fc0d14e910273f79259fa4358f8cae9a49e85","source":{"kind":"arxiv","id":"1702.04305","version":4},"attestation_state":"computed","paper":{"title":"Azumaya loci and discriminant ideals of PI algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Ken A. Brown, Milen T. Yakimov","submitted_at":"2017-02-14T17:29:29Z","abstract_excerpt":"We prove that, under mild assumptions, for all positive integers $\\ell$, the zero set of the discriminant ideal $D_{\\ell}(R/Z(R); tr)$ of a prime polynomial identity (PI) algebra $R$ coincides with the zero set of the modified discriminant ideal $MD_{\\ell}(R/Z(R); tr)$ of $R$. Furthermore, we prove that, when $\\ell$ is the square of the PI-degree of $R$, this zero set is precisely the complement of the Azumaya locus of $R$. This description is used to classify the Azumaya loci of the mutiparameter quantized Weyl algebras at roots of unity. As another application, we prove that the zero set of "},"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":"1702.04305","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2017-02-14T17:29:29Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"f0ea458933d5ee6be90937d8edf0c812a3a24aa33234364a7c65292a158ea16e","abstract_canon_sha256":"d559b3383b0e5a46aa23b745a6f6cfd8476999d84c087f682ba105e3d0748e17"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:41.914431Z","signature_b64":"ihZX02jCWp04Eap/b9lGUd0/h8DdCsBXOn5MJ6cazZWEaNMsqWlt8NE+ABzNMvzMGtWaxWHTdx1sZjxSrvRiDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e5a5ba00418f9879a1a9069876fc0d14e910273f79259fa4358f8cae9a49e85","last_reissued_at":"2026-05-18T00:34:41.913742Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:41.913742Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Azumaya loci and discriminant ideals of PI algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Ken A. Brown, Milen T. Yakimov","submitted_at":"2017-02-14T17:29:29Z","abstract_excerpt":"We prove that, under mild assumptions, for all positive integers $\\ell$, the zero set of the discriminant ideal $D_{\\ell}(R/Z(R); tr)$ of a prime polynomial identity (PI) algebra $R$ coincides with the zero set of the modified discriminant ideal $MD_{\\ell}(R/Z(R); tr)$ of $R$. Furthermore, we prove that, when $\\ell$ is the square of the PI-degree of $R$, this zero set is precisely the complement of the Azumaya locus of $R$. This description is used to classify the Azumaya loci of the mutiparameter quantized Weyl algebras at roots of unity. As another application, we prove that the zero set of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04305","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1702.04305","created_at":"2026-05-18T00:34:41.913857+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.04305v4","created_at":"2026-05-18T00:34:41.913857+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04305","created_at":"2026-05-18T00:34:41.913857+00:00"},{"alias_kind":"pith_short_12","alias_value":"RZNFXIAEDD4Y","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_16","alias_value":"RZNFXIAEDD4YPGQ2","created_at":"2026-05-18T12:31:43.269735+00:00"},{"alias_kind":"pith_short_8","alias_value":"RZNFXIAE","created_at":"2026-05-18T12:31:43.269735+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/RZNFXIAEDD4YPGQ2SBUYO36A2F","json":"https://pith.science/pith/RZNFXIAEDD4YPGQ2SBUYO36A2F.json","graph_json":"https://pith.science/api/pith-number/RZNFXIAEDD4YPGQ2SBUYO36A2F/graph.json","events_json":"https://pith.science/api/pith-number/RZNFXIAEDD4YPGQ2SBUYO36A2F/events.json","paper":"https://pith.science/paper/RZNFXIAE"},"agent_actions":{"view_html":"https://pith.science/pith/RZNFXIAEDD4YPGQ2SBUYO36A2F","download_json":"https://pith.science/pith/RZNFXIAEDD4YPGQ2SBUYO36A2F.json","view_paper":"https://pith.science/paper/RZNFXIAE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.04305&json=true","fetch_graph":"https://pith.science/api/pith-number/RZNFXIAEDD4YPGQ2SBUYO36A2F/graph.json","fetch_events":"https://pith.science/api/pith-number/RZNFXIAEDD4YPGQ2SBUYO36A2F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RZNFXIAEDD4YPGQ2SBUYO36A2F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RZNFXIAEDD4YPGQ2SBUYO36A2F/action/storage_attestation","attest_author":"https://pith.science/pith/RZNFXIAEDD4YPGQ2SBUYO36A2F/action/author_attestation","sign_citation":"https://pith.science/pith/RZNFXIAEDD4YPGQ2SBUYO36A2F/action/citation_signature","submit_replication":"https://pith.science/pith/RZNFXIAEDD4YPGQ2SBUYO36A2F/action/replication_record"}},"created_at":"2026-05-18T00:34:41.913857+00:00","updated_at":"2026-05-18T00:34:41.913857+00:00"}