{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:DEIQCXDLULDZITDC2VOQBZZNLI","short_pith_number":"pith:DEIQCXDL","schema_version":"1.0","canonical_sha256":"1911015c6ba2c7944c62d55d00e72d5a135f2faf3c20070758b5efce7d81c69f","source":{"kind":"arxiv","id":"2506.05652","version":1},"attestation_state":"computed","paper":{"title":"Stability of the centers of group algebras of general affine groups $GA_n(q)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jinkui Wan, Lan Zhou","submitted_at":"2025-06-06T00:49:10Z","abstract_excerpt":"The general affine group $GA_n(q)$ consisting of invertible affine transformations of an affine space of codimension one in the vector space $\\mathbb{F}_q^n$ over a finite field $\\mathbb{F}_q$, can be viewed as a subgroup of the general linear group $GL_{n}(q)$ over $\\mathbb{F}_q$. In the article, we introduce the notion of the type of each matrix in $GA_n(q)$ and give an explicit representative for each conjugacy class. Then the center $\\mathscr{A}_n(q)$ of the integral group algebra $\\mathbb{Z}[GA_n(q)]$ is proved to be a filtered algebra via the length function defined via the reflections l"},"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":"2506.05652","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2025-06-06T00:49:10Z","cross_cats_sorted":[],"title_canon_sha256":"2b50b950af861fd411a441b90ca0059aa3fb8958e95061c859d9d0f0abe42ca1","abstract_canon_sha256":"d112e3c4e5ee823f229a6f58844c94694f866fffaac3677450674a32f69da13e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:17:07.584426Z","signature_b64":"F/yIt/6JbvXvytOS+E2hBXMmi685D2T9KiV66r9DiGmIWDWitmInzrXV43pDaomGivwRpk6MN7+ryFYDruF1AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1911015c6ba2c7944c62d55d00e72d5a135f2faf3c20070758b5efce7d81c69f","last_reissued_at":"2026-07-05T11:17:07.583848Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:17:07.583848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability of the centers of group algebras of general affine groups $GA_n(q)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jinkui Wan, Lan Zhou","submitted_at":"2025-06-06T00:49:10Z","abstract_excerpt":"The general affine group $GA_n(q)$ consisting of invertible affine transformations of an affine space of codimension one in the vector space $\\mathbb{F}_q^n$ over a finite field $\\mathbb{F}_q$, can be viewed as a subgroup of the general linear group $GL_{n}(q)$ over $\\mathbb{F}_q$. In the article, we introduce the notion of the type of each matrix in $GA_n(q)$ and give an explicit representative for each conjugacy class. Then the center $\\mathscr{A}_n(q)$ of the integral group algebra $\\mathbb{Z}[GA_n(q)]$ is proved to be a filtered algebra via the length function defined via the reflections l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.05652","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/2506.05652/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":"2506.05652","created_at":"2026-07-05T11:17:07.583908+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.05652v1","created_at":"2026-07-05T11:17:07.583908+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.05652","created_at":"2026-07-05T11:17:07.583908+00:00"},{"alias_kind":"pith_short_12","alias_value":"DEIQCXDLULDZ","created_at":"2026-07-05T11:17:07.583908+00:00"},{"alias_kind":"pith_short_16","alias_value":"DEIQCXDLULDZITDC","created_at":"2026-07-05T11:17:07.583908+00:00"},{"alias_kind":"pith_short_8","alias_value":"DEIQCXDL","created_at":"2026-07-05T11:17:07.583908+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/DEIQCXDLULDZITDC2VOQBZZNLI","json":"https://pith.science/pith/DEIQCXDLULDZITDC2VOQBZZNLI.json","graph_json":"https://pith.science/api/pith-number/DEIQCXDLULDZITDC2VOQBZZNLI/graph.json","events_json":"https://pith.science/api/pith-number/DEIQCXDLULDZITDC2VOQBZZNLI/events.json","paper":"https://pith.science/paper/DEIQCXDL"},"agent_actions":{"view_html":"https://pith.science/pith/DEIQCXDLULDZITDC2VOQBZZNLI","download_json":"https://pith.science/pith/DEIQCXDLULDZITDC2VOQBZZNLI.json","view_paper":"https://pith.science/paper/DEIQCXDL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.05652&json=true","fetch_graph":"https://pith.science/api/pith-number/DEIQCXDLULDZITDC2VOQBZZNLI/graph.json","fetch_events":"https://pith.science/api/pith-number/DEIQCXDLULDZITDC2VOQBZZNLI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DEIQCXDLULDZITDC2VOQBZZNLI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DEIQCXDLULDZITDC2VOQBZZNLI/action/storage_attestation","attest_author":"https://pith.science/pith/DEIQCXDLULDZITDC2VOQBZZNLI/action/author_attestation","sign_citation":"https://pith.science/pith/DEIQCXDLULDZITDC2VOQBZZNLI/action/citation_signature","submit_replication":"https://pith.science/pith/DEIQCXDLULDZITDC2VOQBZZNLI/action/replication_record"}},"created_at":"2026-07-05T11:17:07.583908+00:00","updated_at":"2026-07-05T11:17:07.583908+00:00"}