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That is, k = F_q(t) and S contains one or both of the places s_0 and s_\\infty corresponding to the polynomial p(t) = t respectively to the point at infinity. The statement is that the finiteness length of G(O_S) is n-1 if S contains one of the two places and is 2n-1 if it contains both places, where n is the F_q-rank of G.\n  For example, the group SL_3(F_q[t,t^{-1}]) is of type F_3 but no"},"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":"1112.2961","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-12-13T17:08:15Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"107fe00ccd91c63809341c0cc3f499e865a4043892e1ff095fe0c1b7f9ead3be","abstract_canon_sha256":"fabb6cde0f698fd374d94e84530f81e638a609208ebd720ec682f375c26ae8af"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:23.133152Z","signature_b64":"kV/Dv2MjdvoBtBnleTNIkkhcrLdQ1fTT5c0ZrM5DkffMCIR9MLnPBGue0ZyzYoXmygLyejUh9HWH5c4xaspSAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"737e6d974067247a64413c958ad101ecc8c8c95499d00cb0b2885e75d1e5c154","last_reissued_at":"2026-05-18T03:45:23.132519Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:23.132519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finiteness Properties of Chevalley Groups over the Ring of (Laurent) Polynomials over a Finite Field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Stefan Witzel","submitted_at":"2011-12-13T17:08:15Z","abstract_excerpt":"In these notes we determine the finiteness length of the groups G(O_S) where G is an F_q-isotropic, connected, noncommutative, almost simple F_q-group and O_S is one of F_q[t], F_q[t^{-1}], and F_q[t,t^{-1}]. That is, k = F_q(t) and S contains one or both of the places s_0 and s_\\infty corresponding to the polynomial p(t) = t respectively to the point at infinity. The statement is that the finiteness length of G(O_S) is n-1 if S contains one of the two places and is 2n-1 if it contains both places, where n is the F_q-rank of G.\n  For example, the group SL_3(F_q[t,t^{-1}]) is of type F_3 but no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2961","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":""},"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":"1112.2961","created_at":"2026-05-18T03:45:23.132626+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.2961v2","created_at":"2026-05-18T03:45:23.132626+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2961","created_at":"2026-05-18T03:45:23.132626+00:00"},{"alias_kind":"pith_short_12","alias_value":"ON7G3F2AM4SH","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"ON7G3F2AM4SHUZCB","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"ON7G3F2A","created_at":"2026-05-18T12:26:37.096874+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/ON7G3F2AM4SHUZCBHSKYVUIB5T","json":"https://pith.science/pith/ON7G3F2AM4SHUZCBHSKYVUIB5T.json","graph_json":"https://pith.science/api/pith-number/ON7G3F2AM4SHUZCBHSKYVUIB5T/graph.json","events_json":"https://pith.science/api/pith-number/ON7G3F2AM4SHUZCBHSKYVUIB5T/events.json","paper":"https://pith.science/paper/ON7G3F2A"},"agent_actions":{"view_html":"https://pith.science/pith/ON7G3F2AM4SHUZCBHSKYVUIB5T","download_json":"https://pith.science/pith/ON7G3F2AM4SHUZCBHSKYVUIB5T.json","view_paper":"https://pith.science/paper/ON7G3F2A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.2961&json=true","fetch_graph":"https://pith.science/api/pith-number/ON7G3F2AM4SHUZCBHSKYVUIB5T/graph.json","fetch_events":"https://pith.science/api/pith-number/ON7G3F2AM4SHUZCBHSKYVUIB5T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ON7G3F2AM4SHUZCBHSKYVUIB5T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ON7G3F2AM4SHUZCBHSKYVUIB5T/action/storage_attestation","attest_author":"https://pith.science/pith/ON7G3F2AM4SHUZCBHSKYVUIB5T/action/author_attestation","sign_citation":"https://pith.science/pith/ON7G3F2AM4SHUZCBHSKYVUIB5T/action/citation_signature","submit_replication":"https://pith.science/pith/ON7G3F2AM4SHUZCBHSKYVUIB5T/action/replication_record"}},"created_at":"2026-05-18T03:45:23.132626+00:00","updated_at":"2026-05-18T03:45:23.132626+00:00"}