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The main point is to identify $H\\cap K$ with the stabilizer of a point for an affine action of a free group on $\\Z^2$, and then to prove, using the Schreier graph of this action, that this stabilizer is not finitely generated. Furthermore, we prove that there exists a sequence of subgroups $H_q, K_q \\leq \\SL(3,\\mathbb{Z})$ such that $\\rank(H_q)=\\rank(K_q)=4$, a"},"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":"2605.25080","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GR","submitted_at":"2026-05-24T13:45:25Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"dcf94be3700f1d3d83ff94f794435cfc0d37bf5c15b1b0e79bfcc1769cd11b94","abstract_canon_sha256":"c4099afcb4008a26372bae73645d1787ec72c62bd4cb1ba99bd0040b0fef3053"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:03:39.078173Z","signature_b64":"kOMh9qKFogwEzbIqvBJyM4Tl6ZUmttHEcQomPtQ7ihsjZq7Fj2KBye9zkuvg7vn1QwcEzH6BjdbghmDsQgxDCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ccb5263bb54e244b68e6cdf47064b50220bf3980e7acd086646dfe306f791b35","last_reissued_at":"2026-05-26T02:03:39.077298Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:03:39.077298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"SL(3,Z) is not Howson","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Qiang Zhang, Shengkui Ye","submitted_at":"2026-05-24T13:45:25Z","abstract_excerpt":"We give an explicit construction of two $2$-generated subgroups $H,K\\leq \\SL(3,\\Z)$ whose intersection is not finitely generated. 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