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We define a set of \\emph{generic points} in $V$, which is Zariski-open in $V$, and show that the groups $\\operatorname{GL}(Gv)$ for $v$ generic are all isomorphic, and isomorphic to a subgroup of every sy"},"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":"1608.06539","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-08-23T15:14:48Z","cross_cats_sorted":["math.MG","math.RT"],"title_canon_sha256":"433c93f6f3dfe8f2692cf499f8f003adaab807d443d3f1eb89431ddf9ff110a6","abstract_canon_sha256":"c69a0d5a6021140a58b186bcd46b8baa49039825d2d123e8d8332e8db8e06e44"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:53.506901Z","signature_b64":"703mpW2WlpVhPz0J4oRz6RTw9NcXMNGCZGZ7peFDe2Bk0jLhrYGKzQnHfakLTRWNJeOS4+ImLRu+uvBDgv/eDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20496fba91de11fa2582b2798414459d8e28e2eb419ba392a590fd31e63178af","last_reissued_at":"2026-05-18T00:02:53.506158Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:53.506158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classification of Affine Symmetry Groups of Orbit Polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG","math.RT"],"primary_cat":"math.GR","authors_text":"Erik Friese, Frieder Ladisch","submitted_at":"2016-08-23T15:14:48Z","abstract_excerpt":"Let $G$ be a finite group acting linearly on a vector space $V$. 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