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We describe precisely all essential pattern groups P that yield finitely constrained groups with maximal Haudorff dimension. For a given size d, d>1, there are exactly 2^{d-1} such pattern groups and they are all maximal in the group of automorphisms of the finite rooted regular tree"},"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":"1406.0522","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-06-02T20:08:03Z","cross_cats_sorted":[],"title_canon_sha256":"b94d8bc56e27d3f6f7249e47d6fe45fcf6176f8e707d23737e4ee2ce33d665cc","abstract_canon_sha256":"7076e189dfd9193dd825f45581bb07bc0cfddbc76fa337b9647e33d42d401114"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:40.259012Z","signature_b64":"EB1wH13iqV7x9rhTCEUIfhfwD4wcIFIDOn4xrRr81qbIR1Q9kxkifnaIdUANEsYRucYQ3e3vUedxonN5HQPXCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d689067920481ce019ac1239b031ee33d743e153fe51b2582e5fb183a946ec3","last_reissued_at":"2026-05-18T01:23:40.258285Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:40.258285Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finitely constrained groups of maximal Hausdorff dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Andrew Penland, Zoran Sunic","submitted_at":"2014-06-02T20:08:03Z","abstract_excerpt":"We prove that if G_P is a finitely constrained group of binary rooted tree automorphisms (a group binary tree subshift of finite type) defined by an essential pattern group P of pattern size d, d>1, and if G_P has maximal Hausdorff dimension (equal to 1-1/2^{d-1}), then G_P is not topologically finitely generated. 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