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This article studies dynamical systems associated with BM groups. A higher rank Cuntz-Krieger algebra $\\mathcal A(\\G)$ is associated both with a 2-dimensional tiling system and with a boundary action of a BM group $\\Gamma$. An explicit expression is given for the K-theory of $\\mathcal A(\\G)$. In particular $K_0=K_1$. A complete enumeration of possible BM groups $\\G$ is"},"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":"1302.5784","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-02-23T10:11:43Z","cross_cats_sorted":[],"title_canon_sha256":"68f2f7eb66cc8412e2bed318e77a65ca6d0945e62e607606246a8bf49201574c","abstract_canon_sha256":"58c2ebea546e23a7c94d7abf033631a12d1fac7a463f2ffc293b8027613d0a30"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:43.795091Z","signature_b64":"Z7lKS4TAvjUsBiT9jxmirNfNZTepzOtP0PD85tQVao4/TvIiaYutM2ZtfnWenB3qlcUrZEJnOLI6ZRdDBnHKCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52c41fcd99ccd4eb180ab560617db371683d5c8c69b7cd6e7c54edeccc118882","last_reissued_at":"2026-05-18T03:32:43.794245Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:43.794245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Groups acting on products of trees, tiling systems and analytic K-theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Guyan Robertson, Jason S. 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