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To be more precise, we prove that given any \\pizu subset $P$ of $\\{0,1\\}^\\NN$ there is a SFT $X$ such that $P\\times\\ZZ^2$ is recursively homeomorphic to $X\\setminus U$ where $U$ is a computable set of points. As a consequence, if $P$ contains a recursive member, $P$ and $X$ have the exact same set of Turing degrees. On the other hand, we prove that if $X$ contains only non-recursive members, some of its members always have different but comparable degrees"},"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":"1108.1012","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-08-04T07:41:00Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"3649c3951764b583d9a2aeeb937807d4460847554f6a79164c55fcf6cfa5895e","abstract_canon_sha256":"1913c378932fb52c368147853d2d0faa798166f14ed21b1264d4249272828ab8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:27.742193Z","signature_b64":"aEkT45Vn2/OnGFEYDwVNnadgUJLW/MsuzrD3nl6xkybeJpYuAkFmNY2P6YdJO4ZdVWL5x3PEFCkHWyqs9VtJCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37cc1aed96b7842e1e0070d1cd7a4effc79c6bb6292e34be16488c78dc145545","last_reissued_at":"2026-05-18T03:54:27.741627Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:27.741627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Turing degrees of multidimensional SFTs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.CC","authors_text":"Emmanuel Jeandel (LIF), Pascal Vanier (LIF)","submitted_at":"2011-08-04T07:41:00Z","abstract_excerpt":"In this paper we are interested in computability aspects of subshifts and in particular Turing degrees of 2-dimensional SFTs (i.e. tilings). 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