{"paper":{"title":"Seas of squares with sizes from a $\\Pi^0_1$ set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.DS","authors_text":"Linda Brown Westrick","submitted_at":"2016-09-23T16:06:51Z","abstract_excerpt":"For each $\\Pi^0_1$ $S\\subseteq \\mathbb{N}$, let the $S$-square shift be the two-dimensional subshift on the alphabet $\\{0,1\\}$ whose elements consist of squares of 1s of various sizes on a background of 0s, where the side length of each square is in $S$. Similarly, let the distinct-square shift consist of seas of squares such that no two finite squares have the same size. Extending the self-similar Turing machine tiling construction of Durand, Romashchenko and Shen, we show that if $X$ is an $S$-square shift or any effectively closed subshift of the distinct square shift, then $X$ is sofic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07411","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}