{"paper":{"title":"Asymptotic density and the coarse computability bound","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Carl G. Jockusch, Denis R. Hirschfeldt, Jr., Paul E. Schupp, Timothy H. McNicholl","submitted_at":"2015-05-08T01:15:16Z","abstract_excerpt":"For $r \\in [0,1]$ we say that a set $A \\subseteq \\omega$ is \\emph{coarsely computable at density} $r$ if there is a computable set $C$ such that $\\{n : C(n) = A(n)\\}$ has lower density at least $r$. Let $\\gamma(A) = \\sup \\{r : A \\hbox{ is coarsely computable at density } r\\}$. We study the interactions of these concepts with Turing reducibility. For example, we show that if $r \\in (0,1]$ there are sets $A_0, A_1$ such that $\\gamma(A_0) = \\gamma(A_1) = r$ where $A_0$ is coarsely computable at density $r$ while $A_1$ is not coarsely computable at density $r$. We show that a real $r \\in [0,1]$ is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01901","kind":"arxiv","version":1},"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"}