{"paper":{"title":"Dense computability, upper cones, and minimal pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Carl G. Jockusch Jr, Denis R. Hirschfeldt, Eric P. Astor","submitted_at":"2018-11-17T14:51:41Z","abstract_excerpt":"This paper concerns algorithms that give correct answers with (asymptotic) density $1$. A dense description of a function $g : \\omega \\to \\omega$ is a partial function $f$ on $\\omega$ such that $\\left\\{n : f(n) = g(n)\\right\\}$ has density $1$. We define $g$ to be densely computable if it has a partial computable dense description $f$. Several previous authors have studied the stronger notions of generic computability and coarse computability, which correspond respectively to requiring in addition that $g$ and $f$ agree on the domain of $f$, and to requiring that $f$ be total. Strengthening the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07172","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"}