{"paper":{"title":"Partial randomness and dimension of recursively enumerable reals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.LO"],"primary_cat":"cs.CC","authors_text":"Kohtaro Tadaki","submitted_at":"2009-06-15T21:40:00Z","abstract_excerpt":"A real \\alpha is called recursively enumerable (\"r.e.\" for short) if there exists a computable, increasing sequence of rationals which converges to \\alpha. It is known that the randomness of an r.e. real \\alpha can be characterized in various ways using each of the notions; program-size complexity, Martin-L\\\"{o}f test, Chaitin \\Omega number, the domination and \\Omega-likeness of \\alpha, the universality of a computable, increasing sequence of rationals which converges to \\alpha, and universal probability. In this paper, we generalize these characterizations of randomness over the notion of par"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.2812","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"}