{"paper":{"title":"Paradoxes of Randomness","license":"","headline":"","cross_cats":["math.LO"],"primary_cat":"math.HO","authors_text":"G. J. Chaitin (IBM Research)","submitted_at":"2001-08-19T09:05:04Z","abstract_excerpt":"I'll discuss how Goedel's paradox \"This statement is false/unprovable\" yields his famous result on the limits of axiomatic reasoning. I'll contrast that with my work, which is based on the paradox of \"The first uninteresting positive whole number\", which is itself a rather interesting number, since it is precisely the first uninteresting number. This leads to my first result on the limits of axiomatic reasoning, namely that most numbers are uninteresting or random, but we can never be sure, we can never prove it, in individual cases. And these ideas culminate in my discovery that some mathemat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0108127","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0108127/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}