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Normal numbers and limit computable Cantor series

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Achilles A. Beros, Konstantinos A. Beros

Logic · Submitted 8 Apr 2014

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Given any oracle, A, we construct a basic sequence Q, computable in the jump of A, such that no A-computable real is Q-distribution-normal.

how it is stated · asserted 1.00 read the record →

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arXiv ID1404.2178 (version 1)
Pith IDTLCS2OJQ, Pith's permanent record of this paper and its review
CitationAchilles A. Beros, Konstantinos A. Beros. "Normal numbers and limit computable Cantor series." arXiv:1404.2178 (2014). https://pith.science/paper/TLCS2OJQ
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,944 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.22 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.07 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Given any oracle, A, we construct a basic sequence Q, computable in the jump of A, such that no A-computable real is Q-distribution-normal. A corollary to this is that there is a Delta^0_{n+1} basic sequence with respect to which no Delta^0_n real is distribution-normal. As a special case, there is a limit computable sequence relative to which no computable real is distribution-normal.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Given any oracle, A, we construct a basic sequence Q, computable in the jump of A, such that no A-computable real is Q-distribution-normal. result 0.70 0.93 0.78 asserted 1.00
s1 A corollary to this is that there is a Delta^0_{n+1} basic sequence with respect to which no Delta^0_n real is distribution-normal. result 0.88 0.87 0.23 asserted 1.00
s2 As a special case, there is a limit computable sequence relative to which no computable real is distribution-normal. result 0.98 0.88 0.25 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Given any oracle, A, we construct a basic sequence Q, computable in the jump of A, such that no A-computable real is Q-distribution-normal. A corollary to this is that there is a Delta^0_{n+1} basic sequence with respect to which no Delta^0_n real is distribution-normal. As a special case, there is a limit computable sequence relative to which no computable real is distribution-normal.

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