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Ito-Sadahiro numbers vs. Parry numbers

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Zuzana Masáková, Edita Pelantová

Number Theory · Submitted 29 Oct 2010

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

The authors' main claim We call such numbers $\beta$ Ito-Sadahiro numbers and we compare their properties with Parry numbers, occurring in the same context for R\'enyi positive base numeration system.

how it is stated · asserted 0.91 read the record →

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arXiv ID1010.6181 (version 1)
Pith IDXA36NHSL, Pith's permanent record of this paper and its review
CitationEdita Pelantov\'a, Zuzana Mas\'akov\'a. "Ito-Sadahiro numbers vs. Parry numbers." arXiv:1010.6181 (2010). https://pith.science/paper/XA36NHSL
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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, 3,043 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.21 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.82 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We consider positional numeration system with negative base, as introduced by Ito and Sadahiro. In particular, we focus on algebraic properties of negative bases $-\beta$ for which the corresponding dynamical system is sofic, which happens, according to Ito and Sadahiro, if and only if the $(-\beta)$-expansion of $-\frac{\beta}{\beta+1}$ is eventually periodic. We call such numbers $\beta$ Ito-Sadahiro numbers and we compare their properties with Parry numbers, occurring in the same context for R\'enyi positive base numeration system.

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 We consider positional numeration system with negative base, as introduced by Ito and Sadahiro. background 0.95 0.20 0.03 asserted 0.84
s1 In particular, we focus on algebraic properties of negative bases $-\beta$ for which the corresponding dynamical system is sofic, which happens, according to Ito and Sadahiro, if and only if the $(-\beta)$-expansion of $-\frac{\beta}{\beta+1}$ is eventually periodic. background 0.67 0.08 0.15 asserted 1.00
s2 We call such numbers $\beta$ Ito-Sadahiro numbers and we compare their properties with Parry numbers, occurring in the same context for R\'enyi positive base numeration system. contribution 0.96 0.63 0.17 asserted 0.91

What kind of paper the classifier reports this is: theoretical result 0.93 · evidence from proof or derivation 0.62.

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

We consider positional numeration system with negative base, as introduced by Ito and Sadahiro. In particular, we focus on algebraic properties of negative bases $-\beta$ for which the corresponding dynamical system is sofic, which happens, according to Ito and Sadahiro, if and only if the $(-\beta)$-expansion of $-\frac{\beta}{\beta+1}$ is eventually periodic. We call such numbers $\beta$ Ito-Sadahiro numbers and we compare their properties with Parry numbers, occurring in the same context for R\'enyi positive base numeration system.

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2 arXiv papers cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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