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A new version of Toom's proof

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Peter Gacs

Formal Languages and Automata Theory · Submitted 12 May 2021

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

The authors' main claim Simon and Berman simplified and strengthened Toom's original proof: the present report is a simplified exposition of their proof.

how it is stated · asserted 1.00 read the record →

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arXiv ID2105.05968 (version 1)
Pith IDESWLACFS, Pith's permanent record of this paper and its review
CitationPeter Gacs. "A new version of Toom's proof." arXiv:2105.05968 (2021). https://pith.science/paper/ESWLACFS
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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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,243 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.26 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.77 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

There are several proofs now for the stability of Toom's example of a two-dimensional stable cellular automaton and its application to fault-tolerant computation. Simon and Berman simplified and strengthened Toom's original proof: the present report is a simplified exposition of their proof.

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 There are several proofs now for the stability of Toom's example of a two-dimensional stable cellular automaton and its application to fault-tolerant computation. background 1.00 0.04 0.09 asserted 1.00
s1 Simon and Berman simplified and strengthened Toom's original proof: the present report is a simplified exposition of their proof. contribution 0.89 0.57 0.32 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.56 · evidence from proof or derivation 0.76.

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

There are several proofs now for the stability of Toom's example of a two-dimensional stable cellular automaton and its application to fault-tolerant computation. Simon and Berman simplified and strengthened Toom's original proof: the present report is a simplified exposition of their proof.

Human review

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References
How the literature uses it

3 arXiv papers cite this in 6 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

Papers citing it · 4 sentences without a confident label

Uses its method or tool 1 paper
Cites it as support 1 paper
  • Rigorous results prove that the ergodicity breaking is robust to essentially any sufficiently small perturbation — even a spatio-temporally correlated one, or a noise distribution which is not itself time-translation invariant [ref] .

    Colloquium: Quantum and Classical Discrete Time Crystals · An absolutely stable open time-crystal: the $π$-Toom model · 0.99

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