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Strong Arcwise Connectedness

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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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Benjamin Espinoza, Paul Gartside, Merve Kovan-Bakan, Ana Mamatelashvili

General Topology · Submitted 24 Sep 2012

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

The authors' main claim It is shown, using ideas from descriptive set theory, that there is no simple characterization of n-sac, or omega-sac, rational continua.

how it is stated · asserted 1.00 read the record →

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arXiv ID1209.5454 (version 1)
Pith IDKCVKL4QT, Pith's permanent record of this paper and its review
CitationAna Mamatelashvili, Benjamin Espinoza, Merve Kovan-Bakan, Paul Gartside. "Strong Arcwise Connectedness." arXiv:1209.5454 (2012). https://pith.science/paper/KCVKL4QT
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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, 6,060 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.73 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.85 · compares with prior results 0.11 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

A space is `n-strong arc connected' (n-sac) if for any n points in the space there is an arc in the space visiting them in order. A space is omega-strong arc connected (omega-sac) if it is n-sac for all n. We study these properties in finite graphs, regular continua, and rational continua. There are no 4-sac graphs, but there are 3-sac graphs and graphs which are 2-sac but not 3-sac. For every n there is an n-sac regular continuum, but no regular continuum is omega-sac. There is an omega-sac rational continuum. For graphs we give a simple characterization of those graphs which are 3-sac. It is shown, using ideas from descriptive set theory, that there is no simple characterization of n-sac, or omega-sac, rational continua.

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 A space is `n-strong arc connected' (n-sac) if for any n points in the space there is an arc in the space visiting them in order. background 1.00 0.12 0.03 asserted 0.98
s1 A space is omega-strong arc connected (omega-sac) if it is n-sac for all n. background 0.99 0.17 0.04 asserted 0.98
s2 We study these properties in finite graphs, regular continua, and rational continua. contribution 0.96 0.76 0.04 asserted 0.82
s3 There are no 4-sac graphs, but there are 3-sac graphs and graphs which are 2-sac but not 3-sac. result 1.00 0.83 0.15 asserted 1.00
s4 For every n there is an n-sac regular continuum, but no regular continuum is omega-sac. result 1.00 0.84 0.17 asserted 1.00
s5 There is an omega-sac rational continuum. result 1.00 0.84 0.21 asserted 1.00
s6 For graphs we give a simple characterization of those graphs which are 3-sac. result 0.62 0.93 0.10 asserted 1.00
s7 It is shown, using ideas from descriptive set theory, that there is no simple characterization of n-sac, or omega-sac, rational continua. result 0.95 0.88 0.18 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

A space is `n-strong arc connected' (n-sac) if for any n points in the space there is an arc in the space visiting them in order. A space is omega-strong arc connected (omega-sac) if it is n-sac for all n. We study these properties in finite graphs, regular continua, and rational continua. There are no 4-sac graphs, but there are 3-sac graphs and graphs which are 2-sac but not 3-sac. For every n there is an n-sac regular continuum, but no regular continuum is omega-sac. There is an omega-sac rational continuum. For graphs we give a simple characterization of those graphs which are 3-sac. It is shown, using ideas from descriptive set theory, that there is no simple characterization of n-sac, or omega-sac, rational continua.

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