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No percolation at criticality

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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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Achillefs Tzioufas

Probability · Submitted 10 Jul 2018

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

The authors' main claim Hammersley showed the existence of phase-transitions regarding independent bond percolation on general $d \geq 2$ dimensional integer-lattices in the late 50's, the continuity (or discontinuity) of which is perhaps the most prominent and long-standing basic open problem in the subsequently extensively developed theory of percolation.

how it is stated · asserted 0.90 read the record →

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arXiv ID1807.03849 (version 2)
Pith IDG2MD5PNC, Pith's permanent record of this paper and its review
CitationAchillefs Tzioufas. "No percolation at criticality." arXiv:1807.03849 (2018). https://pith.science/paper/G2MD5PNC
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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, 2,304 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.19 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Ever since J.M. Hammersley showed the existence of phase-transitions regarding independent bond percolation on general $d \geq 2$ dimensional integer-lattices in the late 50's, the continuity (or discontinuity) of which is perhaps the most prominent and long-standing basic open problem in the subsequently extensively developed theory of percolation.

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 Ever since J.M. background 1.00 0.02 0.01 unclear 1.00
s1 Hammersley showed the existence of phase-transitions regarding independent bond percolation on general $d \geq 2$ dimensional integer-lattices in the late 50's, the continuity (or discontinuity) of which is perhaps the most prominent and long-standing basic open problem in the subsequently extensively developed theory of percolation. background 0.93 0.03 0.05 asserted 0.90

What kind of paper the classifier reports this is: theoretical result 0.87 · evidence from literature 0.51.

What was examined, and what was not

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  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • 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

Ever since J.M. Hammersley showed the existence of phase-transitions regarding independent bond percolation on general $d \geq 2$ dimensional integer-lattices in the late 50's, the continuity (or discontinuity) of which is perhaps the most prominent and long-standing basic open problem in the subsequently extensively developed theory of percolation.

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