Pith. Sign in

RECORD

Watersheds and Explosive percolation

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Hans J. Herrmann, Nuno A. M. Araujo

Statistical Mechanics · Submitted 3 Mar 2011

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

The authors' main claim We show that, to obtain a discontinuous transition it is solely necessary to control the size of the largest cluster, suppressing the growth of a cluster differing significantly, in size, from the average one.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID1103.0765 (version 1)
Pith ID7THTOKRL, Pith's permanent record of this paper and its review
CitationHans J. Herrmann, Nuno A. M. Araujo. "Watersheds and Explosive percolation." arXiv:1103.0765 (2011). https://pith.science/paper/7THTOKRL
Claim paper

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.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,870 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.15 · human participants 0.02 · controlled comparison 0.05 · randomized assignment 0.02 · states quantitative result 0.14 · compares with prior results 0.48 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The recent work by Achlioptas, D'Souza, and Spencer opened up the possibility of obtaining a discontinuous (explosive) percolation transition by changing the stochastic rule of bond occupation. Despite the active research on this subject, several questions still remain open about the leading mechanism and the properties of the system. We review the largest cluster and the Gaussian models recently introduced. We show that, to obtain a discontinuous transition it is solely necessary to control the size of the largest cluster, suppressing the growth of a cluster differing significantly, in size, from the average one. As expected for a discontinuous transition, a Gaussian cluster-size distribution and compact clusters are obtained. The surface of the clusters is fractal, with the same fractal dimension of the watershed line.

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 The recent work by Achlioptas, D'Souza, and Spencer opened up the possibility of obtaining a discontinuous (explosive) percolation transition by changing the stochastic rule of bond occupation. background 1.00 0.03 0.04 hedged possibility 0.95
s1 Despite the active research on this subject, several questions still remain open about the leading mechanism and the properties of the system. gap 0.97 0.04 0.02 asserted 0.98
s2 We review the largest cluster and the Gaussian models recently introduced. contribution 0.81 0.29 0.03 asserted 0.60
s3 We show that, to obtain a discontinuous transition it is solely necessary to control the size of the largest cluster, suppressing the growth of a cluster differing significantly, in size, from the average one. result 0.90 0.83 0.88 asserted 1.00
s4 As expected for a discontinuous transition, a Gaussian cluster-size distribution and compact clusters are obtained. result 0.95 0.71 0.10 asserted 0.99
s5 The surface of the clusters is fractal, with the same fractal dimension of the watershed line. result 1.00 0.74 0.06 asserted 1.00

What kind of paper the classifier reports this is: review 0.54 · evidence from literature 0.38.

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

The recent work by Achlioptas, D'Souza, and Spencer opened up the possibility of obtaining a discontinuous (explosive) percolation transition by changing the stochastic rule of bond occupation. Despite the active research on this subject, several questions still remain open about the leading mechanism and the properties of the system. We review the largest cluster and the Gaussian models recently introduced. We show that, to obtain a discontinuous transition it is solely necessary to control the size of the largest cluster, suppressing the growth of a cluster differing significantly, in size, from the average one. As expected for a discontinuous transition, a Gaussian cluster-size distribution and compact clusters are obtained. The surface of the clusters is fractal, with the same fractal dimension of the watershed line.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

What this paper does with the arXiv papers it cites

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 whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

What it cites · 6 sentences without a confident label

Compares with 1 paper
  • For both models, the fractal perimeter of the largest cluster is intriguingly close to the one found for watersheds ($1.211±0.001$) [ref] , random polymers in strongly disordered media ($1.22±0.02$) [ref] , optimal path cracking [ref] , and several other models [ref] , and we have arguments that they are actually identical.

    Optimal path cracks in correlated and uncorrelated lattices · Final Remarks · 0.89

Cites as background 2 papers
  • A hybrid model has also been proposed [ref] where an additional parameter is included to interpolate between the discontinuous transition, observed for $m=10$, and the continuous one of classical percolation.

    Tricritical point in explosive percolation · Introduction · 0.86

  • Potential applications of explosive percolation are, for instance, the growth dynamics of the Human Protein Homology Network [ref] and the identification of communities in real systems [ref] .

    Using explosive percolation in analysis of real-world networks · Introduction · 0.87

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.