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On the replica symmetric solution of the K-sat model

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Dmitry Panchenko

Probability · Submitted 22 Apr 2013

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

The authors' main claim This approach also yields a larger region of parameters where the system is in a pure state and, in particular, for small connectivity parameter we prove the replica symmetric formula for the free energy at any temperature.

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arXiv ID1304.6052 (version 1)
Pith IDVNGVPRYK, Pith's permanent record of this paper and its review
CitationDmitry Panchenko. "On the replica symmetric solution of the K-sat model." arXiv:1304.6052 (2013). https://pith.science/paper/VNGVPRYK
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,975 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.11 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.14 · compares with prior results 0.62 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

In this paper we translate Talagrand's solution of the K-sat model at high temperature into the language of asymptotic Gibbs measures. Using exact cavity equations in the infinite volume limit allows us to remove many technicalities of the inductions on the system size, which clarifies the main ideas of the proof. This approach also yields a larger region of parameters where the system is in a pure state and, in particular, for small connectivity parameter we prove the replica symmetric formula for the free energy at any temperature.

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 In this paper we translate Talagrand's solution of the K-sat model at high temperature into the language of asymptotic Gibbs measures. contribution 0.95 0.89 0.11 asserted 0.99
s1 Using exact cavity equations in the infinite volume limit allows us to remove many technicalities of the inductions on the system size, which clarifies the main ideas of the proof. method 0.97 0.83 0.08 asserted 0.99
s2 This approach also yields a larger region of parameters where the system is in a pure state and, in particular, for small connectivity parameter we prove the replica symmetric formula for the free energy at any temperature. result 0.99 0.92 0.65 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

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  • P abstract
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  • 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

In this paper we translate Talagrand's solution of the K-sat model at high temperature into the language of asymptotic Gibbs measures. Using exact cavity equations in the infinite volume limit allows us to remove many technicalities of the inductions on the system size, which clarifies the main ideas of the proof. This approach also yields a larger region of parameters where the system is in a pure state and, in particular, for small connectivity parameter we prove the replica symmetric formula for the free energy at any temperature.

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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

What it cites · 10 sentences without a confident label

Uses the method or tool of 1 paper
Cites as background 2 papers
  • In the next section, we will review the definition of asymptotic Gibbs measures and recall the main results from [ref] , namely, the exact cavity equations and the formula for the free energy in terms of asymptotic Gibbs measures.

    Spin glass models from the point of view of spin distributions · Introduction · 0.88

  • One can find a related interpretation in terms of exchangeable random measures in [ref] .

    Exchangeable random measures · Asymptotic Gibbs measures · 0.84

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