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Lyapunov Exponents from Node-Counting Arguments

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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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Antonio Politi, Alessandro Torcini, Stefano Lepri

chao-dyn · Submitted 3 Mar 1998

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

The authors' main claim A conjecture connecting Lyapunov exponents of coupled map lattices and the node theorem is presented.

how it is stated · speculative 0.80 read the record →

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arXiv IDchao-dyn/9803002 (version 1)
Pith IDKR7BIFVA, Pith's permanent record of this paper and its review
CitationAlessandro Torcini, Antonio Politi, Stefano Lepri. "Lyapunov Exponents from Node-Counting Arguments." arXiv:chao-dyn/9803002 (1998). https://pith.science/paper/KR7BIFVA
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, 3,504 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.08 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · 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; .

A conjecture connecting Lyapunov exponents of coupled map lattices and the node theorem is presented. It is based on the analogy between the linear stability analysis of extended chaotic states and the Schr\"odinger problem for a particle in a disordered potential. As a consequence, we propose an alternative method to compute the Lyapunov spectrum. The implications on the foundation of the recently proposed ``chronotopic approach'' are also discussed.

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 conjecture connecting Lyapunov exponents of coupled map lattices and the node theorem is presented. contribution 1.00 0.77 0.48 speculative 0.80
s1 It is based on the analogy between the linear stability analysis of extended chaotic states and the Schr\"odinger problem for a particle in a disordered potential. method 0.49 0.26 0.07 asserted 1.00
s2 As a consequence, we propose an alternative method to compute the Lyapunov spectrum. contribution 0.81 0.70 0.36 asserted 0.42
s3 The implications on the foundation of the recently proposed ``chronotopic approach'' are also discussed. interpretation 0.98 0.50 0.07 unclear 0.49

What kind of paper the classifier reports this is: method or tool 0.71 · evidence from argument 0.99.

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 conjecture connecting Lyapunov exponents of coupled map lattices and the node theorem is presented. It is based on the analogy between the linear stability analysis of extended chaotic states and the Schr\"odinger problem for a particle in a disordered potential. As a consequence, we propose an alternative method to compute the Lyapunov spectrum. The implications on the foundation of the recently proposed ``chronotopic approach'' are also discussed.

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