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Comments on Exchange Graphs in Cluster Algebras

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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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Hyun Kyu Kim, Masahito Yamazaki

Quantum Algebra · Submitted 1 Dec 2016

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

The authors' main claim We present examples and counterexamples for this naive conjecture, and then formulate a better version of the conjecture for acyclic seeds.

how it is stated · asserted 0.99 read the record →

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arXiv ID1612.00145 (version 2)
Pith IDC7KLFG7H, Pith's permanent record of this paper and its review
CitationHyun Kyu Kim, Masahito Yamazaki. "Comments on Exchange Graphs in Cluster Algebras." arXiv:1612.00145 (2016). https://pith.science/paper/C7KLFG7H
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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, 3,590 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.45 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.25 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

An important problem in the theory of cluster algebras is to compute the fundamental group of the exchange graph. A non-trivial closed loop in the exchange graph, for example, generates a non-trivial identity for the classical and quantum dilogarithm functions. An interesting conjecture, partly motivated by dilogarithm functions, is that this fundamental group is generated by closed loops of mutations involving only two of the cluster variables. We present examples and counterexamples for this naive conjecture, and then formulate a better version of the conjecture for acyclic seeds.

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 An important problem in the theory of cluster algebras is to compute the fundamental group of the exchange graph. background 1.00 0.04 0.03 asserted 1.00
s1 A non-trivial closed loop in the exchange graph, for example, generates a non-trivial identity for the classical and quantum dilogarithm functions. background 0.89 0.10 0.04 asserted 0.81
s2 An interesting conjecture, partly motivated by dilogarithm functions, is that this fundamental group is generated by closed loops of mutations involving only two of the cluster variables. background 0.95 0.04 0.08 speculative 0.99
s3 We present examples and counterexamples for this naive conjecture, and then formulate a better version of the conjecture for acyclic seeds. contribution 0.95 0.96 0.61 asserted 0.99

What kind of paper the classifier reports this is: position or commentary 0.69 · evidence from proof or derivation 0.72.

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

An important problem in the theory of cluster algebras is to compute the fundamental group of the exchange graph. A non-trivial closed loop in the exchange graph, for example, generates a non-trivial identity for the classical and quantum dilogarithm functions. An interesting conjecture, partly motivated by dilogarithm functions, is that this fundamental group is generated by closed loops of mutations involving only two of the cluster variables. We present examples and counterexamples for this naive conjecture, and then formulate a better version of the conjecture for acyclic seeds.

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References
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3 arXiv papers cite this in 3 sentences

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

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