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The Colored Jones Polynomial of Singular Knots

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Khaled Bataineh, Mohamed Elhamdadi, Mustafa Hajij

Geometric Topology · Submitted 27 Feb 2016

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

The authors' main claim We generalize the colored Jones polynomial to $4$-valent graphs.

how it is stated · asserted 1.00 read the record →

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arXiv ID1602.08628 (version 2)
Pith IDRAAFURF7, Pith's permanent record of this paper and its review
CitationKhaled Bataineh, Mohamed Elhamdadi, Mustafa Hajij. "The Colored Jones Polynomial of Singular Knots." arXiv:1602.08628 (2016). https://pith.science/paper/RAAFURF7
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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, 2,853 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.31 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We generalize the colored Jones polynomial to $4$-valent graphs. This generalization is given as a sequence of invariants in which the first term is a one variable specialization of the Kauffman-Vogel polynomial. We use the invariant we construct to give a sequence of singular braid group representations.

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 We generalize the colored Jones polynomial to $4$-valent graphs. contribution 1.00 0.94 0.50 asserted 1.00
s1 This generalization is given as a sequence of invariants in which the first term is a one variable specialization of the Kauffman-Vogel polynomial. contribution 0.65 0.76 0.19 asserted 1.00
s2 We use the invariant we construct to give a sequence of singular braid group representations. contribution 0.78 0.94 0.29 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.67 · evidence from proof or derivation 1.00.

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
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  • 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

We generalize the colored Jones polynomial to $4$-valent graphs. This generalization is given as a sequence of invariants in which the first term is a one variable specialization of the Kauffman-Vogel polynomial. We use the invariant we construct to give a sequence of singular braid group representations.

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