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A New Way to Tabulate Knots

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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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Lisa Hernandez, Xiao-Song Lin

Geometric Topology · Submitted 29 Aug 2005

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

The authors' main claim The planar tree pair representations of girth less than 4 for knot diagrams in Rolfsen's table are given.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath/0508590 (version 1)
Pith IDY2TH2DR5, Pith's permanent record of this paper and its review
CitationLisa Hernandez, Xiao-Song Lin. "A New Way to Tabulate Knots." arXiv:math/0508590 (2005). https://pith.science/paper/Y2TH2DR5
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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, 4,148 input tokens.

What the abstract itself states, as probabilities: claims first 0.17 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.18 · compares with prior results 0.14 · mentions code or data availability 0.03.

The abstract, sentence by sentence

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

We introduce a new way to tabulate knots by representing knot diagrams using a pair of planar trees. This pair of trees have their edges labeled by integers, they have no valence 2 vertices, and they have the same number of valence 1 vertices. The number of valence 1 vertices of the trees is called the girth of the knot diagram. The classification problem of knots admitting girth 2 and 3 diagrams is studied. The planar tree pair representations of girth less than 4 for knot diagrams in Rolfsen's table are given.

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 introduce a new way to tabulate knots by representing knot diagrams using a pair of planar trees. contribution 0.93 0.94 0.37 asserted 1.00
s1 This pair of trees have their edges labeled by integers, they have no valence 2 vertices, and they have the same number of valence 1 vertices. method 0.94 0.53 0.07 asserted 1.00
s2 The number of valence 1 vertices of the trees is called the girth of the knot diagram. method 0.86 0.59 0.05 asserted 1.00
s3 The classification problem of knots admitting girth 2 and 3 diagrams is studied. contribution 0.98 0.81 0.11 asserted 0.91
s4 The planar tree pair representations of girth less than 4 for knot diagrams in Rolfsen's table are given. result 0.65 0.88 0.14 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from analysis of existing data 0.52.

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

We introduce a new way to tabulate knots by representing knot diagrams using a pair of planar trees. This pair of trees have their edges labeled by integers, they have no valence 2 vertices, and they have the same number of valence 1 vertices. The number of valence 1 vertices of the trees is called the girth of the knot diagram. The classification problem of knots admitting girth 2 and 3 diagrams is studied. The planar tree pair representations of girth less than 4 for knot diagrams in Rolfsen's table are given.

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