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The Gordon-Litherland pairing and its many applications

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Micah Chrisman

Geometric Topology · Submitted 11 Mar 2025

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

The authors' main claim Gordon and Litherland's paper $\textit{On the Signature of a link}$ introduced a bilinear form that simultaneously unifies both the quadratic forms of Trotter and Goeritz.

how it is stated · asserted 1.00 read the record →

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arXiv ID2503.08500 (version 1)
Pith IDVNPQ6ASS, Pith's permanent record of this paper and its review
CitationMicah Chrisman. "The Gordon-Litherland pairing and its many applications." arXiv:2503.08500 (2025). https://pith.science/paper/VNPQ6ASS
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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, 2,941 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.69 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

Gordon and Litherland's paper $\textit{On the Signature of a link}$ introduced a bilinear form that simultaneously unifies both the quadratic forms of Trotter and Goeritz. This remarkable pairing of combinatorics and topology has had widespread application in low-dimensional topology. In this expository note, we give a picture proof (via Kirby diagrams) of their main result and discuss the numerous ways their theorem has been put to good use.

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 Gordon and Litherland's paper $\textit{On the Signature of a link}$ introduced a bilinear form that simultaneously unifies both the quadratic forms of Trotter and Goeritz. background 0.98 0.04 0.29 asserted 1.00
s1 This remarkable pairing of combinatorics and topology has had widespread application in low-dimensional topology. background 0.86 0.05 0.09 asserted 1.00
s2 In this expository note, we give a picture proof (via Kirby diagrams) of their main result and discuss the numerous ways their theorem has been put to good use. contribution 0.99 0.90 0.24 asserted 0.99

What kind of paper the classifier reports this is: review 0.89 · evidence from proof or derivation 0.81.

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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

Gordon and Litherland's paper $\textit{On the Signature of a link}$ introduced a bilinear form that simultaneously unifies both the quadratic forms of Trotter and Goeritz. This remarkable pairing of combinatorics and topology has had widespread application in low-dimensional topology. In this expository note, we give a picture proof (via Kirby diagrams) of their main result and discuss the numerous ways their theorem has been put to good use.

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