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Adinkra Isomorphisms and `Seeing' Shapes with Eigenvalues

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Keith Burghardt, S. James Gates Jr

High Energy Physics - Theory · Submitted 12 Dec 2012

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

The authors' main claim We create an algorithm to determine whether any two graphical representations (adinkras) of equations possessing the property of supersymmetry in one or two dimensions are isomorphic in shape.

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arXiv ID1212.2731 (version 1)
Pith ID4JWLNHRI, Pith's permanent record of this paper and its review
CitationKeith Burghardt, S. James Gates Jr. "Adinkra Isomorphisms and `Seeing' Shapes with Eigenvalues." arXiv:1212.2731 (2012). https://pith.science/paper/4JWLNHRI
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,297 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.11 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.04 · mentions code or data availability 0.03.

The abstract, sentence by sentence

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

We create an algorithm to determine whether any two graphical representations (adinkras) of equations possessing the property of supersymmetry in one or two dimensions are isomorphic in shape. The algorithm is based on the determinant of `permutation matrices' that are defined in this work and derivable for any adinkra.

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 create an algorithm to determine whether any two graphical representations (adinkras) of equations possessing the property of supersymmetry in one or two dimensions are isomorphic in shape. contribution 1.00 0.95 0.35 asserted 1.00
s1 The algorithm is based on the determinant of `permutation matrices' that are defined in this work and derivable for any adinkra. method 0.99 0.91 0.12 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from proof or derivation 0.94.

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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 create an algorithm to determine whether any two graphical representations (adinkras) of equations possessing the property of supersymmetry in one or two dimensions are isomorphic in shape. The algorithm is based on the determinant of `permutation matrices' that are defined in this work and derivable for any adinkra.

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References
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3 arXiv papers cite this in 9 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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What it cites · 1 sentence without a confident label

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  • Furthermore, despite the comparative inefficiency of this algorithm compared to [ref] the algorithm is much more computer friendly, and can be computed with parallel processors saving even more time in the process.

    Automorphism Properties of Adinkras · Conclusion · 1.00

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