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A General Method for Deriving Vector Potentials Produced by Knotted Solenoids

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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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V. V. Sreedhar

Mathematical Physics · Submitted 6 Jan 2015

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

The authors' main claim A general method for deriving exact expressions for vector potentials produced by arbitrarily knotted solenoids is presented.

how it is stated · asserted 1.00 read the record →

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arXiv ID1501.01095 (version 1)
Pith IDLFLE6IEX, Pith's permanent record of this paper and its review
CitationV. V. Sreedhar. "A General Method for Deriving Vector Potentials Produced by Knotted Solenoids." arXiv:1501.01095 (2015). https://pith.science/paper/LFLE6IEX
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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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,241 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.20 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

A general method for deriving exact expressions for vector potentials produced by arbitrarily knotted solenoids is presented. It consists of using simple physics ideas from magnetostatics to evaluate the magnetic field in a surrogate problem. The latter is obtained by modelling the knot with wire segments carrying steady currents on a cubical lattice. The expressions for a 31 (trefoil) and a 41 (figure-eight) knot are explicitly worked out. The results are of some importance in the study of the Aharonov-Bohm effect generalised to a situation in which charged particles moving through force-free regions are scattered by fluxes confined to the interior of knotted impenetrable tubes.

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 A general method for deriving exact expressions for vector potentials produced by arbitrarily knotted solenoids is presented. contribution 1.00 0.93 0.72 asserted 1.00
s1 It consists of using simple physics ideas from magnetostatics to evaluate the magnetic field in a surrogate problem. method 0.99 0.83 0.06 asserted 1.00
s2 The latter is obtained by modelling the knot with wire segments carrying steady currents on a cubical lattice. method 1.00 0.86 0.04 asserted 1.00
s3 The expressions for a 31 (trefoil) and a 41 (figure-eight) knot are explicitly worked out. result 0.89 0.95 0.14 asserted 1.00
s4 The results are of some importance in the study of the Aharonov-Bohm effect generalised to a situation in which charged particles moving through force-free regions are scattered by fluxes confined to the interior of knotted impenetrable tubes. interpretation 0.99 0.39 0.14 asserted 0.71

What kind of paper the classifier reports this is: method or tool 0.97 · evidence from proof or derivation 0.98.

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
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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

A general method for deriving exact expressions for vector potentials produced by arbitrarily knotted solenoids is presented. It consists of using simple physics ideas from magnetostatics to evaluate the magnetic field in a surrogate problem. The latter is obtained by modelling the knot with wire segments carrying steady currents on a cubical lattice. The expressions for a 31 (trefoil) and a 41 (figure-eight) knot are explicitly worked out. The results are of some importance in the study of the Aharonov-Bohm effect generalised to a situation in which charged particles moving through force-free regions are scattered by fluxes confined to the interior of knotted impenetrable tubes.

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