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"Potato kugel" for nuclear forces and a small one for acoustic waves

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Nikolay Kuznetsov

Analysis of PDEs · Submitted 17 May 2022

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

The authors' main claim The "potato kugel" theorem of Aharonov, Schiffer and Zalcman, which concerns an inverse property of harmonic functions, is extended to the settings of the modified Helmholtz and Helmholtz equations that describe nuclear forces and acoustic waves respectively.

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arXiv ID2205.08593 (version 1)
Pith IDYSODCD7O, Pith's permanent record of this paper and its review
CitationNikolay Kuznetsov. ""Potato kugel" for nuclear forces and a small one for acoustic waves." arXiv:2205.08593 (2022). https://pith.science/paper/YSODCD7O
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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, 1,678 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.44 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The "potato kugel" theorem of Aharonov, Schiffer and Zalcman, which concerns an inverse property of harmonic functions, is extended to the settings of the modified Helmholtz and Helmholtz equations that describe nuclear forces and acoustic waves respectively.

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 The "potato kugel" theorem of Aharonov, Schiffer and Zalcman, which concerns an inverse property of harmonic functions, is extended to the settings of the modified Helmholtz and Helmholtz equations that describe nuclear forces and acoustic waves respectively. contribution 0.97 0.81 0.85 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

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

The "potato kugel" theorem of Aharonov, Schiffer and Zalcman, which concerns an inverse property of harmonic functions, is extended to the settings of the modified Helmholtz and Helmholtz equations that describe nuclear forces and acoustic waves respectively.

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What this paper does with the arXiv papers it cites

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

What it cites

Cites as background 1 paper
  • The recent survey [ref] complements [ref] providing coverage for other results in this area; in particular, various characterizations of balls via harmonic functions as well as characterizations of other domains (strips, annuli etc.) are given.

    Inverse mean value properties (a survey) · Introduction · 0.99

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