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There are Thin Minimizers of the L1TV Functional

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Benjamin Van Dyke, Kevin R. Vixie

Classical Analysis and ODEs · Submitted 19 Jun 2012

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

The authors' main claim In this paper we show the surprising results that while the local reach of the boundary of an L1TV minimizer is bounded below by 1/lambda, the global reach can be smaller.

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arXiv ID1206.4357 (version 1)
Pith IDDJZO7ZN4, Pith's permanent record of this paper and its review
CitationBenjamin Van Dyke, Kevin R. Vixie. "There are Thin Minimizers of the L1TV Functional." arXiv:1206.4357 (2012). https://pith.science/paper/DJZO7ZN4
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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, 2,279 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.24 · human participants 0.02 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.96 · compares with prior results 0.26 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

In this paper we show the surprising results that while the local reach of the boundary of an L1TV minimizer is bounded below by 1/lambda, the global reach can be smaller. We do this by demonstrating several example minimizing sets not equal to the union of the 1/lambda -balls they contain.

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 In this paper we show the surprising results that while the local reach of the boundary of an L1TV minimizer is bounded below by 1/lambda, the global reach can be smaller. result 0.99 0.91 0.85 asserted 1.00
s1 We do this by demonstrating several example minimizing sets not equal to the union of the 1/lambda -balls they contain. method 0.79 0.95 0.14 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.86.

What was examined, and what was not

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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

In this paper we show the surprising results that while the local reach of the boundary of an L1TV minimizer is bounded below by 1/lambda, the global reach can be smaller. We do this by demonstrating several example minimizing sets not equal to the union of the 1/lambda -balls they contain.

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