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Invariance of regularity conditions under definable, locally Lipschitz, weakly bi-Lipschitz mappings

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Malgorzata Czapla

Differential Geometry · Submitted 8 Apr 2009

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

The authors' main claim We also distinguish a class of regularity conditions that are in some sense invariant under definable, locally Lipschitz and weakly bi-Lipschitz homeomorphisms.

how it is stated · asserted 0.88 read the record →

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arXiv ID0904.1316 (version 1)
Pith IDL2PMKMPE, Pith's permanent record of this paper and its review
CitationMalgorzata Czapla. "Invariance of regularity conditions under definable, locally Lipschitz, weakly bi-Lipschitz mappings." arXiv:0904.1316 (2009). https://pith.science/paper/L2PMKMPE
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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, 2,923 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.11 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

In this paper we describe the notion of a weak lipschitzianity of a mapping on a $C^{q}$ stratification. We also distinguish a class of regularity conditions that are in some sense invariant under definable, locally Lipschitz and weakly bi-Lipschitz homeomorphisms. This class includes the Whitney (B) condition and the Verdier condition.

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 describe the notion of a weak lipschitzianity of a mapping on a $C^{q}$ stratification. contribution 0.99 0.85 0.05 asserted 0.97
s1 We also distinguish a class of regularity conditions that are in some sense invariant under definable, locally Lipschitz and weakly bi-Lipschitz homeomorphisms. contribution 0.96 0.88 0.51 asserted 0.88
s2 This class includes the Whitney (B) condition and the Verdier condition. result 0.78 0.53 0.20 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.92 · evidence from proof or derivation 0.92.

What was examined, and what was not

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  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • 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

In this paper we describe the notion of a weak lipschitzianity of a mapping on a $C^{q}$ stratification. We also distinguish a class of regularity conditions that are in some sense invariant under definable, locally Lipschitz and weakly bi-Lipschitz homeomorphisms. This class includes the Whitney (B) condition and the Verdier condition.

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