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Volumes, middle-dimensional systoles, and Whitehead products

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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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Ivan K. Babenko, Mikhail G. Katz, Alexander I. Suciu

dg-ga · Submitted 22 Jul 1997

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

The authors' main claim Thus, Loewner's theorem has no higher-dimensional analogue.

how it is stated · asserted 1.00 read the record →

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arXiv IDdg-ga/9707016 (version 2)
Pith ID26QBAF7W, Pith's permanent record of this paper and its review
CitationAlexander I. Suciu, Ivan K. Babenko, Mikhail G. Katz. "Volumes, middle-dimensional systoles, and Whitehead products." arXiv:dg-ga/9707016 (1997). https://pith.science/paper/26QBAF7W
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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, 2,853 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.19 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.45 · compares with prior results 0.85 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Let X be a closed manifold of dimension 2m >= 6 with torsion-free middle-dimensional homology. We construct metrics on X of arbitrarily small volume, such that every middle-dimensional submanifold of less than unit volume necessarily bounds. Thus, Loewner's theorem has no higher-dimensional analogue.

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 Let X be a closed manifold of dimension 2m >= 6 with torsion-free middle-dimensional homology. background 0.98 0.08 0.03 asserted 0.87
s1 We construct metrics on X of arbitrarily small volume, such that every middle-dimensional submanifold of less than unit volume necessarily bounds. contribution 0.57 0.95 0.38 asserted 1.00
s2 Thus, Loewner's theorem has no higher-dimensional analogue. interpretation 0.98 0.42 0.81 asserted 1.00

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

What was examined, and what was not

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  • arXiv listing abstract v2
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

Let X be a closed manifold of dimension 2m >= 6 with torsion-free middle-dimensional homology. We construct metrics on X of arbitrarily small volume, such that every middle-dimensional submanifold of less than unit volume necessarily bounds. Thus, Loewner's theorem has no higher-dimensional analogue.

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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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