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On the Grace-Danielsson inequality for tetrahedra

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László Lajos

Metric Geometry · Submitted 22 May 2018

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

The authors' main claim The difference between the (squared) sides of the Grace-Danielsson inequality for tetrahedra will be represented as a sum of two nonnegative terms.

how it is stated · asserted 0.97 read the record →

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arXiv ID1805.08435 (version 1)
Pith ID7Z6XRV7P, Pith's permanent record of this paper and its review
CitationL\'aszl\'o Lajos. "On the Grace-Danielsson inequality for tetrahedra." arXiv:1805.08435 (2018). https://pith.science/paper/7Z6XRV7P
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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, 3,494 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.18 · compares with prior results 0.28 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The difference between the (squared) sides of the Grace-Danielsson inequality for tetrahedra will be represented as a sum of two nonnegative terms. This gives another proof of the inequality. Examining the denominator allows us to characterize the infinite triangular prism as a degenerate tetrahedron. We give conditions for equality (for a zero gap) as well, and some examples are included.

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 difference between the (squared) sides of the Grace-Danielsson inequality for tetrahedra will be represented as a sum of two nonnegative terms. contribution 0.60 0.90 0.62 asserted 0.97
s1 This gives another proof of the inequality. result 0.47 0.90 0.31 asserted 1.00
s2 Examining the denominator allows us to characterize the infinite triangular prism as a degenerate tetrahedron. result 0.54 0.87 0.07 asserted 0.97
s3 We give conditions for equality (for a zero gap) as well, and some examples are included. contribution 0.71 0.94 0.10 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

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 difference between the (squared) sides of the Grace-Danielsson inequality for tetrahedra will be represented as a sum of two nonnegative terms. This gives another proof of the inequality. Examining the denominator allows us to characterize the infinite triangular prism as a degenerate tetrahedron. We give conditions for equality (for a zero gap) as well, and some examples are included.

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