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Integer completely positive matrices of order two

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Thomas Laffey, Helena Šmigoc

Optimization and Control · Submitted 12 Feb 2018

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

The authors' main claim We show that every integer doubly nonnegative $2 \times 2$ matrix has an integer cp-factorization.

how it is stated · asserted 1.00 read the record →

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arXiv ID1802.04129 (version 1)
Pith IDYV5BR2XO, Pith's permanent record of this paper and its review
CitationHelena \v{S}migoc, Thomas Laffey. "Integer completely positive matrices of order two." arXiv:1802.04129 (2018). https://pith.science/paper/YV5BR2XO
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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, 1,585 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.15 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.13 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We show that every integer doubly nonnegative $2 \times 2$ matrix has an integer cp-factorization.

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 We show that every integer doubly nonnegative $2 \times 2$ matrix has an integer cp-factorization. result 0.95 0.94 0.94 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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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

We show that every integer doubly nonnegative $2 \times 2$ matrix has an integer cp-factorization.

Human review

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How the literature uses it

1 arXiv paper cite this in 2 sentences

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

Papers citing it · 1 sentence without a confident label

Cites it as background 1 paper

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