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A new family of semifields with 2 parameters

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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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Yue Zhou, Alexander Pott

Combinatorics · Submitted 23 Mar 2011

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

The authors' main claim A new family of commutative semifields with two parameters is presented.

how it is stated · asserted 1.00 read the record →

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arXiv ID1103.4555 (version 1)
Pith IDZIYW2KFM, Pith's permanent record of this paper and its review
CitationAlexander Pott, Yue Zhou. "A new family of semifields with 2 parameters." arXiv:1103.4555 (2011). https://pith.science/paper/ZIYW2KFM
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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, 4,057 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.32 · compares with prior results 0.09 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

A new family of commutative semifields with two parameters is presented. Its left and middle nucleus are both determined. Furthermore, we prove that for any different pairs of parameters, these semifields are not isotopic. It is also shown that, for some special parameters, one semifield in this family can lead to two inequivalent planar functions. Finally, using similar construction, new APN functions are given.

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 A new family of commutative semifields with two parameters is presented. contribution 1.00 0.94 0.58 asserted 1.00
s1 Its left and middle nucleus are both determined. result 0.96 0.92 0.09 asserted 1.00
s2 Furthermore, we prove that for any different pairs of parameters, these semifields are not isotopic. result 0.96 0.95 0.34 asserted 1.00
s3 It is also shown that, for some special parameters, one semifield in this family can lead to two inequivalent planar functions. result 0.98 0.93 0.10 asserted 0.99
s4 Finally, using similar construction, new APN functions are given. contribution 0.65 0.95 0.12 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.98 · 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
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

A new family of commutative semifields with two parameters is presented. Its left and middle nucleus are both determined. Furthermore, we prove that for any different pairs of parameters, these semifields are not isotopic. It is also shown that, for some special parameters, one semifield in this family can lead to two inequivalent planar functions. Finally, using similar construction, new APN functions are given.

Human review

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How the literature uses it

1 arXiv paper cite this in 3 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

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