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Derivation of Cameron-Liebler line classes

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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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Alexander L. Gavrilyuk, Ilia Matkin, Tim Penttila

Combinatorics · Submitted 13 Sep 2016

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

The authors' main claim We construct a new infinite family of Cameron-Liebler line classes in $PG(3,q)$ with parameter $x=\frac{q^2+1}{2}$ for all odd $q$.

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arXiv ID1609.03774 (version 2)
Pith IDVS6DRDLN, Pith's permanent record of this paper and its review
CitationAlexander L. Gavrilyuk, Ilia Matkin, Tim Penttila. "Derivation of Cameron-Liebler line classes." arXiv:1609.03774 (2016). https://pith.science/paper/VS6DRDLN
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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, 1,630 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.39 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.92 · compares with prior results 0.08 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We construct a new infinite family of Cameron-Liebler line classes in $PG(3,q)$ with parameter $x=\frac{q^2+1}{2}$ for all odd $q$.

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 construct a new infinite family of Cameron-Liebler line classes in $PG(3,q)$ with parameter $x=\frac{q^2+1}{2}$ for all odd $q$. contribution 0.79 0.96 0.91 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 v2
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

We construct a new infinite family of Cameron-Liebler line classes in $PG(3,q)$ with parameter $x=\frac{q^2+1}{2}$ for all odd $q$.

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Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

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