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On the minimum blocking semioval in PG(2,11)

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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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Jeremy M. Dover

Combinatorics · Submitted 8 May 2023

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

The authors' main claim The smallest size of a blocking semioval is known for all finite projective planes of order less than 11; we investigate the situation in PG(2,11).

how it is stated · asserted 0.99 read the record →

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arXiv ID2305.04907 (version 1)
Pith IDWTE3LICZ, Pith's permanent record of this paper and its review
CitationJeremy M. Dover. "On the minimum blocking semioval in PG(2,11)." arXiv:2305.04907 (2023). https://pith.science/paper/WTE3LICZ
Claim paper

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.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,363 input tokens.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.17 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.48 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

A blocking semioval is a set of points in a projective plane that is both a blocking set (i.e., every line meets the set, but the set contains no line) and a semioval (i.e., there is a unique tangent line at each point). The smallest size of a blocking semioval is known for all finite projective planes of order less than 11; we investigate the situation in PG(2,11).

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 blocking semioval is a set of points in a projective plane that is both a blocking set (i.e., every line meets the set, but the set contains no line) and a semioval (i.e., there is a unique tangent line at each point). background 1.00 0.05 0.03 asserted 1.00
s1 The smallest size of a blocking semioval is known for all finite projective planes of order less than 11; we investigate the situation in PG(2,11). contribution 0.35 0.24 0.07 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.96 · evidence from proof or derivation 0.65.

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 blocking semioval is a set of points in a projective plane that is both a blocking set (i.e., every line meets the set, but the set contains no line) and a semioval (i.e., there is a unique tangent line at each point). The smallest size of a blocking semioval is known for all finite projective planes of order less than 11; we investigate the situation in PG(2,11).

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