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Variations on Narrow Dots-and-Boxes and Dots-and-Triangles

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Adam Jobson, Levi Sledd, Susan C. White, D. Jacob Wildstrom

Combinatorics · Submitted 30 Jul 2015

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

The authors' main claim We verify a conjecture of Nowakowski and Ottaway that closed $1 \times n$ Dots-and-Triangles is a first-player win when $n \neq 2$.

how it is stated · asserted 0.99 read the record →

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arXiv ID1507.08707 (version 1)
Pith IDCY2DXVID, Pith's permanent record of this paper and its review
CitationAdam Jobson, D. Jacob Wildstrom, Levi Sledd, Susan C. White. "Variations on Narrow Dots-and-Boxes and Dots-and-Triangles." arXiv:1507.08707 (2015). https://pith.science/paper/CY2DXVID
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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, 2,328 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.15 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.52 · compares with prior results 0.48 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We verify a conjecture of Nowakowski and Ottaway that closed $1 \times n$ Dots-and-Triangles is a first-player win when $n \neq 2$. We also prove that in both the open and closed $1 \times n$ Dots-and-Boxes games where $n$ is even, the first player can guarantee a tie.

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 verify a conjecture of Nowakowski and Ottaway that closed $1 \times n$ Dots-and-Triangles is a first-player win when $n \neq 2$. result 0.85 0.93 0.43 asserted 0.99
s1 We also prove that in both the open and closed $1 \times n$ Dots-and-Boxes games where $n$ is even, the first player can guarantee a tie. result 0.97 0.95 0.29 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

We verify a conjecture of Nowakowski and Ottaway that closed $1 \times n$ Dots-and-Triangles is a first-player win when $n \neq 2$. We also prove that in both the open and closed $1 \times n$ Dots-and-Boxes games where $n$ is even, the first player can guarantee a tie.

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