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Extremal Values of Pi

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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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Nikhil Henry Bukowski Sahoo

Metric Geometry · Submitted 16 Jul 2021

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

The authors' main claim We also show that a norm is Euclidean iff it has quarter-turn symmetry in some basis and has pi-value $\pi$.

how it is stated · asserted 1.00 read the record →

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arXiv ID2107.07715 (version 2)
Pith ID7N2PS5DC, Pith's permanent record of this paper and its review
CitationNikhil Henry Bukowski Sahoo. "Extremal Values of Pi." arXiv:2107.07715 (2021). https://pith.science/paper/7N2PS5DC
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.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,552 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.94 · compares with prior results 0.81 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We discuss the classical results of Stanis{\l}aw Go\l\k{a}b, on the values of pi in arbitrary normed planes, including the classification of extremal values. We reprove the result of J. Duncan, D. Luecking, and C. McGregor, which states that any norm with quarter-turn symmetry has pi-value $\geq \pi$. We also show that a norm is Euclidean iff it has quarter-turn symmetry in some basis and has pi-value $\pi$.

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 discuss the classical results of Stanis{\l}aw Go\l\k{a}b, on the values of pi in arbitrary normed planes, including the classification of extremal values. background 0.91 0.17 0.07 asserted 0.70
s1 We reprove the result of J. Duncan, D. Luecking, and C. contribution 0.93 0.68 0.05 asserted 0.81
s2 McGregor, which states that any norm with quarter-turn symmetry has pi-value $\geq \pi$. result 0.46 0.07 0.20 asserted 1.00
s3 We also show that a norm is Euclidean iff it has quarter-turn symmetry in some basis and has pi-value $\pi$. result 0.95 0.88 0.50 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.97.

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 discuss the classical results of Stanis{\l}aw Go\l\k{a}b, on the values of pi in arbitrary normed planes, including the classification of extremal values. We reprove the result of J. Duncan, D. Luecking, and C. McGregor, which states that any norm with quarter-turn symmetry has pi-value $\geq \pi$. We also show that a norm is Euclidean iff it has quarter-turn symmetry in some basis and has pi-value $\pi$.

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