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Is Parallel Postulate Necessary?

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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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Chengpu Wang, Alice Wang

Logic · Submitted 2 Feb 2023

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

The authors' main claim This paper will show that the parallel postulate is unnecessary because the 4th Euclidean axiom can already achieve the same goal.

how it is stated · asserted 1.00 read the record →

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arXiv ID2303.11333 (version 13)
Pith IDMCY2XBHX, Pith's permanent record of this paper and its review
CitationAlice Wang, Chengpu Wang. "Is Parallel Postulate Necessary?." arXiv:2303.11333 (2023). https://pith.science/paper/MCY2XBHX
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, 2,919 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.08 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.75 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v13. Results and the main claim are underlined; .

As a much later addition to the original Euclidean geometry, the parallel postulate distinguishes non-Euclidean geometries from Euclidean geometry. This paper will show that the parallel postulate is unnecessary because the 4th Euclidean axiom can already achieve the same goal. Furthermore, using the 4th Euclidean axiom can measure space curvature locally on manifold, while using the parallel postulate cannot.

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 As a much later addition to the original Euclidean geometry, the parallel postulate distinguishes non-Euclidean geometries from Euclidean geometry. background 1.00 0.04 0.02 asserted 1.00
s1 This paper will show that the parallel postulate is unnecessary because the 4th Euclidean axiom can already achieve the same goal. contribution 0.54 0.74 0.94 asserted 1.00
s2 Furthermore, using the 4th Euclidean axiom can measure space curvature locally on manifold, while using the parallel postulate cannot. result 0.87 0.63 0.12 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.95 · evidence from proof or derivation 0.80.

What was examined, and what was not

sources read
  • arXiv listing abstract v13
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

As a much later addition to the original Euclidean geometry, the parallel postulate distinguishes non-Euclidean geometries from Euclidean geometry. This paper will show that the parallel postulate is unnecessary because the 4th Euclidean axiom can already achieve the same goal. Furthermore, using the 4th Euclidean axiom can measure space curvature locally on manifold, while using the parallel postulate cannot.

Human review

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