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Harmonic morphisms from three-dimensional Euclidean and spherical space forms

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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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M.T. Mustafa, J.C. Wood

dg-ga · Submitted 18 Dec 1996

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

The authors' main claim In this paper, we obtain a description of all harmonic morphisms from any three-dimensional Euclidean and spherical space form to a surface, namely that any such harmonic morphism is the composition of a standard harmonic morphism and a weakly conformal map.

how it is stated · asserted 1.00 read the record →

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arXiv IDdg-ga/9612013 (version 1)
Pith ID2VLCS4OO, Pith's permanent record of this paper and its review
CitationJ.C. Wood, M.T. Mustafa. "Harmonic morphisms from three-dimensional Euclidean and spherical space forms." arXiv:dg-ga/9612013 (1996). https://pith.science/paper/2VLCS4OO
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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,535 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.11 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.81 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

P. Baird and the second author studied harmonic morphisms from a three-dimensional simply-connected space form to a surface and obtained a complete local and global classification of them. In this paper, we obtain a description of all harmonic morphisms from any three-dimensional Euclidean and spherical space form to a surface, namely that any such harmonic morphism is the composition of a standard harmonic morphism and a weakly conformal map. We list the standard harmonic morphisms.

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 P. background 0.93 0.03 0.01 unclear 1.00
s1 Baird and the second author studied harmonic morphisms from a three-dimensional simply-connected space form to a surface and obtained a complete local and global classification of them. background 1.00 0.21 0.04 asserted 1.00
s2 In this paper, we obtain a description of all harmonic morphisms from any three-dimensional Euclidean and spherical space form to a surface, namely that any such harmonic morphism is the composition of a standard harmonic morphism and a weakly conformal map. result 0.83 0.96 0.96 asserted 1.00
s3 We list the standard harmonic morphisms. contribution 0.90 0.91 0.04 asserted 0.93

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
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

P. Baird and the second author studied harmonic morphisms from a three-dimensional simply-connected space form to a surface and obtained a complete local and global classification of them. In this paper, we obtain a description of all harmonic morphisms from any three-dimensional Euclidean and spherical space form to a surface, namely that any such harmonic morphism is the composition of a standard harmonic morphism and a weakly conformal map. We list the standard harmonic morphisms.

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