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What's in a name? Parallel Universes

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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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Jane Gilman

Group Theory · Submitted 1 May 2023

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

The authors' main claim Here we establish necessary and sufficient conditions on the fixed point structure as given by Harvey's surface kernel map for the image group to lift to the three sphere.

how it is stated · asserted 1.00 read the record →

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arXiv ID2305.00862 (version 2)
Pith IDKFK7XUOP, Pith's permanent record of this paper and its review
CitationJane Gilman. "What's in a name? Parallel Universes." arXiv:2305.00862 (2023). https://pith.science/paper/KFK7XUOP
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, 3,556 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.22 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.44 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Every compact oriented Riemann surface with a finite group of self homeomorphisms can be embedded conformally in Euclidean three space so that the image group acts conformally. Here we establish necessary and sufficient conditions on the fixed point structure as given by Harvey's surface kernel map for the image group to lift to the three sphere. This builds upon topological work of Ni, Wang and Wang. It gives rise to a discussion of how terms emerge and are used for equivalent phenomena that are described in the language of different fields.

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 Every compact oriented Riemann surface with a finite group of self homeomorphisms can be embedded conformally in Euclidean three space so that the image group acts conformally. result 0.54 0.34 0.46 asserted 1.00
s1 Here we establish necessary and sufficient conditions on the fixed point structure as given by Harvey's surface kernel map for the image group to lift to the three sphere. contribution 0.56 0.92 0.52 asserted 1.00
s2 This builds upon topological work of Ni, Wang and Wang. background 1.00 0.06 0.02 asserted 0.95
s3 It gives rise to a discussion of how terms emerge and are used for equivalent phenomena that are described in the language of different fields. interpretation 0.79 0.43 0.05 asserted 0.94

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

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

Every compact oriented Riemann surface with a finite group of self homeomorphisms can be embedded conformally in Euclidean three space so that the image group acts conformally. Here we establish necessary and sufficient conditions on the fixed point structure as given by Harvey's surface kernel map for the image group to lift to the three sphere. This builds upon topological work of Ni, Wang and Wang. It gives rise to a discussion of how terms emerge and are used for equivalent phenomena that are described in the language of different fields.

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