Three dimensional central configurations in H3 and S3

Shuqiang Zhu; Suo Zhao

RECORD

Three dimensional central configurations in H3 and S3

Suo Zhao, Shuqiang Zhu

Classical Analysis and ODEs · Submitted 27 May 2016

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

The authors' main claim We show that each central configuration in the three-dimensional hyperbolic sphere is equivalent to one central configuration on a particular two- dimensional hyperbolic sphere.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

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, 2,254 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.41 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.16 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We show that each central configuration in the three-dimensional hyperbolic sphere is equivalent to one central configuration on a particular two- dimensional hyperbolic sphere. However, there exist both special and ordinary central configurations in the three-dimensional sphere that are not confined to any two-dimensional sphere.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We show that each central configuration in the three-dimensional hyperbolic sphere is equivalent to one central configuration on a particular two- dimensional hyperbolic sphere.	result 0.98	0.89	0.42	asserted 1.00
s1	However, there exist both special and ordinary central configurations in the three-dimensional sphere that are not confined to any two-dimensional sphere.	result 0.97	0.79	0.30	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

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 show that each central configuration in the three-dimensional hyperbolic sphere is equivalent to one central configuration on a particular two- dimensional hyperbolic sphere. However, there exist both special and ordinary central configurations in the three-dimensional sphere that are not confined to any two-dimensional sphere.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

3 arXiv papers cite this in 4 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 1 sentence without a confident label

Cites it as background 3 papers

This breakthrough then gave rise to further results for the $n≥2$ case in [ref] – [ref] and [ref] – [ref] .

Polygonal rotopulsators of the curved $n$-body problem · Introduction · 0.86
This breakthrough then gave rise to further results for the $n≥2$ case in [ref] – [ref] and [ref] , [ref] and [ref] – [ref] .

Circular non-collision orbits for a large class of n-body problems · Introduction · 0.84
This breakthrough then gave rise to further results for the $n≥2$ case in [ref] – [ref] , [ref] , [ref] , [ref] and [ref] – [ref] .

Equal masses results for choreographies $n$-body problems · Introduction · 0.81

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.