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Stable Strata of Geodesics in Outer Space

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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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Yael Algom-Kfir, Ilya Kapovich, Catherine Pfaff

Group Theory · Submitted 2 Jun 2017

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

The authors' main claim We show that the analogous Outer space "principal" periodic geodesics share certain stability properties with the principal stratum geodesics of Teichm\"uller space.

how it is stated · asserted 1.00 read the record →

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arXiv ID1706.00673 (version 1)
Pith ID4UASNP6F, Pith's permanent record of this paper and its review
CitationCatherine Pfaff, Ilya Kapovich, Yael Algom-Kfir. "Stable Strata of Geodesics in Outer Space." arXiv:1706.00673 (2017). https://pith.science/paper/4UASNP6F
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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, 3,644 input tokens.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.50 · human participants 0.01 · controlled comparison 0.21 · randomized assignment 0.01 · states quantitative result 0.03 · 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; .

In this paper we propose an Outer space analogue for the principal stratum of the unit tangent bundle to the Teichm\"uller space $\mathcal{T}(S)$ of a closed hyperbolic surface $S$. More specifically, we focus on properties of the geodesics in Teichm\"uller space determined by the principal stratum. We show that the analogous Outer space "principal" periodic geodesics share certain stability properties with the principal stratum geodesics of Teichm\"uller space. We also show that the stratification of periodic geodesics in Outer space exhibits some new pathological phenomena not present in the Teichm\"uller space context.

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 In this paper we propose an Outer space analogue for the principal stratum of the unit tangent bundle to the Teichm\"uller space $\mathcal{T}(S)$ of a closed hyperbolic surface $S$. contribution 0.99 0.81 0.08 asserted 0.80
s1 More specifically, we focus on properties of the geodesics in Teichm\"uller space determined by the principal stratum. contribution 0.78 0.38 0.05 asserted 0.86
s2 We show that the analogous Outer space "principal" periodic geodesics share certain stability properties with the principal stratum geodesics of Teichm\"uller space. result 1.00 0.95 0.57 asserted 1.00
s3 We also show that the stratification of periodic geodesics in Outer space exhibits some new pathological phenomena not present in the Teichm\"uller space context. result 1.00 0.94 0.18 asserted 0.98

What kind of paper the classifier reports this is: theoretical result 0.99 · 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

In this paper we propose an Outer space analogue for the principal stratum of the unit tangent bundle to the Teichm\"uller space $\mathcal{T}(S)$ of a closed hyperbolic surface $S$. More specifically, we focus on properties of the geodesics in Teichm\"uller space determined by the principal stratum. We show that the analogous Outer space "principal" periodic geodesics share certain stability properties with the principal stratum geodesics of Teichm\"uller space. We also show that the stratification of periodic geodesics in Outer space exhibits some new pathological phenomena not present in the Teichm\"uller space context.

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What this paper does with the arXiv papers it cites

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

What it cites · 10 sentences without a confident label

Cites as support 2 papers

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