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On the Hurwitz action on quasipositive factorizations of 3-braids

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Stepan Yu. Orevkov

Group Theory · Submitted 16 Sep 2014

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

The authors' main claim We prove that every orbit contains an element of a special form.

how it is stated · asserted 1.00 read the record →

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arXiv ID1409.4726 (version 3)
Pith ID2XTWOMF7, Pith's permanent record of this paper and its review
CitationStepan Yu. Orevkov. "On the Hurwitz action on quasipositive factorizations of 3-braids." arXiv:1409.4726 (2014). https://pith.science/paper/2XTWOMF7
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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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,570 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.13 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.96 · compares with prior results 0.08 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

We consider the Hurwitz action on quasipositive factorizations of 3-braids. We prove that every orbit contains an element of a special form. This fact provides an algorithm of finding representatives of every orbit for a given braid. We prove also that (1) any 3-braid has a finite number of orbits; (2) a Birman-Ko-Lee positive 3-braid has a single orbit; (3) a 3-braid of algebraic length two has at most two orbits.

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 We consider the Hurwitz action on quasipositive factorizations of 3-braids. background 0.58 0.44 0.04 unclear 0.60
s1 We prove that every orbit contains an element of a special form. result 0.99 0.96 0.51 asserted 1.00
s2 This fact provides an algorithm of finding representatives of every orbit for a given braid. interpretation 0.62 0.90 0.21 asserted 0.99
s3 We prove also that (1) any 3-braid has a finite number of orbits; (2) a Birman-Ko-Lee positive 3-braid has a single orbit; (3) a 3-braid of algebraic length two has at most two orbits. result 1.00 0.94 0.34 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v3
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 consider the Hurwitz action on quasipositive factorizations of 3-braids. We prove that every orbit contains an element of a special form. This fact provides an algorithm of finding representatives of every orbit for a given braid. We prove also that (1) any 3-braid has a finite number of orbits; (2) a Birman-Ko-Lee positive 3-braid has a single orbit; (3) a 3-braid of algebraic length two has at most two orbits.

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