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Miura maps for St\"{a}ckel systems

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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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Krzysztof Marciniak, Maciej B{l}aszak

Exactly Solvable and Integrable Systems · Submitted 3 Jul 2023

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

The authors' main claim This construction yields a new way of generating multi-Hamiltonian representations for St\"{a}ckel systems.

how it is stated · asserted 1.00 read the record →

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arXiv ID2307.01340 (version 1)
Pith IDGMDEHJAI, Pith's permanent record of this paper and its review
CitationKrzysztof Marciniak, Maciej B{\l}aszak. "Miura maps for St\"{a}ckel systems." arXiv:2307.01340 (2023). https://pith.science/paper/GMDEHJAI
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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, 2,901 input tokens.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.04 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.09 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We introduce the concept of Miura maps between parameter-dependent algebraic curves of hyperelliptic type. These Miura maps induce Miura maps between St\"{a}ckel systems defined (on the extended phase space) by the considered algebraic curves. This construction yields a new way of generating multi-Hamiltonian representations for St\"{a}ckel systems.

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 introduce the concept of Miura maps between parameter-dependent algebraic curves of hyperelliptic type. contribution 1.00 0.93 0.13 asserted 1.00
s1 These Miura maps induce Miura maps between St\"{a}ckel systems defined (on the extended phase space) by the considered algebraic curves. result 0.59 0.76 0.21 asserted 1.00
s2 This construction yields a new way of generating multi-Hamiltonian representations for St\"{a}ckel systems. interpretation 0.55 0.88 0.67 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.96 · evidence from proof or derivation 0.98.

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 introduce the concept of Miura maps between parameter-dependent algebraic curves of hyperelliptic type. These Miura maps induce Miura maps between St\"{a}ckel systems defined (on the extended phase space) by the considered algebraic curves. This construction yields a new way of generating multi-Hamiltonian representations for St\"{a}ckel systems.

Human review

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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

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