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On the Duality Theory for the Monge-Kantorovich Transport Problem

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Mathias Beiglböck (VUT), Christian Léonard (MODAL'X), Walter Schachermayer (VUT)

Classical Analysis and ODEs · Submitted 26 Oct 2010

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

The authors' main claim We explain the methods used in this article in an elementary setting and present two examples complementing the results obtained therein.

how it is stated · asserted 0.99 read the record →

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arXiv ID1010.5403 (version 1)
Pith IDSUGC3D7D, Pith's permanent record of this paper and its review
CitationChristian L\'eonard (MODAL'X), Mathias Beiglb\"ock (VUT), Walter Schachermayer (VUT). "On the Duality Theory for the Monge-Kantorovich Transport Problem." arXiv:1010.5403 (2010). https://pith.science/paper/SUGC3D7D
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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.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,230 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.17 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.24 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The paper is accompanying "A general Duality Theorem for the Monge-Kantorovich Transport Problem". We explain the methods used in this article in an elementary setting and present two examples complementing the results obtained therein.

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 The paper is accompanying "A general Duality Theorem for the Monge-Kantorovich Transport Problem". background 0.96 0.18 0.05 asserted 1.00
s1 We explain the methods used in this article in an elementary setting and present two examples complementing the results obtained therein. contribution 0.98 0.91 0.09 asserted 0.99

What kind of paper the classifier reports this is: position or commentary 0.90 · evidence from proof or derivation 0.59.

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

The paper is accompanying "A general Duality Theorem for the Monge-Kantorovich Transport Problem". We explain the methods used in this article in an elementary setting and present two examples complementing the results obtained therein.

Human review

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How the literature uses it

Papers whose main result relates to this one's

How each label was checked · JSON

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

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